Getting Started With ABAQUS

197
Getting Started with ABAQUS/Explicit Trademarks and Legal Notices Conversion Tables, Constants, and Material Properties HKS Offices and Representatives 1. Introduction ABAQUS is a suite of powerful engineering simulation programs, based on the finite element method, t simple linear analyses to the most challenging nonlinear simulations. ABAQUS contains an extensive l geometry. It has an equally extensive library of material models that can simulate the behavior of m rubber, polymers, composites, reinforced concrete, crushable and resilient foams, and geotechnical m general-purpose simulation tool, ABAQUS can be used to study more than just structural (stress/displ diverse areas as heat transfer, mass diffusion, thermal management of electrical components (coupled mechanics (coupled pore fluid-stress analyses), and piezoelectric analysis. ABAQUS is simple to use even though it offers the user a wide range of capabilities. Even the most c simulations the user need provide only the engineering data, such as the model's geometry, material ABAQUS automatically chooses appropriate time incrementation and makes continuous adjustments during efficiency. The user rarely has to control the solution aspects of the analysis. 1.1 The ABAQUS modules ABAQUS consists of two main analysis modules--ABAQUS/Standard and ABAQUS/Explicit. There are also tw ABAQUS/Standard--ABAQUS/Aqua and ABAQUS/Design. In addition, ABAQUS/Safe provides fatigue postproces MOLD are interfaces to ADAMS/Flex, CATIA, and C-MOLD, respectively. ABAQUS/CAE is the complete ABAQU creating ABAQUS models, interactively submitting and monitoring ABAQUS jobs, and evaluating results. includes just the postprocessing functionality. The relationship between these modules is shown in F Figure 1-1 ABAQUS modules. ABAQUS/Standard ABAQUS/Standard is a general-purpose analysis module that can solve a wide range of linear and nonli thermal, and electrical response of components. ABAQUS/Standard is not discussed in this guide but i Started with ABAQUS/Standard. ABAQUS/Explicit ABAQUS/Explicit is a special-purpose analysis module that uses an explicit dynamic finite element fo transient dynamic events, such as impact and blast problems, and is also very efficient for highly n conditions, such as forming simulations. This module is the main subject of this guide. ABAQUS/CAE ABAQUS/CAE (Complete ABAQUS Environment) is an interactive, graphical environment for ABAQUS. It all producing or importing the geometry of the structure to be analyzed and decomposing the geometry int can be assigned to the geometry, together with loads and boundary conditions. ABAQUS/CAE contains ve verify the resulting analysis model. Once the model is complete, ABAQUS/CAE can submit, monitor, and can then be used to interpret the results. Only the visualization module of ABAQUS/CAE (ABAQUS/Viewer) is covered in this guide. If you want to are unable to attend a seminar, you can obtain a copy of the ABAQUS/CAE training material. ABAQUS/Viewer ABAQUS/Viewer is the visualization module of ABAQUS/CAE; it is an interactive, graphical postprocess ABAQUS analysis modules and provides a wide range of options for interpreting the results. ABAQUS/Vi ABAQUS/Aqua ABAQUS/Aqua is a set of optional capabilities that can be added to ABAQUS/Standard. It is intended f oil platforms. Some of the optional capabilities include the effects of wave and wind loading and bu ABAQUS/ADAMS ABAQUS/ADAMS allows ABAQUS finite element models to be included as flexible components within the MD on the component mode synthesis formulation of ADAMS/Flex. ABAQUS/ADAMS is not discussed in this gui ABAQUS/CAT ABAQUS/CAT allows ABAQUS analyses to be set up and postprocessed entirely in CATIA. ABAQUS/CAT is no ABAQUS/C-MOLD ABAQUS/C-MOLD translates finite element mesh, material property, and initial stress data from a C-MO

description

ádsadsadasd

Transcript of Getting Started With ABAQUS

Page 1: Getting Started With ABAQUS

Getting Started with ABAQUS/ExplicitTrademarks and Legal NoticesConversion Tables, Constants, and Material PropertiesHKS Offices and Representatives1.  IntroductionABAQUS is a suite of powerful engineering simulation programs, based on the finite element method, that can solve problems ranging from relatively simple linear analyses to the most challenging nonlinear simulations. ABAQUS contains an extensive library of elements that can model virtually any geometry. It has an equally extensive library of material models that can simulate the behavior of most typical engineering materials including metals, rubber, polymers, composites, reinforced concrete, crushable and resilient foams, and geotechnical materials such as soils and rock. Designed as a general-purpose simulation tool, ABAQUS can be used to study more than just structural (stress/displacement) problems. It can simulate problems in such diverse areas as heat transfer, mass diffusion, thermal management of electrical components (coupled thermal-electrical analyses), acoustics, soil mechanics (coupled pore fluid-stress analyses), and piezoelectric analysis.ABAQUS is simple to use even though it offers the user a wide range of capabilities. Even the most complicated analyses can be modeled easily. In most simulations the user need provide only the engineering data, such as the model's geometry, material behavior, boundary conditions, and applied loads. ABAQUS automatically chooses appropriate time incrementation and makes continuous adjustments during the analysis to ensure accuracy as well as efficiency. The user rarely has to control the solution aspects of the analysis.1.1  The ABAQUS modulesABAQUS consists of two main analysis modules--ABAQUS/Standard and ABAQUS/Explicit. There are also two special-purpose add-on analysis products for ABAQUS/Standard--ABAQUS/Aqua and ABAQUS/Design. In addition, ABAQUS/Safe provides fatigue postprocessing; while ABAQUS/ADAMS, ABAQUS/CAT, and ABAQUS/C-MOLD are interfaces to ADAMS/Flex, CATIA, and C-MOLD, respectively. ABAQUS/CAE is the complete ABAQUS environment that includes capabilities for creating ABAQUS models, interactively submitting and monitoring ABAQUS jobs, and eval uating results. ABAQUS/Viewer is a subset of ABAQUS/CAE that includes just the postprocessing functionality. The relationship between these modules is shown in Figure 1-1  .Figure 1-1  ABAQUS modules.ABAQUS/StandardABAQUS/Standard is a general-purpose analysis module that can solve a wide range of linear and nonlinear problems involving the static, dynamic, thermal, and electrical response of components. ABAQUS/Standard is not discussed in this guide but is described in the companion publication Getting Started with ABAQUS/Standard.ABAQUS/ExplicitABAQUS/Explicit is a special-purpose analysis module that uses an explicit dynamic finite element formulation. It is suitable for modeling brief, transient dynamic events, such as impact and blast problems, and is also very efficient for highly nonlinear problems involving changing contact conditions, such as forming simulations. This module is the main subject of this guide.ABAQUS/CAEABAQUS/CAE (Complete ABAQUS Environment) is an interactive, graphical environment for ABAQUS. It allows models to be created quickly and easily by producing or importing the geometry of the structure to be analyzed and decomposing the geometry into meshable regions. Physical and material properties can be assigned to the geometry, together with loads and boundary conditions. ABAQUS/CAE contains very powerful options to mesh the geometry and to verify the resulting analysis model. Once the model is complete, ABAQUS/CAE can submit, monitor, and control the analysis jobs. The visualization module can then be used to interpret the results.Only the visualization module of ABAQUS/CAE (ABAQUS/Viewer) is covered in this guide. If you want to learn how to use other aspects of ABAQUS/CAE but are unable to attend a seminar, you can obtain a copy of the ABAQUS/CAE training material.ABAQUS/ViewerABAQUS/Viewer is the visualization module of ABAQUS/CAE; it is an interactive, graphical postprocessor that supports all of the capabilities in the ABAQUS analysis modules and provides a wide range of options for interpreting the results. ABAQUS/Viewer is discussed in this guide.ABAQUS/AquaABAQUS/Aqua is a set of optional capabilities that can be added to ABAQUS/Standard. It is intended for the simulation of offshore structures, such as oil platforms. Some of the optional capabilities include the effects of wave and wind loading and buoyancy. ABAQUS/Aqua is not discussed in this guide.ABAQUS/ADAMSABAQUS/ADAMS allows ABAQUS finite element models to be included as flexible components within the MDI ADAMS family of products. The interface is based on the component mode synthesis formulation of ADAMS/Flex. ABAQUS/ADAMS is not discussed in this guide.ABAQUS/CATABAQUS/CAT allows ABAQUS analyses to be set up and postprocessed entirely in CATIA. ABAQUS/CAT is not discussed in this guide.ABAQUS/C-MOLDABAQUS/C-MOLD translates finite element mesh, material property, and initial stress data from a C-MOLD mold filling analysis to an ABAQUS input file. ABAQUS/C-MOLD is not discussed in this guide. ABAQUS/DesignABAQUS/Design is a set of optional capabilities that can be added to ABAQUS/Standard to perform design sensitivity calculations. ABAQUS/Design is not discussed in this guide.ABAQUS/SafeABAQUS/Safe is the fatigue analysis module in ABAQUS. Using results from ABAQUS analyses, it determines the fatigue life of a component. ABAQUS/Safe is not discussed in this guide. 1.2  Getting started with ABAQUS/ExplicitThis is an introductory text designed to give new users guidance in analyzing continuum, shell, and framework problems with ABAQUS/Explicit and viewing the results in ABAQUS/Viewer. You do not need any previous knowledge of ABAQUS to benefit from this guide, although some previous exposure to the finite element method is recommended.1.2.1  How to use this guideThere are seven chapters in this guide, each of which introduces one or more topics. Most chapters contain a discussion of pertinent topics as well as one or two tutorial examples. You should work through the examples carefully since they contain a great deal of practical advice on using ABAQUS. The capabilities of ABAQUS/Viewer are introduced as they are needed to visualize the results. 

Page 2: Getting Started With ABAQUS

This chapter is a short introduction to ABAQUS and this guide. Chapter 2, "ABAQUS Basics," which is centered around a simple truss example, covers the basics of ABAQUS input. By the end of Chapter 2, "ABAQUS Basics," you will know how to prepare input data for an ABAQUS simulation, check the data, solve the analysis, and view the results in ABAQUS/Viewer. Chapter 3, "Overview of Explicit Dynamics," introduces the concept of explicit dynamics and explains the concept of "stability" using a wave propagation example and a simple oscillating spring example.Chapter 4, "Finite Elements and Rigid Bodies," presents an overview of the main element families available in ABAQUS/Explicit and includes an example problem to illustrate hourglassing in a mesh. Material modeling, with an emphasis on elastic-plastic metals and hyperelastic rubbers, is presented in Chapter 5, "Materials." The example problem is a blast loading on a stiffened steel plate. Chapter 6, "Contact," explains contact modeling, which is illustrated with two examples: a circuit board, housed in protective foam packaging, impacting the floor and an energy-absorbing square tube crushed between two rigid plates. Using ABAQUS/Explicit to solve quasi-static problems is presented in Chapter 7, "Quasi-Static Analysis." The illustrative example is a multi-stage sheet metal forming simulation, which requires importing between ABAQUS/Explicit and ABAQUS/Standard to perform the forming and springback analyses efficiently.1.2.2  Conventions used in this guideDifferent text styles used in the tutorial examples follow:텶 nput in COURIER FONT should be typed into the input file, ABAQUS/Viewer, or your computer exactly as shown. For example,*SOLID SECTION, ELSET=LUG, MATERIAL=STEELwould be entered into an input file.abaqus job=skew_nlwould be typed on your computer to run ABAQUS.텶 tems in <italics> indicate that user data such as a name or value should be substituted:*SOLID SECTION, ELSET=<element set>,  MATERIAL=<material name>텺 enu selections, tabs within dialog boxes, and labels of items on the screen in ABAQUS/Viewer are indicated in bold:View->View Options->HardwareDeformed Shape Plot Options1.3  ABAQUS documentationThe documentation for ABAQUS is extensive and complete. You will need to refer to the manuals regularly as you use ABAQUS. The following documentation and publications are available from HKS, unless otherwise specified, in printed form and through our online documentation server. For more information on accessing the online books, refer to the discussion of execution procedures in the ABAQUS/Explicit User's Manual.ABAQUS/Explicit User's ManualThis is the ABAQUS manual that you will use most often. It is the reference manual for all of the capabilities in ABAQUS/Explicit. This guide regularly refers to the ABAQUS/Explicit User's Manual, so you should have a copy available as you work through the examples.ABAQUS Keywords ManualThis manual contains a complete description of all the input options available in ABAQUS, including any parameters that may be used with a given option.ABAQUS/Viewer User's ManualThis basic reference document for ABAQUS/Viewer includes an introductory tutorial as well as a complete description of how to use ABAQUS/Viewer to display your model and results.Using ABAQUS Online DocumentationThis online manual contains instructions on using the ABAQUS online documentation server to read the online manuals.Other documentation available from HKS:ABAQUS Example Problems ManualThis manual contains more than 75 detailed examples designed to illustrate the approaches and decisions needed to perform meaningful linear and nonlinear analysis. Typical cases are large motion of an elastic-plastic pipe hitting a rigid wall; inelastic buckling collapse of a thin-walled elbow; explosive loading of an elastic, viscoplastic thin ring; consolidation under a footing; buckling of a composite shell with a hole; and deep drawing of a metal sheet. The description of each problem includes a discussion of the choice of element type and mesh density. When you want to use a feature that you have not used before, you should look up one or more examples that use that feature. Then, use the example to familiarize yourself with the correct usage of the capability. To find an example that uses a certain feature, search the online documentation or use the abaqus findkeyword utility (see ``Execution procedure for querying the keyword/problem database,'' Section 3.2.8 of the ABAQUS/Explicit User's Manual, for more information). All the input files associated with the examples are provided as part of the ABAQUS installation. A utility that gives you access to these files, called ABAQUS/Fetch, is provided with every ABAQUS release. The syntax for this utility isabaqus fetch job=<file name>You may fetch any of the example files from the installation directory, so that you can run the simulations yourself and review the results. You can also access the input files through the ABAQUS Input Files electronic book.ABAQUS Benchmarks ManualThis volume (available online and, if requested, in print) contains benchmark problems and standard analyses used to evalagainst exact calculations and other published results. These problems, like the example problems, offer a good starting point for learning about the behavior of elements and material models. The NAFEMS benchmark problems are included in this manual. The input files are also supplied as part of the installation and can be accessed just like example problem input files.ABAQUS Verification ManualThis online-only volume contains basic test problems that provide quality assurance testing of each individual program feature (procedures, output options, MPCs, etc.). It may be useful to run these problems when learning to use a new capability. The input files are also supplied as part of the installation and can be accessed just like example problem input files.ABAQUS Input FilesThis online manual contains all the input files that are included with the ABAQUS release and referred to in the ABAQUS Example Problems Manual, the ABAQUS Benchmarks Manual,

Page 3: Getting Started With ABAQUS

and the ABAQUS Verification Manual. They are listed under the title of the problem that refers to them. The input file references in the manuals hyperlink directly to this book. Although the input files in this book cannot be saved directly to a file, they can be saved by copying and pasting them into an editor.ABAQUS Theory ManualThis volume (available online and, if requested, in print) contains detailed, precise discussions of the theoretical aspects of ABAQUS. It is written to be understood by users with an engineering background and is not required on a routine basis.ABAQUS/CAE User's ManualThis reference document for ABAQUS/CAE includes three comprehensive tutorials as well as detailed descriptions of how to use ABAQUS/CAE for model generation, analysis, and results eval uation.ABAQUS/Standard User's ManualSplit into three volumes, this is the reference manual for all of the capabilities in ABAQUS/Standard.Release NotesThis document contains brief descriptions of the new features available in the latest release of the ABAQUS product line.Site GuideThis document, which is provided with each ABAQUS license, describes how to install ABAQUS and how to configure the installation for particular circumstances. Some of this information, of most relevance to users, is also included in the User's manuals.Quality Assurance PlanThis document describes HKS's QA procedures. It is a controlled document, provided to customers who subscribe to either HKS's Nuclear QA Program or the Quality Monitoring Service.Lecture NotesNotes and workshops are available for many features and applications for which ABAQUS is used, such as metal forming or heat transfer. The notes are used in the technical seminars that HKS offers to help users improve their understanding and usage of ABAQUS. While they are not intended as stand-alone tutorial material, they are sufficiently comprehensive that they can be used in that mode. Frequently, the lecture notes on a topic serve as a good introduction to the topic, making the User's Manual easier to understand. The list of available lecture notes is included in the Documentation Price List or can be found under Products on the ABAQUS Home Page atNewsletters HKS publishes ABAQUS/News and ABAQUS/Answers on a regular schedule. ABAQUS/News includes topical information about program releases, training seminars, etc. ABAQUS/Answers includes technical articles on particular topics related to ABAQUS usage. These newsletters are distributed at no cost to users who wish to subscribe. Please contact your local ABAQUS support office if you wish to be added to the mailing list for these publications. They are also archived in the Reference Shelf on the ABAQUS Home Page.ABAQUS Web serverHKS has a home page on the World Wide Web (www.abaqus.com), containing a variety of useful information about the ABAQUS suite of programs, including:텳 requently asked questions텮 BAQUS systems information and machine requirements텯 enchmark timing documents텲 rror status reports텮 BAQUS documentation price list톂 raining seminar schedule텻 ewslettersUser's manuals for ABAQUS/ADAMS, ABAQUS/CAT, ABAQUS/C-MOLD, and ABAQUS/Safe are also available.1.4  SupportHKS offers both technical (engineering) support and systems support for ABAQUS. Technical and systems support are provided through the nearest local support office. We regard technical support as an important part of the service we offer and encourage you to contact us with any questions or concerns that you have about your ABAQUS analyses. You can contact our offices by telephone, fax, electronic mail, or regular mail. Information on how to contact each office is listed in the front of each ABAQUS manual. Support information is also available by visiting the ABAQUS Home Page on the World Wide Web. When contacting your local support office, please specify whether you would like technical support (you have encountered problems performing an ABAQUS analysis) or systems support (ABAQUS will not install correctly, licensing does not work correctly, or other hardware-related issues have arisen).We welcome any suggestions for improvements to the support program or documentation. We will ensure that any enhancement requests you make are considered for future releases. If you wish to file a complaint about the service or products provided by HKS, refer to the ABAQUS Home Page.1.4.1  Technical supportHKS technical support engineers can assist in clarifying ABAQUS features and checking errors by giving both general information on using ABAQUS and information on its application to specific analyses. If you have concerns about an analysis, we suggest that you contact us at an early stage, since it is usually easier to solve problems at the beginning of a project rather than trying to correct an analysis at the end.Please have the following information ready before calling the technical support hotline, and include it in any written contacts:톂 he version of ABAQUS that are you using. -The version numbers for ABAQUS/Standard and ABAQUS/Explicit are given at the top of the data (.dat) file.-The version numbers for ABAQUS/CAE and ABAQUS/Viewer can be found by selecting Help->On version from the main menu bar.-The version number for ABAQUS/CAT is given at the top of the input (.inp) file as well as the data file.-The version numbers for ABAQUS/ADAMS and ABAQUS/C-MOLD are output to the screen.-The version number for ABAQUS/Safe is given under the ABAQUS logo in the main window.톂 he type of computer on which you are running ABAQUS.톂 he symptoms of any problems, including the exact error messages, if any.톆 orkarounds or tests that you have already tried.For support about a specific problem, any available ABAQUS output files may be helpful in answering questions that the support engineer may ask you.

Page 4: Getting Started With ABAQUS

The support engineer will try to diagnose your problem from the model description and a description of the difficulties you are having. Frequently, the support engineer will need model sketches, which can be faxed to HKS or sent in the mail. Plots of the final results or the results near the point that the analysis terminated may also be needed to understand what may have caused the problem.If the support engineer cannot diagnose your problem from this information, you may be asked to send the input data. The data can be sent by means of e-mail, tape, or disk. Please check the ABAQUS Home Page at www.abaqus.com for the media formats that are currently accepted.All support calls are logged into a database, which enables us to monitor the progress of a particular problem and to check that we are resolving support issues efficiently. If you would like to know the log number of your particular call for future reference, please ask the support engineer. If you are calling to discuss an existing support problem and you know the log number, please mention it so that we can consult the database to see what the latest action has been and, thus, avoid duplication of effort. In addition, please give the receptionist the support engineer's name (or include it at the top of any e-mail correspondence).1.4.2  Systems supportHKS systems support engineers can help you resolve issues related to the installation and running of ABAQUS, including licensing difficulties, that are not covered by technical support.You should install ABAQUS by carefully following the instructions in the ABAQUS Site Guide. If you encounter problems with the installation or licensing, first review the instructions in the ABAQUS Site Guide to ensure that they have been followed correctly. If this does not resolve the problems, look on the ABAQUS Home Page under Technical Support for information about known installation problems. If this does not address your situation, please contact your local support office. Send whatever information is available to define the problem: error messages from an aborted analysis or a detailed explanation of the problems encountered. Whenever possible, please send the output from the abaqus info=env and abaqus info=sys commands.1.4.3  Support for academic institutionsUnder the terms of the Academic License Agreement, we do not provide support to users at academic institutions unless the institution has also purchased technical support. Please contact us for more information.1.5  Review of the finite element methodA review of the fundamental concepts related to the finite element method can be found in ``A quick review of the finite element method,'' Section 1.5 of Getting Started with ABAQUS/Standard: Keywords Version. The extension of the finite element method to explicit dynamics is covered in ``Finite element method for explicit dynamics,'' Section 3.2.2.  ABAQUS BasicsA complete ABAQUS/Explicit analysis usually consists of three distinct stages: preprocessing, simulation, and postprocessing. These three stages are linked together by files as shown below:Preprocessing (ABAQUS/CAE)In this stage you define the model of the physical problem and create an ABAQUS input file. The model is usually created graphically using ABAQUS/CAE or another preprocessor, although the ABAQUS input file for a simple analysis can be created directly using a text editor.Simulation (ABAQUS/Explicit)The simulation, which normally is run as a background process, is the stage in which ABAQUS/Explicit solves the numerical problem defined in the input file. Examples of output from a stress analysis include displacements and stresses that are stored in files ready for postprocessing. Depending on the complexity of the simulation and the power of the computer, solution time may range from seconds to days.Postprocessing (ABAQUS/Viewer)When the simulation has completed or while it is running, you can eval uate the results interactively using ABAQUS/Viewer or another postprocessor. ABAQUS/Viewer provides a variety of options for displaying the results, including color contour plots, animations, deformed shape plots, and X-Y plots.2.1  Components of an ABAQUS modelAn ABAQUS model is composed of several components that together describe the physical problem to be analyzed and the results to be obtained. At minimum the model consists of the following information: geometry, element section properties, material data, loads and boundary conditions, analysis type, and output requests.GeometryFinite elements, nodes, and rigid bodies define the basic geometry of the model. Each element in the model represents a discrete portion of the physical structure, which is, in turn, represented by many interconnected elements. Elements are connected to one another by shared nodes. The coordinates of the nodes and the connectivity of the elements--that is, which nodes belong to which elements--comprise the model geometry. The collection of all the elements and nodes in a model is called the mesh. Generally, the mesh will be only an approximation of the structure's actual geometry.The element type, shape, and location, as well as the overall number of elements used in the mesh, affect the results obtained from a simulation. The greater the mesh density (i.e., the greater the number of elements in the mesh), the more accurate the results. As the mesh density increases, the analysis results converge to a unique solution (except in rare cases), and the computer time required for the analysis increases. The solution from the numerical model is generally an approximation to the solution of the physical problem being simulated. The extent of the approximations made in the model's geometry, material behavior, boundary conditions, and loading determines how well the numerical simulation matches the physical problem.Element section propertiesThe geometry of many elements in ABAQUS/Explicit is not defined completely by the nodal coordinates. For example, the layers of a composite shell or the dimensions of an I-beam section are not defined by the nodes of the element. Such additional geometric data are defined as physical properties of the element and are necessary to define the model geometry completely. Chapter 4, "Finite Elements and Rigid Bodies," describes the necessary section properties for each element type.Material dataMaterial properties for all elements must be specified. The validity of results from ABAQUS/Explicit is limited by the quality of the material data.Loads and boundary conditionsABAQUS/Explicit provides a variety of loading options, the most common of which include:톚 oint loads;톚 ressure loads on surfaces;톌 ody forces, such as the force of gravity; and톞 hermal loads.

Page 5: Getting Started With ABAQUS

Boundary conditions are used to constrain portions of the model to remain fixed (zero displacements) or to move by a prescribed amount (nonzero displacements).Analysis typeThe most common type of simulation performed in ABAQUS/Explicit is an explicit dynamic analysis, where the dynamic response of a structure to the applied loads is obtained. Fully coupled thermal stress analyses, which simulate the coupled thermal-mechanical response of a body, and annealing analyses, which simulate the relaxation of stresses and plastic strains that occurs as metals are heated to a high temperature, can also be performed in ABAQUS/Explicit. Only explicit dynamic analyses are discussed in this guide.Output requestsA finite element analysis can generate a large amount of output. Making use of the variety of available output options, you can request only the output necessary for you to interpret the results adequately.2.2  Format of the input fileThe ABAQUS input file is the means of communication between the preprocessor, usually ABAQUS/CAE, and the solver, ABAQUS/Explicit. The input file, which contains a complete description of the numerical model, is a text file with an intuitive, keyword-based format. It is easily modified using a text editor. Indeed, the input file for small analyses can be specified by typing it directly into an editor. If you are using ABAQUS/CAE, you will not need to see the input file. However, by understanding the input file, you will get a good understanding of how to use ABAQUS/Explicit.We use the example of an overhead hoist shown in Figure 2-1   to illustrate the basic format of the ABAQUS input file. The hoist is a simple, pin-jointed framework that is constrained at the left-hand end and mounted on rollers at the right-hand end. The members can rotate freely at the joints. Since the model is two-dimensional, the frame is prevented from moving out of plane. A simulation is performed to determine the structure's deflection and the peak stress in its members when a 10 kN load is applied as shown in Figure 2-1Figure 2-1  Schematic of an overhead hoist.Since this problem is very simple, the ABAQUS input file is compact and easy to understand. The complete ABAQUS input file for this example, which is shown in Figure 2-2in ``Overhead hoist frame,'' Section A.1, is split into two distinct parts. The first section contains model data and includes all the information required to define the structure. The second section contains history data that define the model's loading history. The history can be further subdivided into a sequence of steps, each defining a separate stage of the simulation.The input file is composed of a number of option blocks that contain data describing a part of the model. Each option block begins with a keyword line, which is usually followed by one or more data lines. These lines cannot exceed 256 characters.Figure 2-2  Input for overhead hoist model.2.2.1  Keyword linesKeywords (or options) always begin with a star or asterisk (*). For example, *NODE is the keyword for specifying the nodal coordinates, and *ELEMENT is the keyword for specifying the element connectivity. Keywords are often followed by parameters, which may be required or optional. The *ELEMENT option requires the TYPE parameter because the element type must always be given when defining elements. For example,*ELEMENT, TYPE=T2D2 indicates that we are defining T2D2 elements (two-dimensional truss elements with two nodes). Many parameters are optional and are defined only in certain circumstances. For example,*NODE, NSET=PART1indicates that all the nodes defined in this option block will be put into a set called PART1. It is not essential to put nodes into sets, although it is often convenient.Keywords and parameters are case independent and must use enough characters to make them unique. Parameters are separated by commas. If a parameter has a value, use an equal sign (=) to associate the value with the parameter.Occasionally, so many parameters are required that they will not all fit on a single 256-character line. In this case a comma is placed at the end of the line to indicate that the next line is a continuation line. For example,*ELEMENT, TYPE = T2D2,ELSET = FRAMEis a valid keyword line.Details of the keywords are documented in the ABAQUS Keywords Manual.2.2.2  Data linesKeyword lines are usually followed by data lines, which provide data that are more easily specified as lists than as parameters on the keyword line. Examples of such data include nodal coordinates; element connectivities; or tables of material properties, such as stress-strain curves. The data required for particular option blocks are specified in the ABAQUS Keywords Manual. For example, the option block defining the nodes for the overhead hoist model is:*NODE101, 0., 0., 0.102, 1., 0., 0.103, 2., 0., 0.104, 0.5, 0.866, 0.105, 1.5, 0.866, 0.The first piece of data on each data line is an integer that defines the node number. The second, third, and fourth entries are floating-point numbers that specify the , ,of the node.The data can consist of a mixture of integer, floating-point, or alphanumeric values. Floating point values can be entered in a variety of ways; for example, ABAQUS interprets all of the following as the number four: 4.04.44.0E+0.4E+140.E-1

Page 6: Getting Started With ABAQUS

Data items are separated by commas, as in Figure 2-2  , which allows fairly arbitrary spacing of the input values on the data line. If there is only one item on a data line, it must be followed by a comma.2.3  Creating an input fileThe simulation of the pin-jointed, overhead hoist in Figure 2-1   is used to illustrate the creation of an ABAQUS input file using an editor. As you read through this section, you should type the data into a file using one of the editors available on your computer. The ABAQUS input file must have a .inp file extension. For convenience, name the input file frame_xpl.inp. The file identifier, which can be chosen to identify the analysis, is called the jobname. In this case use the jobname "frame_xpl" to easily associate it with the input file called frame_xpl.inp.All of the other examples in this guide assume that you will be using a preprocessor, such as ABAQUS/CAE, to generate the mesh if you are going to create the model from scratch. Input files for all the examples are available. See ``Execution procedure for ABAQUS/Fetch,'' Section 3.2.9 of the ABAQUS/Explicit User's Manual, for instructions on how to retrieve these input files. However, since the purpose of this example is to help you understand the structure and format of the ABAQUS input file, you should type this input file in directly, rather than use a preprocessor or copy the input file that is provided.2.3.1  UnitsBefore starting to define this or any model, you need to decide which system of units you will use. ABAQUS has no built-in system of units. All input data must be specified in consistent units. Some common systems of consistent units are shown in Table 2-1  .Table 2-1  Common systems of consistent units.QuantitySISI (mm)US Unit (ft)US Unit (inch)LengthmmmftinForceNNlbflbfMasskgtonne (103 kg)sluglbf s2/inTimessssStressPa (N/m2)MPa (N/mm2)lbf/ft2psi (lbf/in2)EnergyJmJ (10-3 J)ft lbfin lbfDensitykg/m3tonne/mm3slug/ft3lbf s2/in4The SI system of units is used throughout this guide. Users working in the systems labeled "US Unit" should be careful with the units of density; often the densities given in handbooks of material properties are multiplied by the acceleration due to gravity.2.3.2  Coordinate systemsYou also need to decide which coordinate system to use. The global coordinate system in ABAQUS is a right-handed, rectangular (Cartesian) system. For this example define the global 1-axis to be the horizontal axis of the hoist and the global 2-axis to be the vertical axis (Figure 2-3  ). The global 3-axis is normal to the plane of the framework. The origin (=0, =0, =0) is the bottom left-hand corner of the frame.

Page 7: Getting Started With ABAQUS

Figure 2-3  Coordinate system and origin for model.For two-dimensional problems, such as this one, ABAQUS requires that the model lie in a plane parallel to the global 1-2 plane.2.3.3  MeshYou must select the element types and design the mesh. Creating a proper mesh for a given problem requires experience. For this example you will use a single truss element to model each member of the frame, as shown in Figure 2-4  .Figure 2-4  Finite element mesh.A truss element, which can carry only tensile and compressive axial loads, is ideal for modeling pin-jointed frameworks, such as the overhead hoist. Truss elements are described in Chapter 4, "Finite Elements and Rigid Bodies," and also in the ABAQUS/Explicit User's Manual, which describes every element available in ABAQUS/Explicit. The index of element types in the ABAQUS/Explicit User's Manual makes locating a particular element easy. Whenever you are using an element for the first time, you should read the description, which includes the element connectivity and any element section properties needed to define the element's geometry.The connectivity for the truss elements used in the overhead hoist model is shown in Figure 2-5  .Figure 2-5  Connectivity for the 2-node truss element (T2D2).Node and element numbers are merely identification labels. They are usually generated automatically by ABAQUS/CAE or another preprocessor. The only requirement for node and element numbers is that they must be positive integers. Gaps in the numbering are allowed, and the order in which nodes and elements are defined does not matter. Any nodes that are defined but not associated with an element are removed automatically and are not included in the simulation.In this case we use the node and element numbers shown in Figure 2-6  .Figure 2-6  Node and element numbers for the hoist model.2.3.4  Model dataThe first part of the input file must contain all of the model data. These data define the structure being analyzed. In the overhead hoist example the model data consist of the following:텴 eometry:  Nodal coordinates. Element connectivity. Element section properties.텺 aterial properties.HeadingThe first option in any ABAQUS input file must be *HEADING. The data lines that follow the *HEADING option are lines of text describing the problem being simulated. You should provide an accurate description to allow the input file to be identified at a later date. Moreover, it is often helpful to specify the system of units, directions of the global coordinate system, etc. For example, the *HEADING option block for the hoist problem contains the following:*HEADINGTwo-dimensional overhead hoist frameSI units (kg, m, s, N)Data file printing optionsBy default, ABAQUS will not print an echo of the input file or the model and history definition data to the printed output (.dat) file. However, it is recommended that you check your model and history definition in a datacheck run before performing the analysis. The datacheck run is discussed later in this chapter.To request a printout of the input file and of the model and history definition data, add*PREPRINT, ECHO=YES, MODEL=YES, HISTORY=YES to the input file.Nodal coordinatesThe coordinates of each node can be defined once you select the mesh design and node numbering scheme. For this problem use the numbering shown in Figure 2-6coordinates of nodes are defined using the *NODE option, and the value of the NSET parameter defines the name of the node set to which the nodes belong. Each data line of this option block has the form<node number>,-coordinate>,-coordinate>,-coordinate>The nodes for the hoist model belong to the node set NALL, and they are defined as follows:*NODE, NSET=NALL101, 0., 0., 0.102, 1., 0., 0.103, 2., 0., 0.104, 0.5, 0.866, 0.105, 1.5, 0.866, 0.Element connectivityThe members of the overhead hoist are modeled with truss elements. The format of each data line for a truss element is<element number>, <node 1>, <node 2> where node 1 and node 2 are at the ends of the element (see Figure 2-5  ). For example, element 16 connects nodes 103 and 105 (see Figure 2-6element is16, 103, 105The TYPE parameter on the *ELEMENT option must be used to specify the kind of element being defined. In this case you will use T2D2 truss elements.One of the most useful features in ABAQUS is the availability of node and element sets that are referenced by name. By using the ELSET parameter on the *ELEMENT option, all of the elements defined in the option block are added to an element set called FRAME. A set name can have as many as 80 characters and must start with a letter. Since element section properties are assigned through element set names, all elements in the model must belong to at least one element set.The complete *ELEMENT option block for the overhead hoist model (see Figure 2-6  ) is shown below:

Page 8: Getting Started With ABAQUS

*ELEMENT, TYPE=T2D2, ELSET=FRAME11, 101, 10212, 102, 10313, 101, 10414, 102, 10415, 102, 10516, 103, 10517, 104, 105Element section propertiesEach element must reference an element section property. The appropriate element section option for each element and the additional geometric data (if any) needed for each element are described in the ABAQUS/Explicit User's Manual.For the T2D2 element you must use the *SOLID SECTION option and give one data line with the cross-sectional area of the element. If you leave the data line blank, the cross-sectional area is assumed to be 1.0.In this case all the members are circular bars that are 5 mm in diameter. Their cross-sectional area is 1.963 ?10-5 m2.The MATERIAL parameter, which is required for most element section options, references the name of a material property definition that is to be used with the elements. The name can have up to 80 characters and must begin with a letter.In this example all of the elements have the same section properties and are made of the same material. Typically, there will be several different element section properties in an analysis; for example, different components in a model may be made of different materials. The elements are associated with material properties through element sets. For the overhead hoist model the elements were included in an element set called FRAME. Element set FRAME is then used as the value of the ELSET parameter on the element section option. Add the following option block to your input file:MaterialsOne of the features that makes ABAQUS easy to use is that almost any material model can be used with any element. Once the mesh has been created, material models can be associated, as appropriate, with the elements in the mesh.ABAQUS has a large number of material models, many of which include nonlinear behavior. In this overhead hoist example we use the simplest form of material behavior: linear elasticity. A discussion of all the material models available in ABAQUS/Explicit can be found in the ABAQUS/Explicit User's Manual.Linear elasticity is appropriate for many materials at small strains, particularly for metals up to their yield point. It is characterized by a linear relationship between stress and strain (Hooke's law), as shown in Figure 2-7  .Figure 2-7  Linear elastic material.The material behavior is characterized by two constants: Young's modulus, , and Poisson's ratio, .A material definition in the ABAQUS input file starts with a *MATERIAL option. The parameter NAME is used to associate a material with an element section property. For example,Material suboptions directly follow their associated *MATERIAL option. Several suboptions may be required to complete the material definition. All material suboptions are associated with the material that is listed on the most recent *MATERIAL option until another *MATERIAL option or a non-material option block is given.Without considering thermal expansion effects (which would be defined with the *EXPANSION material option), two material options, *ELASTIC and *DENSITY, are required to define a linear elastic material. The form of this option block is the following:*ELASTIC<>,<>*DENSITY<>, Therefore, the complete, isotropic, linear elastic material definition for the hoist members, which are made of steel, should be entered into your input file as*MATERIAL, NAME=STEEL*ELASTIC200.E9, 0.3*DENSITY7800.,The model definition portion of this problem is now complete since all the components describing the structure have been specified.2.3.5  History dataThe history data define the sequence of events for the simulation. This loading history is divided into a series of steps, each defining a different stage in the structure's loading. Each step contains the following information:톂 he type of simulation (dynamic, fully coupled thermal-stress, or anneal).톂 he loads and constraints.톂 he output required.In this example we are interested in the dynamic response of the overhead hoist to a suddenly applied load of 10 kN at the center, with the left-hand end fully constrained and a roller constraint on the right-hand end (see Figure 2-1  ). This loading is a single event, so only a single step is needed for the simulation.The *STEP option is used to mark the start of a step. Like the *HEADING option, this option may be followed by data lines containing a title for the step. You can choose whether or not to include nonlinear geometric effects in the analysis by setting the NLGEOM parameter equal to YES or NO. The default is YES. In your hoist model use the following *STEP option block:*STEP10kN central loadAnalysis procedureThe analysis procedure (the type of simulation) must be defined immediately following the *STEP option block. In ABAQUS/Explicit the three analysis options are *DYNAMIC, EXPLICIT; *DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT; and *ANNEAL. The *DYNAMIC TEMPERATURE-DISPLACEMENT procedure simulates the fully coupled thermal-

Page 9: Getting Started With ABAQUS

mechanical response of a body, while the *ANNEAL procedure simulates the relaxation of stresses and plastic strains that occurs as metals are heated to a high temperature. In this simulation we want to determine the dynamic response of the structure over a period of 0.01 s. Thus, we will use *DYNAMIC, EXPLICIT. Add the following lines to your input file:*DYNAMIC, EXPLICIT, 0.01The remaining input data in the step define the boundary conditions, loads, and desired output and can be given in any convenient order.Boundary conditionsBoundary conditions are applied to those parts of the model where the displacements are known. Such parts may be constrained to remain fixed (have zero displacement) during the simulation or may have specified, nonzero displacements. In either situation the constraints are applied directly to the nodes of the model.In some cases a node may be constrained completely and, thus, cannot move in any direction (for example, node 101 in our case). In other cases a node is constrained in some directions but is free to move in others. For example, node 103 is fixed in the vertical direction but is free to move in the horizontal direction. The directions in which a node is able to move are called degrees of freedom (dof). In the case of our two-dimensional hoist, each node can move in the global 1- and 2-directions; therefore, there are two degrees of freedom at each node. If the hoist could move out of plane, the problem would be three-dimensional, and each node would have three degrees of freedom. Nodes attached to beam and shell elements have additional degrees of freedom representing the components of rotation and, thus, may have up to six degrees of freedom.The labeling convention used for the degrees of freedom in ABAQUS is shown in Figure 2-8  .Figure 2-8  Labeling convention for degrees of freedom.The degrees of freedom active at a node depend on the type of elements attached to that node. The two-dimensional truss element, T2D2, has two degrees of freedom active at each node: translation in the 1- and 2-directions (dof 1 and dof 2).Constraints on nodes are defined by using the *BOUNDARY option and specifying the constrained degrees of freedom. Each data line is of the form<node number>, <first dof>, <last dof>, <magnitude of displacement>The first degree of freedom and last degree of freedom are used to give a range of degrees of freedom that will be constrained. For example,101, 1, 3, 0.0 constrains degrees of freedom 1, 2, and 3 at node 101 to have zero displacement (the node cannot move in any of the global 1-, 2-, or 3-directions).If the magnitude of the displacement is not specified on the data line, it is assumed to be zero. If the node is constrained in one direction only, the third field should be blank or equal to the second field. For example, to constrain node 103 in the 2-direction (degree of freedom 2) only, any of the following data line formats can be used:103, 2, 2, 0.0 or103, 2, 2 or103, 2Boundary conditions on a node are cumulative. Thus, the following input constrains node 101 in both directions 1 and 2:101, 1101, 2Rather than specifying each constrained degree of freedom, some of the more common constraints can be given directly using the following named constraints:ENCASTREConstraint on all displacements and rotations at a node.PINNEDConstraint on all translational degrees of freedom.XSYMMSymmetry constraint about a plane of constant .YSYMMSymmetry constraint about a plane of constant .ZSYMMSymmetry constraint about a plane of constant .XASYMMAntisymmetry constraint about a plane of constant .YASYMMAntisymmetry constraint about a plane of constant .ZASYMMAntisymmetry constraint about a plane of constant .Thus, another way to constrain all the active degrees of freedom at node 101 in the hoist model is101, ENCASTREThe complete *BOUNDARY option block for our hoist problem is*BOUNDARY101, ENCASTRE103, 2In this example all of the constraints are in the global 1- or 2-directions. In many cases constraints are required in directions that are not aligned with the global directions. The *TRANSFORM option can be used in such cases to define a local coordinate system for boundary condition application.LoadingLoading is anything that causes the displacement or deformation of the structure, including:톍 oncentrated loads;톚 ressure loads;

Page 10: Getting Started With ABAQUS

톘 onzero boundary conditions;톌 ody loads; and톞 emperature (with thermal expansion of the material defined).In reality there is no such thing as a concentrated, or point, load; the load will always be applied over some finite area. However, if the area being loaded is similar to or smaller than the elements in that area, it is an appropriate idealization to treat the load as a concentrated load applied to a node.Concentrated loads are specified using the *CLOAD option. The data lines for this option have the form<node number>, <dof>, <load magnitude> In this simulation a load of -10 kN is applied in the 2-direction to node 102. The option block is the following:*CLOAD102, 2, -10.E3 By default, ABAQUS/Explicit assumes that the load is applied instantaneously at the start of the analysis.Output requestsFinite element analyses can create vast amounts of output. ABAQUS allows you to control and manage this output so that only data required to interpret the results of your simulation are produced. Three types of output are available from ABAQUS/Explicit:텽 utput database (ODB) output (.odb file). Writes a neutral binary file used by ABAQUS/Viewer for postprocessing.톀 estart output (.res file). Used to continue the analysis, thus allowing a simulation to be run in stages.텳 ile output (.fil file). Writes results in a binary format; primarily used for subsequent postprocessing with third-party software.You will use the first of these in the overhead hoist simulation.By default, ABAQUS/Explicit writes a preselected set of the most commonly used output variables to the output database file. A list of preselected variables for default output database output is given in the ABAQUS/Explicit User's Manual. You do not need to add any output requests to accept these defaults. For this example, the default output database output includes the deformed configuration.Since you have now finished defining all the data required for the step, use the *END STEP option to mark the end of the step:*END STEPThe input file is now complete. Compare the input file you have generated to the complete input file given in Figure 2-22.4  Checking the input dataHaving generated the input file for this simulation, you are ready to run the analysis. Unfortunately, it is possible to have errors in the input file because of typing errors or incorrect or missing data. You should perform a datacheck analysis first before running the simulation. To run a datacheck analysis, make sure that you are in the directory where the input file frame_xpl.inp is located, and type the following command:abaqus job=frame_xpl datacheck interactiveIf this command results in an error message, the ABAQUS installation on your computer has been customized. You should contact your systems administrator to find out the appropriate command to run ABAQUS. The job=frame_xpl parameter specifies that the jobname for this analysis is frame_xpl. All the files associated with this analysis will have this jobname as their identifier, which allows them to be recognized easily.The analysis will run interactively, and messages similar to the following will appear on your screen:ABAQUS JOB frame_xplBegin Solver Input File ProcessorTue Oct 17 14:46:06 2000Run /usr/abaqus/exec/pre.xABAQUS/EXPLICIT is running on a Category A machineand has checked out 4 Network Tokens.Tue Oct 17 14:46:24 2000End Solver Input File ProcessorBegin ABAQUS/Explicit PackagerTue Oct 17 14:46:25 2000Run /usr/abaqus/exec/package.xABAQUS/EXPLICIT is running on a Category A machineand has checked out 4 Network Tokens. . . .Tue Oct 17 14:46:33 2000End ABAQUS/Explicit PackagerBegin ABAQUS/Explicit AnalysisTue Oct 17 14:46:33 2000Run /usr/abaqus/exec/explicit.xABAQUS/EXPLICIT is running on a Category A machineand has checked out 4 Network Tokens.Tue Oct 17 14:46:36 2000End ABAQUS/Explicit AnalysisABAQUS JOB frame_xpl COMPLETEDWhen the datacheck analysis is complete, you will find that a number of additional files have been created by ABAQUS. If any errors are encountered during the datacheck analysis, messages will be written to the data file, frame_xpl.dat. This data file is a text file that can be viewed in an editor or printed. Part of this data file is shown in Figure 2-9

Page 11: Getting Started With ABAQUS

Figure 2-12  .Figure 2-9  ABAQUS input file echo and list of options processed.Figure 2-10  Model data in data file.Figure 2-11  History data in data file.Figure 2-12  Summary of problem and file sizes.Try viewing the data file in a text editor. The file can contain lines up to 256 characters long, so the editor should be able to accommodate that many characters. At the top of the file is a header page that contains information about the version of ABAQUS used to run the analysis. The header page also contains the phone number, address, and contact information of your local ABAQUS office or representative who can offer technical support and advice.Following this header page is an echo of the input file (Figure 2-9  ). The input data echo is generated by adding the option *PREPRINT, ECHO=YES to the input file. By default, the parameter ECHO is set to NO.Following the input data echo is a list of the options processed by ABAQUS (Figure 2-9  ). This is the first point at which error and warning messages appear. All error messages are prefixed with ***ERROR, while warnings begin with ***WARNING. Since these messages always begin the same way, searching the data file for warning and error messages is straightforward. When the error is a syntax problem (i.e., when ABAQUS cannot understand the input), the error message is followed by the line from the input file that is causing the error.The rest of the data file is a series of tables containing all of the model data (Figure 2-10  ) and the history data (Figure 2-11omissions. These tables are generated by including the option *PREPRINT, MODEL=YES, HISTORY=YES in the input file. However, these tables may take up a large amount of disk space for large models. By default, the parameters MODEL and HISTORY are set to NO. You should always check your model by setting MODEL=YES and HISTORY=YES to make sure that what was in the input file was interpreted by ABAQUS in the way you intended. Once you have confirmed that you have the correct input data, you can reduce or suppress this printout if necessary.Any warning or error messages are written to the data file, frame_xpl.dat, or written to your screen during an interactive analysis. If you submit an analysis without the interactive option, analysis warnings and errors are written to the status file, frame_xpl.sta.Finally, there is a summary of the size of the numerical model (see Figure 2-12  ). The comment at the end of the data file that states AN OUTPUT DATABASE REQUEST THAT REQUIRES THE CALCULATOR HAS BEEN FOUND indicates that some of the requested output needs to be converted prior to postprocessing with ABAQUS/Viewer. The types of output that require such conversion using the postprocessing calculator are discussed in ``The postprocessing calculator,'' Section 4.3.1 of the ABAQUS/Explicit User's Manual.2.5  Running the analysisExit the editor, and make any necessary corrections to your input file. When the datacheck analysis completes with no error messages, run the analysis itself by using the commandabaqus job=frame_xpl continue interactiveMessages like the following will appear on the screen:ABAQUS JOB frame_xplBegin ABAQUS/Explicit AnalysisTue Oct 17 14:53:20 2000Run /usr/abaqus/exec/explicit.xABAQUS/EXPLICIT is running on a Category A machineand has checked out 4 Network Tokens. . . . -------------------------------------------------------------------------------  SOLUTION PROGRESS -------------------------------------------------------------------------------    STEP 1  ORIGIN 0.00000E+00     Total memory used for step 1 is approximately 34.1 kilowords   Global time estimation algorithm will be used.   Scaling factor :  1.0000               STEP      TOTAL       CPU     STABLE      CRITICAL  KINETIC  INCREMENT  TIME      TIME        TIME   INCREMENT    ELEMENT   ENERGY         0  0.000E+00 0.000E+00   00:00:00 1.841E-04      13   0.000E+00 ODB Field Frame Number    0 of   20 requested intervals at increment zero.         3  5.524E-04 5.524E-04   00:00:00 1.840E-04      17   1.451E+01 ODB Field Frame Number    1 of   20 requested intervals at  5.523613E-04         6  1.104E-03 1.104E-03   00:00:00 1.835E-04      13   1.459E+01  ODB Field Frame Number    2 of   20 requested intervals at  1.103952E-03         9  1.654E-03 1.654E-03   00:00:00 2.141E-04      13   4.725E+00 . . .         49  1.000E-02 1.000E-02   00:00:01 2.131E-04      13   1.132E+01 ODB Field Frame Number   20 of   20 requested intervals at  1.000000E-02

Page 12: Getting Started With ABAQUS

 Restart Number  1 at 1.00000E-02     THE ANALYSIS HAS COMPLETED SUCCESSFULLY  Tue Oct 17 14:53:25 2000End ABAQUS/Explicit AnalysisABAQUS JOB frame_xpl COMPLETEDIt is desirable to perform a datacheck analysis before running a simulation to ensure that the input data are correct. However, it is possible to combine the datacheck and analysis phases of the simulation by using the following command:abaqus job=frame_xpl interactiveIf a simulation is expected to take a substantial amount of time, it is convenient to run it in the background by omitting the interactive parameter:abaqus job=frame_xpl(The above commands apply for the standard ABAQUS installation on a workstation. However, ABAQUS jobs can be run in batch queues on some computers. If you have any questions, ask your systems administrator how to run ABAQUS on your system. Details of the ABAQUS commands are documented in Chapter 3, "Execution Procedures," of the ABAQUS/Explicit User's Manual.)2.6  Postprocessing with ABAQUS/ViewerGraphical postprocessing is important because of the great volume of data created during a simulation. ABAQUS/Viewer allows you to view the results graphically using a variety of methods, including deformed shape plots, contour plots, symbol plots, animations, and X-Y plots. All of these methods are discussed in this guide. For more information on any of the postprocessing features discussed in this guide, consult the ABAQUS/Viewer User's Manual. For this example you will use ABAQUS/Viewer to do some basic model checks and to display the deformed shape of the frame.Start ABAQUS/Viewer by typingabaqus viewerat the operating system prompt. The ABAQUS/Viewer window appears.Reading the output database fileTo begin this exercise, open the output database file that ABAQUS/Explicit generated during the analysis of the problem.To open the output database file:1.From the main menu bar, select File->Open; or use the  tool in the toolbar.The Open Database dialog box appears.2.From the list of available output database files, select frame_xpl.odb.3.Click OK.Tip:  You can also open the output database frame_xpl.odb by typing abaqus viewer odb=frame_xpl at the operating system prompt.ABAQUS/Viewer displays a fast plot of the model. A fast plot is a basic representation of your undeformed model shape and is an indication that you have opened the desired file.Important:  The fast plot does not display results and cannot be customized; for example, to display element and node numbers. You must display the undeformed model shape to customize the appearance of the model.The title block at the bottom of the viewport indicates the following:톂 he description of the model (from the first line of the *HEADING option in the input file).톂 he name of the output database (from the name of the analysis job).톂 he product name (ABAQUS/Standard or ABAQUS/Explicit) and version used to generate the output database.톂 he date the output database was last modified.The state block at the bottom of the viewport indicates the following:톆 hich step is being displayed.톂 he increment within the step.톂 he step time.The view orientation triad indicates the orientation of the model in the global coordinate system.Displaying and customizing an undeformed shape plotYou will now display the undeformed model shape and use the plot options to enable the display of node and element numbering in the plot.From the main menu bar, select Plot->Undeformed Shape; or use the  tool in the toolbox. ABAQUS/Viewer displays the undeformed model shape, as shown in Figure 2-13Figure 2-13  Undeformed model shape.To display node numbers:1.From the main menu bar, select Options->Undeformed Shape.The Undeformed Shape Plot Options dialog box appears.2.Click the Labels tab.3.Toggle on Show node labels.4.Click Apply.ABAQUS/Viewer applies the change and keeps the dialog box open. The customized undeformed plot is shown in Figure 2-14  .Figure 2-14  Node number plot.To display element numbers:1.In the Undeformed Shape Plot Options dialog box, toggle on Show element labels.

Page 13: Getting Started With ABAQUS

2.Click OK. ABAQUS/Viewer applies the change and closes the dialog box.The resulting plot is shown in Figure 2-15  .Figure 2-15  Node and element number plot.To suppress the display of node and element numbers in the undeformed shape plot, repeat the above procedure and toggle off Show node labels and Show element labels.Displaying and customizing a deformed shape plotYou will now display the deformed model shape and use the plot options to change the deformation scale factor and overlay the undeformed model shape on the deformed model shape.From the main menu bar, select Plot->Deformed Shape; or use the  tool in the toolbox. ABAQUS/Viewer displays the deformed model shape, as shown in Figure 2-16Figure 2-16  Deformed model shape.The scale factor for the deformed plot is displayed in the state block. By default, the displaced shape is not scaled. For this analysis, change the deformation scale factor so that the displaced shape is evident.To change the deformation scale factor:1.From the main menu bar, select Options->Deformed Shape.2.In the Deformed Shape Plot Options dialog box, click the Basic tab if it is not already selected.3.From the Deformation Scale Factor area, toggle on Uniform and enter 40.0 in the Value field.4.Click Apply to redisplay the deformed shape.The plot title displays the new scale factor.To return to the default deformed plot, repeat the above procedure and, in the Deformation Scale Factor field, toggle on Auto-compute.To overlay the undeformed model shape on the deformed model shape:1.In the Deformed Shape Plot Options dialog box, toggle on Superimpose undeformed plot.2.Click OK.By default, ABAQUS/Viewer plots the undeformed model shape in green and the deformed model shape in white. Change the line style of the undeformed model shape to more clearly distinguish the two plots.To change the undeformed model shape's line style:1.From the main menu bar, select Options->Undeformed Shape.The Undeformed Shape Plot Options dialog box appears.2.Click the Color & Style tab.3.In the Edge Attributes area, choose the dotted line style.4.Click OK.The customized plot is shown in Figure 2-17  .Figure 2-17  Undeformed and deformed model shapes.To return the undeformed plot's line style to solid, repeat the above procedure and select the solid line style. Alternatively, to return all the undeformed plot options to their default values, you can click Defaults in the Undeformed Shape Plot Options dialog box.Checking history data with ABAQUS/ViewerBy default, both the model data and history data are written to the output database file during the datacheck phase. Thus, you can use ABAQUS/Viewer to check that the input data are correct before running the simulation. You have already learned how to draw plots of the model and to display the node and element numbers. These are useful tools for checking that ABAQUS is using the correct mesh.The boundary conditions applied to the overhead hoist model can also be displayed using ABAQUS/Viewer. To display boundary conditions on the undeformed model:1.From the main menu bar, select Plot->Undeformed Shape; or use the  tool in the toolbox.2.From the main menu bar, select View->ODB Display Options.3.In the ODB Display Options dialog box, click the BC tab.4.Toggle on Show boundary conditions.5.Click OK.ABAQUS/Viewer displays symbols to indicate the applied boundary conditions, as shown in Figure 2-18  .Figure 2-18  Applied boundary conditions on the overhead hoist.Exiting ABAQUS/ViewerFrom the main menu bar, select File->Exit to exit ABAQUS/Viewer.2.7  Summary톂 he ABAQUS input file contains a complete description of the analysis model. It is the means of communication between the preprocessor (ABAQUS/CAE) and the analysis code (ABAQUS/Explicit). If you are using ABAQUS/CAE, you will not need to edit the input file since everything can be done within ABAQUS/CAE.톂 he input file contains two sections: the model data, which define the structure, and the history data, which define the loading.텲 ach section of the input file comprises a number of option blocks, each consisting of a keyword line that may be followed by data lines.톉 ou can perform a datacheck analysis once you have created the input file. Along with descriptions of how ABAQUS/Explicit has interpreted your model, error and warning messages are printed in the data (.dat) and status (.sta) files.톃 se ABAQUS/Viewer to verify the model geometry and boundary conditions graphically, using the output database file generated during the datacheck phase.텶 t is often easiest to check the data file for mistakes in the material definition, section properties, etc. Use *PREPRINT, MODEL=YES, HISTORY=YES to check the model.톂 o run the analysis after a successful datacheck analysis without repeating the datacheck phase, use the following command: abaqus job=<jobname> continue.톂 he output database file contains results for graphical postprocessing with ABAQUS/Viewer.텮 BAQUS/Viewer allows you to visualize analysis results graphically in a variety of ways.

Page 14: Getting Started With ABAQUS

3.  Overview of Explicit DynamicsThe explicit dynamics procedure can be an effective tool for solving a wide variety of nonlinear solid and structural mechanics problems. It is often complimentary to an implicit solver such as ABAQUS/Standard. From a user standpoint, the distinguishing characteristics of the explicit and implicit methods are:텲 xplicit methods require a small time increment size that depends solely on the highest natural frequencies of the model and is independent of the type and duration of loading. Simulations generally take on the order of 10,000 to 1,000,000 increments, but the computational cost per increment is relatively small.텶 mplicit methods do not place an inherent limitation on the time increment size; increment size is generally determined from accuracy and convergence considerations. Implicit simulations typically take orders of magnitude fewer increments than explicit simulations. However, since a global set of equations must be solved in each increment, the cost per increment of an implicit method is far greater than that of an explicit method.Knowing these characteristics of the two procedures can help you decide which methodology is appropriate for your problems.3.1  Types of problems suited for ABAQUS/ExplicitBefore discussing how the explicit dynamics procedure works, it is helpful to understand what classes of problems are well-suited to ABAQUS/Explicit. Throughout this manual we have incorporated pertinent examples of the following classes of problems commonly performed in ABAQUS/Explicit:High-speed dynamic eventsThe explicit dynamics method was originally developed to analyze high-speed dynamic events that can be extremely costly to analyze using implicit programs, such as ABAQUS/Standard. As an example of such a simulation, the effect of a short-duration blast load on a steel plate is analyzed in Chapter 5, "Materials." Since the load is applied rapidly and is very severe, the response of the structure changes rapidly. Accurate tracking of stress waves through the plate is important for capturing the dynamic response. Since stress waves are associated with the highest frequencies of the system, obtaining an accurate solution requires many small time increments.Complex contact problemsContact conditions are formulated more easily using an explicit dynamics method than using an implicit method. The result is that ABAQUS/Explicit can readily analyze problems involving complex contact interaction between many independent bodies. ABAQUS/Explicit is particularly well-suited for analyzing the transient dynamic response of structures that are subject to impact loads and subsequently undergo complex contact interaction within the structure. An example of such a problem is the circuit board drop test presented in Chapter 6, "Contact." In the example a circuit board sitting in foam packaging is dropped on the floor from a height of 1 m. The problem involves impact between the packaging and the floor, as well as rapidly changing contact conditions between the circuit board and the packaging.Complex postbuckling problemsUnstable postbuckling problems are solved readily in ABAQUS/Explicit. In such problems the stiffness of the structure changes drastically as the loads are applied. Postbuckling response often includes the effects of contact interactions. An illustration of both situations is the tube crushing example in Chapter 6, "Contact." As the tube is crushed, it buckles severely and folds over onto itself, causing self-contact on both its inside and outside surfaces.Highly nonlinear quasi-static problemsFor a variety of reasons ABAQUS/Explicit is often very efficient in solving certain classes of problems that are essentially static. Quasi-static process simulation problems involving complex contact such as forging, rolling, and sheet-forming generally fall within these classes. Sheet forming problems usually include very large membrane deformations, wrinkling, and complex frictional contact conditions. Bulk forming problems are characterized by large distortions, flash formation, and contact interaction with the dies. An example of a quasi-static sheet forming simulation is presented in Chapter 7, "Quasi-Static Analysis."Materials with degradation and failureMaterial degradation and failure often lead to severe convergence difficulties in implicit analysis programs, but ABAQUS/Explicit models such materials well. An example of material degradation is the concrete cracking model, in which tensile cracking causes the material stiffness to become negative. An example of material failure is the ductile failure model for metals, in which material stiffness can degrade until it reduces to zero, at which time the elements are removed from the model entirely.Each of these types of analyses can include temperature and heat transfer effects.3.2  Finite element method for explicit dynamicsThis section contains a conceptual and an algorithmic description of the ABAQUS/Explicit solver as well as a discussion on the advantages of the method.3.2.1  Stress wave propagation illustratedThis section attempts to provide some conceptual understanding of how forces propagate through a model when using the explicit dynamics method. In this illustrative example we consider the propagation of a stress wave along a rod modeled with three elements, as shown in Figure 3-1  . We study the state of the rod as we increment through time.Figure 3-1  Initial configuration of a rod with a concentrated load, , at the free end.In the first time increment node 1 has an acceleration, , as a result of the concentrated force, , applied to it. The acceleration causes node 1 to have a velocity, , which, in turn, causes a strain rate, , in element 1. The increment of strain, , in element 1 is obtained by integrating the strain rate through the time of increment 1. The total strain, , is the sum of the initial strain, , and the increment in strain. In this case the initial strain is zero. Once the element strain has been calculated, the element stress, , is obtained by applying the material constitutive model. For a linear elastic material the stress is simply the elastic modulus times the total strain. This process is shown in Figure 3-2move in the first increment since no force is applied to them.Figure 3-2  Configuration at the end of increment 1 of a rod with a concentrated load, , at the free end.In the second increment the stresses in element 1 apply internal, element forces to the nodes associated with element 1, as shown in Figure 3-3used to calculate dynamic equilibrium at nodes 1 and 2. Figure 3-3  Configuration of the rod at the beginning of increment 2.The process continues so that at the start of the third increment there are stresses in both elements 1 and 2, and there are forces at nodes 1, 2, and 3, as shown in Figure 3-4process continues until the analysis reaches the desired total time.Figure 3-4  Configuration of the rod at the beginning of increment 3.3.2.2  Time integrationABAQUS/Explicit uses a central difference rule to integrate the equations of motion explicitly through time, using the kinematic conditions at one increment to calculate the kinematic conditions at the next increment. At the beginning of the increment the program solves for dynamic equilibrium, which states that the nodal mass matrix, , times the nodal accelerations, , equals the total nodal forces (the difference between the external applied forces, , and internal element forces, ):The accelerations at the beginning of the current increment (time ) are calculated asSince the explicit procedure always uses a diagonal, or lumped, mass matrix, solving for the accelerations is trivial; there are no simultaneous equations to solve. The acceleration of

Page 15: Getting Started With ABAQUS

any node is determined completely by its mass and the net force acting on it, making the nodal calculations very inexpensive.The accelerations are integrated through time using the central difference rule, which calculates the change in velocity assuming that the acceleration is constant. This change in velocity is added to the velocity from the middle of the previous increment to determine the velocities at the middle of the current increment:The velocities are integrated through time and added to the displacements at the beginning of the increment to determine the displacements at the end of the increment:Thus, satisfying dynamic equilibrium at the beginning of the increment provides the accelerations. Knowing the accelerations, the velocities and displacements are advanced ``explicitly'' through time. The term ``explicit'' refers to the fact that the state at the end of the increment is based solely on the displacements, velocities, and accelerations at the beginning of the increment. This method integrates constant accelerations exactly. For the method to produce accurate results, the time increments must be quite small so that the accelerations are nearly constant during an increment. Since the time increments must be small, analyses typically require many thousands of increments. Fortunately, each increment is inexpensive because there are no simultaneous equations to solve. Most of the computational expense lies in the element calculations to determine the internal forces of the elements acting on the nodes. The element calculations include determining element strains and applying material constitutive relationships (the element stiffness) to determine element stresses and, consequently, internal forces.Here is a summary of the explicit dynamics algorithm:1.Nodal calculations.a.Dynamic equilibrium. b.Integrate explicitly through time.2.Element calculations.a.Compute element strain increments, , from the strain rate, .b.Compute stresses, , from constitutive equations. c.Assemble nodal internal forces, .3.Set  to  and return to Step 1.3.2.3  Advantages of the explicit time integration methodThe explicit method is especially well-suited to solving high-speed dynamic events that require many small increments to obtain a high-resolution solution. If the duration of the event is short, the solution can be obtained efficiently.Contact conditions and other extremely discontinuous events are readily formulated in the explicit method and can be enforced on a node-by-node basis without iteration. The nodal accelerations can be adjusted to balance the external and internal forces during contact.The most striking feature of the explicit method is the lack of a global tangent stiffness matrix, which is required with implicit methods. Since the state of the model is advanced explicitly, iterations and tolerances are not required.3.3  Automatic time incrementation and stabilityThe stability limit dictates the maximum time increment used by the ABAQUS/Explicit solver. It is a critical factor in the performance of ABAQUS/Explicit. The following sections describe the stability limit and discuss how ABAQUS/Explicit determines this value. Issues surrounding the model design parameters that affect the stability limit are also addressed. These model parameters include the model mass, material, and mesh.3.3.1  Conditional stability of the explicit methodWith the explicit method the state of the model is advanced through an increment of time, , based on the state of the model at the start of the increment at time . The amount of time that the state can be advanced and still remain an accurate representation of the problem is typically quite short. If the time increment is larger than this maximum amount of time, the increment is said to have exceeded the stability limit. A possible effect of exceeding the stability limit is a numerical instability, which may lead to an unbounded solution. It generally is not possible to determine the stability limit exactly, so conservative estimates are used instead. The stability limit has a great effect on reliability and accuracy, so it must be determined consistently and conservatively. For computational efficiency ABAQUS/Explicit chooses the time increments to be as close as possible to the stability limit without exceeding it.3.3.2  Definition of the stability limitThe stability limit is defined in terms of the highest frequency in the system (). Without damping the stability limit is defined by the expressionand with damping it is defined by the expression where  is the fraction of critical damping in the mode with the highest frequency. (Critical damping defines the limit between oscillatory and non-oscillatory motion in the context of free-damped vibration. ABAQUS/Explicit always introduces a small amount of damping in the form of bulk viscosity to control high-frequency oscillations.) Perhaps contrary to engineering intuition, damping always reduces the stability limit.The actual highest frequency in the system is based on a complex set of interacting factors, and it is not computationally feasible to calculate its exact value. Alternately, we use a simple estimate that is efficient and conservative. Instead of looking at the global model, we estimate the highest frequency of each individual element in the model, which is always associated with the dilatational mode. It can be shown that the highest element frequency determined on an element-by-element basis is always greater than or equal to the highest frequency in the assembled finite element model.Based on the element-by-element estimate, the stability limit can be redefined using the element length, , and the wave speed of the material, :For most element types--a distorted quadrilateral element, for example--the above equation is only an estimate of the actual element-by-element stability limit because it is not clear how the element length should be determined. As an approximation the shortest element distance can be used, but the resulting estimate is not always conservative. The shorter the element length, the smaller the stability limit. The wave speed is a property of the material. For a linear elastic material with a Poisson's ratio of zerowhere  is Young's modulus and  is the mass density. The stiffer the material, the higher the wave speed, resulting in a smaller stability limit. The higher the density, the lower the wave speed, resulting in a larger stability limit.Our simplified stability limit definition provides some intuitive understanding. The stability limit is the transit time of a dilatational wave across the distance defined by the characteristic element length. If we know the size of the smallest element dimension and the wave speed of the material, we can estimate the stability limit. For example, if the smallest element dimension is 5 mm and the dilatational wave speed is 5000 m/s, the stable time increment is on the order of 1 ?10-6 s.3.3.3  Automatic time incrementation in ABAQUS/ExplicitABAQUS/Explicit uses equations such as those discussed in the previous section to adjust the time increment size throughout the analysis so that the stability limit, based on the current stage of the model, is never exceeded. Time incrementation is automatic and requires no user intervention, not even a suggested initial time increment. The stability limit is a mathematical concept resulting from the numerical model. Since the finite element program has all of the relevant details, it can determine an efficient and conservative stability

Page 16: Getting Started With ABAQUS

limit. However, ABAQUS/Explicit does allow the user to override the automatic time incrementation, if desired. ``Summary,'' Section 3.9, briefly discusses manual time incrementation controls.3.3.4  Mass scaling to control time incrementationSince the mass density influences the stability limit, under some circumstances scaling the mass density can potentially increase the efficiency of an analysis. For example, because of the complex discretization of many models, there are often regions containing very small or poorly shaped elements that control the stability limit. These controlling elements are often few in number and may exist in localized areas. By increasing the mass of only these controlling elements, the stability limit can be increased significantly, while the effect on the overall dynamic behavior of the model may be negligible.The automatic mass scaling features in ABAQUS/Explicit can keep offending elements from hindering the stability limit. There are two fundamental approaches used in mass scaling: defining a scaling factor directly or defining a desired element-by-element stable time increment for the elements whose mass is to be scaled. These two approaches, described in detail in the ABAQUS/Explicit User's Manual, permit additional user control over the stability limit. However, use caution when employing mass scaling since significantly changing the mass of the model may change the physics of the problem.3.3.5  Effect of material on stability limitThe material model affects the stability limit through its effect on the dilatational wave speed. In a linear material the wave speed is constant; therefore, the only changes in the stability limit during the analysis result from changes in the smallest element dimension during the analysis. In a nonlinear material, such as a metal with plasticity, the wave speed changes as the material yields and the stiffness of the material changes. ABAQUS/Explicit monitors the effective wave speeds in the model throughout the analysis, and the current material state in each element is used for stability estimates. After yielding, the stiffness decreases, reducing the wave speed and, consequently, increasing the stability limit.3.3.6  Effect of mesh on stability limitSince the stability limit is roughly proportional to the shortest element dimension, it is advantageous to keep the element size as large as possible. Unfortunately, for accurate analyses a fine mesh is often necessary. To obtain the highest possible stability limit while using the required level of mesh refinement, the best approach is to have a mesh that is as uniform as possible. Since the stability limit is based on the smallest element dimension in the model, even a single small or poorly shaped element can reduce the stability limit drastically. For diagnostic purposes ABAQUS/Explicit provides a list in the status (.sta) file of the 10 elements in the mesh with the lowest stability limit. If the model contains some elements whose stability limits are much lower than those of the rest of the mesh, remeshing the model more uniformly may be worthwhile.3.3.7  Numerical instabilityABAQUS/Explicit remains stable for most elements under most circumstances. It is possible, however, to define spring and dashpot elements such that they become unstable during the course of an analysis. Therefore, it is useful to be able to recognize a numerical instability if it occurs in your analysis. If it does occur, the result typically will be unbounded, nonphysical, and often oscillatory solutions. The examples at the end of this chapter use simple spring and dashpot problems to illustrate instabilities.3.4  Example: stress wave propagation in a barThis example demonstrates some of the fundamental ideas in explicit dynamics described earlier in the discussion of how stress propagates along the length of a bar. It also illustrates stability limits and the effect of mesh refinement and materials on the solution time.The bar has the dimensions shown in Figure 3-5  . Figure 3-5  Problem description for wave propagation in a bar.To make the problem a one-dimensional strain problem, all four lateral faces are on rollers; thus, the three-dimensional model simulates a one-dimensional problem. The material is steel with the properties shown in Figure 3-5  . The free end of the bar is subjected to a blast load with a magnitude of 1.0 ?105 Pa, as shown in Figure 3-6the blast load is 3.88 ?10-5 s.Figure 3-6  Blast amplitude versus time.Using the material properties (neglecting Poisson's ratio), we can calculate the wave speed of the material using the equations introduced in the previous section.At this speed the wave passes to the fixed end of the bar in 1.94 ?10-4 s. Since we would like to see the stress propagate along the length of the bar through time, we need an adequately refined mesh to capture the stress wave accurately. It seems adequate to have the blast load take place over the span of 10 elements. Since the blast duration is 3.88 ?10-5 s, this means that we would like the blast duration times the wave speed to equal the length of 10 elements:The length of 10 elements is 0.2 m. Since the length of the bar is 1.0 m, this means that we would like to have 50 elements along the length. To keep the mesh uniform, we will also have 10 elements in each of the transverse directions, making the mesh 50 ?10 ?10. This mesh is shown in Figure 3-7  .Figure 3-7  50 ?10 ?10 mesh.Create this mesh in your preprocessor. Use the coordinate system shown in Figure 3-7  .3.4.1  Node and element setsYou will need to have node and element sets defined to apply the loads and boundary conditions and to visualize output. Define the node sets on their respective faces, as shown in Figure 3-8  .Figure 3-8  Node sets.Define the element sets shown in Figure 3-9  . Figure 3-9  Element sets for modeling.In addition, define an element set containing three elements in the center of the bar. Select these elements such that their faces nearest to the free end are at distances 0.25 m, 0.5 m, and 0.75 m from the free end, as shown in Figure 3-10  . These elements will be used for postprocessing.Figure 3-10  Element sets for postprocessing.3.4.2  Reviewing the input file--the model dataAt this point we assume that you have created the basic mesh using your preprocessor. In this section you will review your input file and include additional information.Model descriptionThe following would be a suitable description in the *HEADING option for this simulation:*HEADINGStress wave propagation in a bar -- 50x10x10 elementsSI units (kg, m, s, N)Element connectivityCheck to make sure that you are using the correct element type (C3D8R). It is possible that the preprocessor specified the element type incorrectly. The *ELEMENT option block in

Page 17: Getting Started With ABAQUS

your model should begin with the following:*ELEMENT, TYPE=C3D8R, ELSET=BARThe name given for the ELSET parameter in your model may not be BAR. If necessary, change the name to BAR.Section propertiesThe section properties are the same for all elements. Use element set BAR to assign the material properties to the elements.*SOLID SECTION, ELSET=BAR, MATERIAL=STEELMaterial propertiesThe bar is made of steel, which we assume to be linear elastic with a Young's modulus of 207 ?109 Pa, a Poisson's ratio of 0.3, and a density of 7800 kg/m3. Use the following material option block in your model:*MATERIAL, NAME=STEEL*ELASTIC207.0E9, 0.3*DENSITY7800.0,Fixed boundary conditionsFix all the translations at the built-in, right-hand end of the bar. Constrain the front, back, top, and bottom faces of the bar so that these faces are on rollers and the strain is uniaxial. Using the node sets that you defined previously, apply the following boundary conditions to your model:*BOUNDARYNFIX, 1, 3NFRONT, 3, 3NBACK, 3, 3NTOP, 2, 2NBOT, 2, 2Amplitude definitionThe blast load is applied at its maximum value instantaneously and is held constant for 3.88 ?10-5 s. Then the load is suddenly removed and held constant at zero. The *AMPLITUDE option is used to define the time variation of loads and boundary conditions. On the data lines following the *AMPLITUDE option, pairs of data are given in the form:<time>, <amplitude>, <time>, <amplitude>, etc.Up to four data pairs can be entered on each data line. ABAQUS considers the amplitude to be held constant following the last amplitude value given. Define the amplitude for the blast load as follows:*AMPLITUDE, NAME=BLAST0., 1., 3.88E-5, 1., 3.89E-5, 0, 3.90E-5, 0.3.4.3  Reviewing the input file--the history dataWe will now review the history data associated with this problem, including the step definition, loading, bulk viscosity, and output requests.Step definitionThe step definition indicates that this is an explicit dynamics analysis with a duration of 2.0 ?10-4 s. You can also include a descriptive title for the step.*STEPBlast loading*DYNAMIC, EXPLICIT, 2.0E-4LoadingApply the pressure load with a value of 1.0 ?105 Pa to the free face of the bar, which you previously defined to be in an element set called ELOAD. The pressure load at any given time is the magnitude specified under the *DLOAD option times the value interpolated from the amplitude curve. To apply the load correctly, you need to determine the face identifier label of the free element faces. For the model defined in ``Stress wave propagation in a bar,'' Section A.2, the free face is face number 3, which corresponds to the pressure identifier P3. The face identifier depends on the order in which the nodes are defined on the *ELEMENT option, as shown in Figure 3-11when applying the pressure load.*DLOAD, AMPLITUDE=BLASTELOAD, <P1, P2, P3, P4, P5, or P6>, 1.0E5If you define the pressure load in your preprocessor, the correct face identifier should be determined automatically.Figure 3-11  Face label identifier for a C3D8R element.Bulk viscosityTo keep the stress wave as sharp as possible, set the quadratic bulk viscosity (discussed in ``Bulk viscosity,'' Section 3.6.1) to zero.*BULK VISCOSITY, 0.0Output requestsBy default, many preprocessors create an ABAQUS input file that has a large number of output request options. If, when you edit your input file, you find that these default output options were created, delete them all because they will generally generate too much output.You want to have an output database file created during the analysis so that you can use ABAQUS/Viewer to postprocess the results. Four output database frames (intervals at which data are written to the output database) are adequate to show the stress wave propagating through the mesh. Set the parameter VARIABLE=PRESELECT on the *OUTPUT, FIELD option to write the default field data for a *DYNAMIC, EXPLICIT procedure to the output database file. In addition, request stress (S) history output in element set EOUT every 1.0 ?10-6 s.*OUTPUT, FIELD, VARIABLE=PRESELECT, NUMBER INTERVAL=4

Page 18: Getting Started With ABAQUS

*OUTPUT, HISTORY, TIME INTERVAL=1.0E-6*ELEMENT OUTPUT, ELSET=EOUT S,*END STEP3.4.4  Running the analysisAfter storing your input in a file called wave_50x10x10.inp, run the analysis using the following command:abaqus job=wave_50x10x10If your analysis does not complete, check the data file, wave_50x10x10.dat, and status file, wave_50x10x10.sta, for error messages. Modify your input file to remove the errors. If you still have trouble running your analysis, compare your input file to the one given in ``Stress wave propagation in a bar,'' Section A.2.Status fileThe status file, wave_50x10x10.sta, contains information about moments of inertia, followed by information concerning the initial stability limit. The 10 elements with the lowest stable time limits are listed in rank order.    Most critical elements :     Element number   Rank    Time increment   Increment ratio    ----------------------------------------------------------          101          1       1.931897E-06      1.000000E+00          105          2       1.931897E-06      1.000000E+00          107          3       1.931897E-06      1.000000E+00          111          4       1.931897E-06      1.000000E+00          115          5       1.931897E-06      1.000000E+00          119          6       1.931897E-06      1.000000E+00          401          7       1.931897E-06      1.000000E+00          405          8       1.931897E-06      1.000000E+00          407          9       1.931897E-06      1.000000E+00The status file continues with information about the progress of the solution.  STEP 1  ORIGIN 0.00000E+00     Total memory used for step 1 is approximately 2.8 megawords   Global time estimation algorithm will be used.   Scaling factor :  1.0000               STEP      TOTAL       CPU     STABLE      CRITICAL  KINETIC  INCREMENT  TIME      TIME        TIME   INCREMENT    ELEMENT   ENERGY         0  0.000E+00 0.000E+00   00:00:02 1.932E-06     101   0.000E+00 Results number  0 at increment zero. ODB Field Frame Number    0 of    4 requested intervals at increment zero.         6  1.159E-05 1.159E-05   00:00:05 1.932E-06     401   4.487E-05        12  2.318E-05 2.318E-05   00:00:07 1.932E-06     101   9.566E-05        16  3.332E-05 3.332E-05   00:00:09 3.104E-06     101   1.389E-04        20  4.572E-05 4.572E-05   00:00:10 3.088E-06     101   1.712E-04        22  5.189E-05 5.189E-05   00:00:11 3.082E-06     101   1.695E-04 ODB Field Frame Number    1 of    4 requested intervals at  5.188920E-05        26  6.420E-05 6.420E-05   00:00:13 3.071E-06     101   1.699E-04...3.4.5  PostprocessingStart ABAQUS/Viewer by typingabaqus viewer odb=wave_50x10x10at the operating system prompt.Plotting the stress along a pathWe would like to look at how the stress distribution along the length of the bar changes with time. To do so, we will look at the stress distribution at three different times throughout the course of the analysis.Create a curve of the stress in the 1-direction (S11) approximately along the center of the bar for each of the first three frames of the output database file. You first need to define a straight path along the center of the bar using a node list.To create a node list path along the center of the bar:1.From the main menu bar, select Tools->Path->Create.The Create Path dialog box appears.2.Name the path Center. Accept the default selection of Node list as the path type, and click Continue.The Edit Node List Path dialog box appears.3.In the Node Labels table, enter the nodes along the center of the bar and click OK. For example, if you created your mesh using the input file shown in ``Stress wave propagation

Page 19: Getting Started With ABAQUS

in a bar,'' Section A.2, the table entry is 100011:105011:100. (This input specifies a range of nodes from 100011 to 105011 in increments of 100.)Tip:  If you did not use the input file shown in ``Stress wave propagation in a bar,'' Section A.2, and need to identify the nodes along the center of the bar, plot the undeformed model shape and turn on the node labels using the undeformed plot options. From the main menu bar, select Plot->Undeformed Shape; then select Options->Undeformed Shape to open the Undeformed Shape Plot Options dialog box. You can use the view manipulation tools in the toolbar  to alter the default isometric view of the bar.To save X-Y plots of stress along the path at three different times:1.From the main menu bar, select Tools->XY Data->Manager.2.In the XY Data Manager dialog box that appears, click Create.The Create XY Data dialog box appears.3.Choose Path as the X-Y data source, and click Continue.The Create XY Data from Path  dialog box appears with the path that you created visible in the list of available paths. If the undeformed model shape is currently displayed, the path you select is highlighted in the plot.4.Accept True distance as the selection in the X Values portion of the dialog box. 5.Click Field Output in the Y Values portion of the dialog box to open the Field Output dialog box. 6.Select the S11 stress component, and click OK.The field output variable in the Create XY Data from Path dialog box changes to indicate that stress data in the 1-direction (S11) will be created.Note:  ABAQUS/Viewer warns you that the field output variable will not affect the current image. Leave the plot mode As is, and click OK to continue.7.Click Step/Frame in the Y Values portion of the Create XY Data from Path dialog box.8.In the Step/Frame dialog box that appears, choose the second of the five recorded frames. (The first frame listed, frame 0, is the base state of the model at the beginning of the step.) Click OK.The Y Values portion of the Create XY Data from Path dialog box changes to indicate that data from Step 1, frame 1 will be created.9.To save the X-Y data, click Save As.The Save XYData As dialog box appears.10.Name the X-Y data S11_T1, and click OK.S11_T1 appears in the XY Data Manager.11.Repeat Steps 7 through 10 to create X-Y data for frames 2 and 3. Name the data sets S11_T2 and S11_T3, respectively.12.To close the Create XY Data from Path dialog box, click Cancel. To plot the stress curves:1.In the XY Data Manager dialog box, drag the cursor to highlight all three X-Y data sets. 2.Click Plot.ABAQUS/Viewer plots the stress in the 1-direction along the center of the bar for frames 1, 2, and 3, corresponding to simulation times of 5.1208 ?10-5 s, 1.0016 ?10-4 s, and 1.5175 ?10-4 s, respectively. Customize the plot by changing tick mark intervals, axis titles, and the curve line styles.To customize the X-Y plot:1.From the main menu bar, select Options->XY Plot.The XY Plot Options dialog box appears.2.Click the Tick Marks tab.The Tick Marks options become available.3.Specify that the Y-axis major tick marks occur at 20 ?103 s increments.4.For both the X-axis and Y-axis minor tick mark options, specify zero minor tick marks between each major tick mark interval.You can also customize the axis titles.5. Click the Titles tab to make the Titles options available.6.In the X-axis area, select a User-specified title source. In the Title text field, enter Distance along bar.7.In the Y-axis area, specify Stress - S11 as the Y-axis title. 8.Click OK to apply the customized X-Y plot parameters and to close the XY Plot Options dialog box.To customize the appearance of the curves in the X-Y plot:1.From the main menu bar, select Options->XY Curve.The XY Curve Options dialog box appears.2.In the XY Data field, select S11_T2.3.Choose the dotted line style for the S11_T2 curve.The S11_T2 curve becomes dotted.4.Repeat Steps 2 and 3 to make the S11_T3 curve dashed.5.Click Dismiss to close the XY Curve Options dialog box.The customized plot appears in Figure 3-12  .Figure 3-12  Stress (S11) along the bar at three different times.We can see that the length of the bar affected by the stress wave is approximately 0.2 m in each of the three curves. This distance should correspond to the distance that the blast wave travels during its time of application, which can be checked by a simple calculation. If the length of the wave front is 0.2 m and the wave speed is 5.15 ?103 m/s, the time it takes for the wave to travel 0.2 m is 3.88 ?10-5 s. As expected, this is the duration of the blast load that we applied. The stress wave is not exactly square as it passes along the bar. In particular, there is ``ringing'' or oscillation of the stress behind the sudden changes in stress. Linear bulk viscosity, discussed later in this chapter, damps the ringing so that it does not affect the results adversely.Creating a history plotAnother way to study the results is to view the time history of stress at three different points within the bar.

Page 20: Getting Started With ABAQUS

To plot the stress history of the elements in set EOUT:1.From the main menu bar, select Result->History Output.ABAQUS/Viewer displays the History Output dialog box. The Output Variables field contains a list of all the variables in the history portion of the output database; these are the only variables you can plot. To see the complete description of the variable choices, increase the width of the History Output dialog box by dragging the right or left edge.2.Drag the cursor to highlight stress in the 1-direction (S11) for all three elements in element set EOUT.3.At the bottom of the History Output dialog box, click Plot.ABAQUS/Viewer displays an X-Y plot of the longitudinal stress in each element versus time.4.Click Dismiss to close the dialog box. As before, you can customize the appearance of the plot.To customize the X-Y plot:1.From the main menu bar, select Options->XY Plot.The XY Plot Options dialog box appears. 2.Click the Titles tab. The Titles options become available.3.In the X-axis area, specify Total time as the X-axis title. 4. Click OK to apply the customized X-Y plot options and to close the dialog box. To customize the appearance of the curves in the X-Y plot:1.From the main menu bar, select Options->XY Curve. The XY Curve Options dialog box appears.2. In the XY Data field, select the temporary X-Y data label that corresponds to the element closest to the free end of the bar. (Of the elements in this set, this one is affected first by the stress wave.)3.Select a User-specified legend source. 4.In the Legend text field, enter S11-0.25. 5.In the XY Data field, select the temporary X-Y data label that corresponds to the element in the middle of the bar. (This is the element affected next by the stress wave.)6.Specify S11-0.5 as the curve legend text, and change the curve style to dotted.7.In the XY Data field, select the temporary X-Y data label that corresponds to the element closest to the fixed end of the bar. (This is the element affected last by the stress wave.)8.Specify S11-0.75 as the curve legend text, and change the curve style to dashed.9.Click Dismiss to close the dialog box. The customized plot appears in Figure 3-13  .Figure 3-13  Time history of stress (S11) at three points along the length of the bar (0.25 m, 0.5 m, and 0.75 m). In the history plot we can see that stress at a given point increases as the stress wave travels through the point. Once the stress wave has passed completely through the point, the stress at the point oscillates about zero.3.4.6  How the mesh affects the stable time increment and CPU timeIn ``Automatic time incrementation and stability,'' Section 3.3, we discussed how mesh refinement affects the stability limit and the CPU time. Here we will illustrate the effect with the wave propagation problem. We began with a reasonably refined mesh of square elements with 50 elements along the length and 10 elements in each of the two transverse directions. For illustrative purposes, we will now use a coarse mesh of 25 ?5 ?5 elements and observe how refining the mesh in the various directions changes the CPU time. The four meshes are shown in Figure 3-14  . Figure 3-14  Meshes from least to most refined.Table 3-1   shows how the CPU time (normalized with respect to the coarse mesh model result) changes with mesh refinement for this problem. The first half of the table provides the expected results, based on the simplified stability equations presented in this guide; the second half of the table provides the results obtained by running the analyses in ABAQUS/Explicit on a desktop workstation.Table 3-1  Mesh refinement and solution time.MeshSimplified TheoryActual (s)Number of ElementsCPU Time (s)Max  (s)Number of ElementsNormalized CPU Time25 ?5 ?5ABC6.06e-6625150 ?5 ?5A/22B

Page 21: Getting Started With ABAQUS

4C3.14e-61250450 ?10 ?5A/24B8C3.12e-625008.3350 ?10 ?10A/28B16C3.11e-6500016.67For the theoretical results we choose the coarsest mesh, 25 ?5 ?5, as the base state, and we define the stable time increment, the number of elements, and the CPU time as variables A, B, and C, respectively. As the mesh is refined, two things happen: the smallest element dimension decreases, and the number of elements in the mesh increases. Each of these effects increases the CPU time. In the first level of refinement, the 50 ?5 ?5 mesh, the smallest element dimension is cut in half and the number of elements is doubled, increasing the CPU time by a factor of four over the previous mesh. However, further doubling the mesh to 50 ?10 ?5 does not change the smallest element dimension; it only doubles the number of elements. Therefore, the CPU time increases by only a factor of two over the 50 ?5 ?5 mesh. Further refining the mesh so that the elements are uniform and square in the 50 ?10 ?10 mesh again doubles the number of elements and the CPU time.This simplified calculation predicts quite well the trends of how mesh refinement affects the stable time increment and CPU time. However, there are reasons why we did not compare the predicted and actual stable time increment values. First, recall that we made the approximation that the stable time increment isWe then assumed that the characteristic element length, , is the smallest element dimension, whereas ABAQUS/Explicit actually determines the characteristic element length based on the overall size and shape of the element. Another complication is that ABAQUS/Explicit employs a global stability estimator, which allows a larger stable time increment to be used. These factors make it difficult to predict the stable time increment accurately before running the analysis. However, since the trends follow nicely from the simplified theory, it is straightforward to predict how the stable time increment will change with mesh refinement.3.4.7  How the material affects the stable time increment and CPU timeThe same wave propagation analysis performed on different materials would take different amounts of computer time, depending on the wave speed of the material. For example, if we were to change the material from steel to aluminum, the wave speed would change from 5.15 ?103 m/s to The change from aluminum to steel has minimal effect on the stable time increment, because the stiffness and the density differ by nearly the same amount. In the case of lead the difference is more substantial, as the wave speed decreases towhich is approximately one-fifth the wave speed of steel. The stable time increment for the lead bar would be five times the stable time increment of our steel bar.3.5  Comparison of explicit and implicit proceduresABAQUS/Explicit and ABAQUS/Standard are capable of solving a wide variety of problems. The characteristics of implicit and explicit procedures determine which method is appropriate for a given problem. For those problems that can be solved with either method, the question of which solver to use has a direct bearing on the efficiency with which the problem is solved. Understanding the characteristics of implicit and explicit procedures will help you answer this question.3.5.1  General comparisonFor both the explicit and the implicit time integration procedures, equilibrium is defined in terms of the external applied forces, , the internal element forces, , and the nodal accelerations:where  is the mass matrix. Both procedures solve for nodal accelerations and use the same element calculations to determine the internal element forces. The biggest difference between the two procedures lies in the manner in which the nodal accelerations are computed. In the implicit procedure a set of linear equations is solved by a direct solution method. The computational cost of solving this set of equations is high when compared to the relatively low cost of the nodal calculations with the explicit method.3.5.2  Review of implicit procedure in ABAQUS/StandardABAQUS/Standard uses automatic incrementation based on the full Newton iterative solution method. Newton's method seeks to satisfy dynamic equilibrium at the end of the increment at time  and compute displacements at the same time. The time increment, , is relatively large compared to that used in the explicit method because the implicit scheme is unconditionally stable. For a nonlinear problem each increment typically requires several iterations to obtain a solution within the prescribed tolerances. Each Newton iteration solves for a correction, , to the incremental displacements, . Each iteration requires the solution of a set of simultaneous equations,which is an expensive procedure for large models. The effective stiffness matrix, , is a linear combination of the tangent stiffness matrix and the mass matrix for the iteration. The iterations continue until several quantities--force residual, displacement correction, etc.--are within the prescribed tolerances. For a smooth nonlinear response Newton's method has a quadratic rate of convergence, as illustrated below:IterationRelative Error11210-23

Page 22: Getting Started With ABAQUS

10-4......However, if the model contains highly discontinuous processes, such as contact and frictional sliding, quadratic convergence may be lost and a large number of iterations may be required. Cutbacks in the time increment size may become necessary to satisfy equilibrium. In extreme cases the resulting time increment size in the implicit analysis may be on the same order as a typical stable time increment for an explicit analysis, while still carrying the high solution cost of implicit iteration. In some cases convergence may not be possible using the implicit method.Each iteration in an implicit analysis requires solving a large system of linear equations, a procedure that requires considerable computation, disk space, and memory. For large problems these equation solver requirements are dominant over the requirements of the element and material calculations, which are similar for an analysis in ABAQUS/Explicit. As the problem size increases, the equation solver requirements grow rapidly so that, in practice, the maximum size of an implicit analysis that can be solved on a given machine often is dictated by the amount of disk space and memory available on the machine rather than by the required computation time.3.5.3  Advantages of ABAQUS/ExplicitFor many analyses it is clear whether ABAQUS/Standard or ABAQUS/Explicit should be used. For example, earlier in this chapter we saw that ABAQUS/Explicit is the clear choice for a wave propagation analysis; on the other hand, ABAQUS/Standard is more efficient for solving smooth nonlinear problems. There are, however, certain static or nearly static problems that can be simulated well with either program. Typically, these are problems that usually would be solved with ABAQUS/Standard but may have difficulty converging because of contact or material complexities, resulting in a large number of iterations. Such analyses are expensive in ABAQUS/Standard because each iteration is expensive and requires a large set of linear equations to be solved.Whereas ABAQUS/Standard must iterate to determine the solution to a nonlinear problem, ABAQUS/Explicit determines the solution without iterating by explicitly advancing the kinematic state from the previous increment. Even though a static analysis requires a large number of time increments using the explicit method, the analysis can be more efficient in ABAQUS/Explicit if the same analysis in ABAQUS/Standard would require many expensive iterations.Another advantage of ABAQUS/Explicit is that it requires much less disk space and memory than ABAQUS/Standard for the same simulation. For some problems in which the computational cost of the two programs may be comparable, the substantial disk space and memory savings of ABAQUS/Explicit make it attractive.3.5.4  Cost of mesh refinement in explicit and implicit analysesUsing the explicit method, the computational cost is proportional to the number of elements and roughly inversely proportional to the smallest element dimension. Mesh refinement, therefore, increases the computational cost by increasing the number of elements and reducing the smallest element dimension. As an example, consider a three-dimensional model with uniform, square elements. If the mesh is refined by a factor of two in all three directions, the computational cost increases by a factor of 2 ?2 ?2 as a result of the increase in number of elements and by a factor of 2 as a result of the decrease in the smallest element dimension. The total computational cost of the analysis increases by a factor of 24, or 16, by refining the mesh. Disk space and memory requirements are proportional to the number of elements with no dependence on element dimensions; thus, these requirements increase by a factor of 8.Whereas predicting the cost increase with mesh refinement for the explicit method is rather straightforward, cost is more difficult to predict when using the implicit method. The difficulty arises from the problem-dependent relationship between element connectivity and solution cost, a relationship that does not exist in the explicit method. Using the implicit method, experience shows that for many problems the computational cost is roughly proportional to the square of the number of degrees of freedom. Consider the same example of a three-dimensional model with uniform, square elements. Refining the mesh by a factor of two in all three directions increases the number of degrees of freedom by approximately 23, causing the computational cost to increase by a factor of roughly (23)2, or 64. The disk space and memory requirements increase in the same manner, although the actual increase is difficult to predict.The explicit method shows great cost savings over the implicit method as the model size increases, as long as the mesh is relatively uniform. Figure 3-15of cost versus model size using the explicit and implicit methods. For this problem the number of degrees of freedom scales with the number of elements.Figure 3-15  Cost versus model size in using the explicit and implicit methods.3.6  Damping of dynamic oscillationsThere are two reasons for adding damping to a model: to limit numerical oscillations or to add physical damping to the system. ABAQUS/Explicit provides several methods of introducing damping into the analysis.3.6.1  Bulk viscosityBulk viscosity introduces damping associated with volumetric straining. Its purpose is to improve the modeling of high-speed dynamic events. ABAQUS/Explicit contains linear and quadratic forms of bulk viscosity. You can set bulk viscosity to nondefault values from step to step by using the *BULK VISCOSITY option, although it is rarely necessary to do so. The bulk viscosity pressure is not included in the material point stresses because it is intended as a numerical effect only. As such, it is not considered part of the material's constitutive response.Linear bulk viscosityBy default, linear bulk viscosity is always included to damp "ringing" in the highest element frequency. It generates a bulk viscosity pressure that is linear in the volumetric strain rate, according to the following equation:where  is a damping coefficient, whose default value is 0.06,  is the current material density,  is the current dilatational wave speed,volumetric strain rate.Quadratic bulk viscosityQuadratic bulk viscosity is included only in continuum elements (except for the plane stress element, CPS4R) and is applied only if the volumetric strain rate is compressive. The bulk viscosity pressure is quadratic in the strain rate, according to the following equation:where  is the damping coefficient, whose default value is 1.2.The quadratic bulk viscosity smears a shock front across several elements and is introduced to prevent elements from collapsing under extremely high velocity gradients. Consider a simple one-element problem in which the nodes on one side of the element are fixed and the nodes on the other side have an initial velocity in the direction of the fixed nodes, as

Page 23: Getting Started With ABAQUS

shown in Figure 3-16  . The stable time increment size is precisely the transit time of a dilatational wave across the element. Therefore, if the initial nodal velocity is equal to the dilatational wave speed of the material, the element collapses to zero volume in one time increment. The quadratic bulk viscosity pressure introduces a resisting pressure that prevents the element from collapsing. Figure 3-16  Element with fixed nodes and prescribed velocities.Fraction of critical damping due to bulk viscosityThe bulk viscosity pressures are based on only the dilatational modes of each element. The fraction of critical damping in the highest element mode is given by the following equation:where  is the fraction of critical damping. The linear term alone represents 6% of critical damping, whereas the quadratic term is usually much smaller.3.6.2  Viscous pressureViscous pressure loads are commonly used in structural problems and quasi-static problems to damp out the low-frequency dynamic effects, thus allowing static equilibrium to be reached in a minimal number of increments. These loads are applied as distributed loads (*DLOAD) defined by the following formula:where  is the pressure applied to the body;  is the viscosity, given on the data line as the magnitude of the load;  is the velocity of the point on the surface where the viscous pressure is being applied; and  is the unit outward normal to the surface at the same point. For typical structural problems it is not desirable to absorb all of the energy. Typically,set equal to a small percentage--perhaps 1 or 2 percent--of the quantity  as an effective way of minimizing ongoing dynamic effects.3.6.3  Material dampingThe material model itself may provide damping in the form of plastic dissipation or viscoelasticity. For many applications such damping may be adequate. Another option is to use Rayleigh damping defined using the *DAMPING option, which is part of the *MATERIAL option block. There are two damping factors associated with Rayleigh damping:proportional damping and  for stiffness proportional damping.Mass proportional dampingThe  factor defines a damping contribution proportional to the mass matrix for an element. The damping forces that are introduced are caused by the absolute velocities of nodes in the model. The resulting effect can be likened to the model moving through a viscous fluid so that any motion of any point in the model triggers damping forces. Reasonable mass proportional damping does not reduce the stability limit significantly.Stiffness proportional dampingThe  factor defines damping proportional to the elastic material stiffness. A ``damping stress,'' , proportional to the total strain rate is introduced, using the following formula:where  is the strain rate. For hyperelastic and hyperfoam materials  is defined as the initial elastic stiffness. For all other materialsdamping stress is added to the stress caused by the constitutive response at the integration point when the dynamic equilibrium equations are formed, but it is not included in the stress output. Damping can be introduced for any nonlinear analysis and provides standard Rayleigh damping for linear analyses. For a linear analysis stiffness proportional damping is exactly the same as defining a damping matrix equal to  times the stiffness matrix. Stiffness proportional damping must be used with caution because it may significantly reduce the stability limit.3.6.4  Discrete dashpotsYet another option is to define individual dashpot elements. Each dashpot element provides a damping force proportional to the relative velocity of its two nodes. The advantage of this approach is that it enables you to apply damping only at points where you decide it is necessary. Dashpots always should be used in parallel with other elements, such as springs or trusses, so that they do not cause a significant reduction in the stability limit.3.7  Energy balanceEnergy output is often an important part of an ABAQUS/Explicit analysis. Comparisons between various energy components can be used to help evalyielding an appropriate response. 3.7.1  Statement of energy balanceAn energy balance for the entire model can be written aswhere  is the internal energy,  is the viscous energy dissipated,  is the frictional energy dissipated,  is the kinetic energy, andsum of these energy components is , which should be constant. In the numerical model  is only approximately constant, generally with an error of less than 1%.Internal energyThe internal energy is the sum of the recoverable elastic strain energy, ; the energy dissipated through inelastic processes such as plasticity, ; the energy dissipated through viscoelasticity or creep, ; and the artificial strain energy, : The artificial strain energy includes energy stored in hourglass resistances and transverse shear in shell and beam elements. Large values of artificial strain energy indicate that mesh refinement or other changes to the mesh are necessary.Viscous energyThe viscous energy is the energy dissipated by damping mechanisms, including bulk viscosity damping and material damping. A fundamental variable in the global energy balance, viscous energy is not part of the energy dissipated through viscoelasticity or inelastic processes.External work of applied forcesThe external work is integrated forward continuously, defined entirely by nodal forces (moments) and displacements (rotations). Prescribed boundary conditions also contribute to the external work.3.7.2  Output of the energy balanceEach of the energy quantities can be requested as output and can be plotted as time histories summed over the entire model, particular element sets, individual elements, or as energy density within each element. The variable names associated with the energy quantities summed over the entire model or element sets are as listed in Table 3-2Table 3-2  Whole model energy output variables.Variable NameEnergy QuantityALLIE Internal energy,  :ALLIE = ALLSE + ALLPD + ALLCD + ALLAE.ALLKE Kinetic energy, .

Page 24: Getting Started With ABAQUS

ALLVDViscous dissipated energy, .ALLFD Frictional dissipated energy, .ALLCDEnergy dissipated by viscoelasticity, .ALLWK Work of the external forces, .ALLSE Stored strain energy, .ALLPD Inelastic dissipated energy, .ALLAE Artificial strain energy, .ETOTALEnergy balance: .In addition, ABAQUS/Explicit can produce element-level energy output and energy density output, as listed in Table 3-3Table 3-3  Whole element energy output variables.Variable NameWhole Element Energy QuantityELSE Elastic strain energy.ELPD Plastic dissipated energy.ELCDCreep dissipated energy.ELVD Viscous dissipated energy.ELASEArtificial energy = drill energy + hourglass energy.EKEDENKinetic energy density in the element.ESEDENElastic strain energy density in the element.EPDDENPlastic energy density dissipated in the element.EASEDENArtificial strain energy density in the element.ECDDENCreep strain energy density dissipated in the element.EVDDENViscous energy density dissipated in the element.3.8  Potential instabilities with springs and dashpotsSome element types fall outside the stability calculations performed by ABAQUS/Explicit. The following elements have the potential to destabilize an analysis:톁 pring elements텱 ashpot elementsThe following elements cannot destabilize the analysis but can only help to stabilize an analysis:텺 ass elements톀 otary inertia elements텵 ydrostatic fluid elements텲 lements that are part of a rigid bodyWe will use simple models to illustrate instabilities in ABAQUS/Explicit. While the program has been designed to provide efficient and stable solutions in almost all cases, there are some unusual situations involving springs and dashpots in which a solution may become unstable. It is useful to be able to recognize such instabilities when they occur.The following example uses very simple models to illustrate stability problems that could also occur in larger, more complex models. Once you understand how to determine whether these simple analyses have become unstable, you can then use the same methods to determine whether your own engineering analyses have become unstable. With larger models it is necessarily more difficult to determine ahead of time whether or not the analysis will become unstable because the locations and loadings on the springs and dashpots become a factor. For example, an analysis that might have otherwise become unstable could be subjected to a contact constraint that keeps the instability from occurring.Springs, as well as elements such as continuum elements, impose certain stability requirements on an analysis. Each element has its own maximum stable time increment based on the stiffness and mass associated with the element. Since a spring element has stiffness but no mass of its own, mass is associated with a spring element through its connection to other elements containing mass. If a spring element is connected to continuum elements, for example, it generally is not possible to determine what mass is associated with the spring element. Therefore, it is not possible for ABAQUS/Explicit to calculate the stable time increment for a spring element. If the stable time increment required by the spring is

Page 25: Getting Started With ABAQUS

smaller than the smallest stable time increment of the rest of the model, the spring defines the controlling stable time increment for the model, and the analysis may become unstable.The model shown in Figure 3-17   is made up of two separate, simple bodies: a single truss element and a spring element with a mass element at the free end. The left-hand side of both bodies is fixed, while the right-hand side is loaded. Since the truss element has both stiffness and mass, ABAQUS/Explicit determines a stable time increment for the truss element. Since the spring element has stiffness but no mass, ABAQUS/Explicit does not calculate a stable time increment for the spring element. Likewise, ABAQUS/Explicit does not calculate a stable time increment for the mass element, which has mass but no stiffness. The details of the input file corresponding to this model are not discussed here; the input file itself can be found in ``Potential instabilities with springs and dashpots,'' Section A.3.Figure 3-17  Model consisting of a truss, spring, and mass element.In this simple example, however, we can calculate the stability requirements of the spring-mass system analytically because the mass associated with the spring is simply the mass of the mass element. Since the spring stiffness and associated mass are constant throughout the analysis, the maximum stable time increment for the spring-mass system is also constant. The stable time increment for the truss, however, changes throughout the analysis, as the length and, thus, the stiffness of the truss changes. At the start of the analysis the stable time increment for the truss is smaller than that required for the spring-mass system. As the truss stretches, its stable time increment increases, and eventually the stable time increment for the spring-mass system becomes the controlling factor in the analysis. When the stable time increment for the analysis as determined by the truss becomes greater than that required by the spring-mass system, the analysis becomes unstable. The stable time increment versus time is illustrated in Figure 3-18Figure 3-18  Stable time increment versus time for the truss element and the spring-mass system.3.8.1  Determining the stable time incrementThe spring-mass system is loaded dynamically with a constant force of 1000 N, causing the mass to accelerate and the spring to stretch. Since the force is applied as a step function, the spring will oscillate according to the applied force and the mass, and the stiffness of the spring. With a spring stiffness of 1 ?105 N/m and a force of 1 ?103 N, the average displacement of the spring is 0.01 m, and the maximum displacement is 0.02 m. We can calculate the stable time increment for the spring-mass system just as we would for any other element. Recall that the stable time increment of an element is related to its frequency, according to the following relation:To calculate the undamped circular natural frequency of the spring-mass system, we use the following equation:Therefore, the stable time increment for the spring isFor the truss element ABAQUS/Explicit calculates the stable time increment using the following relations:where  is the wave speed of the material and  is the characteristic element length, defined as  At the start of the analysis , making the stable time incrementThe truss stretches with a constant velocity of 1.0 m/s; thus, the length of the truss element at any given time isand the stable time increment is At time  0.169 s the stable time increment for the analysis, which conforms to the stable time increment for the truss, begins to exceed the stable time increment for the spring-mass system. Since ABAQUS/Explicit does not consider the spring-mass system in the stable time increment calculation, the spring-mass system becomes unstable once the stable time increment for the truss exceeds that for the spring-mass system.3.8.2  Identifying the instabilityFetch the input file stability.inp, and run the analysis. Examine the contents of the status (.sta) file, and plot the displacement history of the spring's free end and the energy history of the model to determine the source of the instability.Status fileThe output from the analysis provides us with several indications that the analysis has become unstable. The status file is particularly useful:... -------------------------------------------------------------------------------  STABLE TIME INCREMENT INFORMATION -------------------------------------------------------------------------------       The stable time increment estimate for each element is based on    linearization about the initial state.        Initial time increment = 3.13065E-03      Statistics for all elements:       Mean = 3.13065E-03       Standard deviation = 0.00000E+00      Most critical elements :     Element number   Rank    Time increment   Increment ratio    ----------------------------------------------------------            3          1       3.130655E-03      1.000000E+00      The single precision ABAQUS/Explicit executable will be used in this analysis.  

Page 26: Getting Started With ABAQUS

   -------------------------------------------------------------------------------  SOLUTION PROGRESS -------------------------------------------------------------------------------    STEP 1  ORIGIN 0.00000E+00     Total memory used for step 1 is approximately 28.4 kilowords   Global time estimation algorithm will be used.   Scaling factor :  1.0000               STEP      TOTAL       CPU     STABLE      CRITICAL  KINETIC  INCREMENT  TIME      TIME        TIME   INCREMENT    ELEMENT   ENERGY    MONITOR         0  0.000E+00 0.000E+00   00:00:00 3.131E-03       3   2.500E-01 0.000E+00 Results number  0 at increment zero. ODB Field Frame Number    0 of    1 requested intervals at increment zero.        20  1.005E-01 1.005E-01   00:00:00 9.438E-03       3   6.271E+00 1.561E-02        27  2.015E-01 2.015E-01   00:00:00 2.552E-02       3   2.765E+03-6.320E-01   ***WARNING: Large rotation detected for SPRINGA element 1. The analysis may go              unstable. This message is printed during the first applicable              increment, but will not be printed during subsequent increments              for the remainder of the step.   ***WARNING: Large rotation is detected in 1 1D element (truss, spring, or              dashpot). The analysis may go unstable.          31  3.099E-01 3.099E-01   00:00:00 2.979E-02       3   5.797E+11-1.290E+04        34  4.025E-01 4.025E-01   00:00:00 3.305E-02       3   9.504E+18 5.903E+07        37  5.049E-01 5.049E-01   00:00:00 3.632E-02       3   6.254E+26-5.333E+11        40  6.172E-01 6.172E-01   00:00:00 3.960E-02       3   1.414E+35 8.834E+15...For this analysis we suspected in advance that the spring-mass system would become unstable; therefore, we selected the right-hand node of the spring as the monitor node. The data in the monitor column are, therefore, the displacement of the mass element. The first few increments show that the mass has a displacement, as expected, between 0 m and 0.02 m. However, in increment 27 at a time of 0.2015 s the displacement of node 2 has become  m, well outside the correct range. We anticipated that the spring-mass system would become unstable once the time exceeded 0.169 s, and increment 27 is the first increment in the status file beyond a time of 0.169 s. Between increments 27 and 31 the displacement of the mass remains negative and the first warning messages regarding analysis stability appear. In this case the warning indicates that the SPRINGA element has undergone a large rotation. This rotation does not refer to a rotational degree of freedom (which spring elements do not possess) but rather a rigid rotation of the spring that has occured because the mass is displaced in the negative direction (the spring has effectively turned inside out). Beyond increment 31 the displacement of the mass increases rapidly to a value of 8.834 ?1015 m in increment 40.Displacement historyThe displacement history of the spring's free end is shown graphically in Figure 3-19  . Notice that the distance increases between subsequent symbols on the displacement history plot, indicating that the time increment used by ABAQUS/Explicit increases throughout the analysis. It is clear from the unrealistic displacements that the spring-mass system has become unstable.Figure 3-19  Displacement history of the free end of the spring (node 2).Using energy to determine instabilityIn a more complicated analysis you may not know ahead of time which parts of the model are likely to become unstable. You must then have other means of determining whether or not the solution has become unstable besides monitoring the displacements at a single node. The kinetic energy shown for each increment in the status file provides another simple indication of stability. The advantage of checking the kinetic energy over monitoring a particular degree of freedom is that the kinetic energy shown in the status file is the summation of the kinetic energy over the entire model. An unrealistic growth in the kinetic energy may indicate that the analysis has become unstable but does not indicate the problem area. In this example the kinetic energy starts to grow unrealistically at the same time that the stretch in the spring becomes unrealistic, indicating that the two effects have the same cause.The energies are useful indications of the solution stability, and the most general way to view the energies is to create history plots in ABAQUS/Viewer. Figure 3-20history of the energy balance (ETOTAL), the kinetic and internal energies (ALLKE, ALLIE), as well as the external work (ALLWK).Figure 3-20  Plots of total model energies from the selected results file.Up to approximately 0.16 s the energy balance remains nearly constant at zero. A constant energy balance is an indication that the solution is stable; conversely, a grossly nonconstant energy balance strongly suggests that the solution is unstable. The energy plots show that when the time reaches 0.16 s, the energy balance increases dramatically, as do the other energies.3.8.3  Removing the instability

Page 27: Getting Started With ABAQUS

Three methods of removing the instability are discussed in the following sections.Adding massThe preferred method of removing an instability caused by springs is to increase the mass associated with the springs. Usually, springs are used to model stiffness without modeling the more complex response of the associated continuum. Springs can model the stiffness accurately, but they do not account for the mass. The natural frequency of the spring-mass system decreases as the mass associated with the spring increases; correspondingly, the stable time increment of the spring-mass system increases. If enough mass is added to the nodes associated with the spring, the stable time increment of the spring-mass system can be increased such that it will always be greater than the stable time increment of the rest of the model. At that level the spring will have the desired effect on the behavior of the structure without controlling the stability of the analysis.We can calculate the mass necessary to add to the right-hand node of the spring element so that the spring-mass system remains stable throughout the analysis, which lasts 2 seconds. As shown previously, by the end of the step the stable time increment for the truss has increased toWe can then determine the natural frequency of the spring-mass system necessary to have a factor of safety of four over the truss's maximum stable time increment. Setting the spring's stable time increment equal to four times the truss's maximum stable time increment, we can solve for the necessary mass at the free end of the spring:Solving for the mass, , with  0.3043 s gives a mass of  37050 kg, which means adding 37045 kg. For this simple spring-mass system the additional mass changes the structural response drastically. However, for a larger and more massive model the additional mass would likely have little effect on the structural response; rather, the mass would serve only to stabilize the numerical solution. The displacement of the free end of the spring is shown in Figure 3-21  .Figure 3-21  Spring-mass system response with a 37050 kg mass at the right-hand node.In a real analysis springs can be used not only to connect a structure to ground (a fixed boundary condition), as shown previously, but also to connect one part of a structure to another part. In such a model both ends of the spring are free to move, as shown in Figure 3-22  . Figure 3-22  Spring-mass system with both ends free.Both ends may require additional mass for numerical stability. The natural frequency for this case iswhere is the mass associated with one node of the spring, and  is the mass associated with the other node. If the same mass is associated with each node, the effective mass and natural frequency simplify to andIf we desired a specific stability limit for the spring-mass system, we could again solve the equation for the stable time increment for the spring () for the mass to determine the necessary total mass to add to each of the nodes. If we include a factor of safety of four, the equation becomesThe effect of dampingDashpot elements are often used in conjunction with spring elements to provide damping at discrete points within a model. Using dashpots requires some caution and understanding of the effects of damping on stability. As with springs, dashpots affect the stable time increment of the analysis, yet ABAQUS/Explicit does not consider dashpots when calculating the stable time increment. In fact, a dashpot in parallel with a spring always lowers the actual stable time increment of the spring. On the other hand, ABAQUS/Explicit does consider the effects of material damping on the stable time increment.With no material dampingwhereas with material dampingwhere  is the ratio of the applied damping to the critical damping.The stable time increment for case  is always less than it is for case . Generally, it is not possible to calculate  because you do not know the value for critical damping. Therefore, it is difficult to determine ahead of time at what value of  an analysis will become unstable.Table 3-4   summarizes the mass that should be added to spring and spring-dashpot systems to ensure stability up to the desired time increment. For simplicity, the spring-dashpot systems are solved for  instead of .Table 3-4  Added mass to ensure stability.CaseAdded Mass (with 4?factor of safety)i)ii)iii)iv)Controlling the time incrementationIf adding mass to the spring nodes is not physically appropriate, you can retain stability by controlling the time incrementation. The *DYNAMIC, EXPLICIT option offers several useful parameters. The FIXED TIME INCREMENTATION parameter causes ABAQUS/Explicit to persist with the stable time increment that was calculated at the start of the analysis. In this example using the FIXED TIME INCREMENTATION parameter eliminates the instability from the solution because the stable time increment is not permitted to increase beyond the initial, stable level. To include an additional factor of safety, you can set the SCALE FACTOR parameter to the desired value.3.9  Summary텮 BAQUS/Explicit uses a central difference rule to integrate the kinematics explicitly through time.톂 he explicit method requires many small time increments. Since there are no simultaneous equations to solve, each increment is inexpensive.톂 he explicit method has great cost savings over the implicit method as the model size increases.톂 he stability limit is the maximum time increment that can be used to advance the kinematic state and still remain accurate.텮 BAQUS/Explicit automatically controls the time increment size throughout the analysis to maintain stability.텮 s the material stiffness increases, the stability limit decreases; as the material density increases, the stability limit increases.텳 or a mesh with a single material, the stability limit is roughly proportional to the smallest element dimension.텶 n some situations an ABAQUS/Explicit analysis may become unstable. The example problems in this chapter describe how to recognize and rectify instabilities.4.  Finite Elements and Rigid BodiesFinite elements and rigid bodies are the fundamental components of an ABAQUS/Explicit model. Finite elements are deformable, whereas rigid bodies move through space without changing shape. While users of "finite element" analysis programs tend to have some understanding of what finite elements are, the general concept of rigid bodies within a finite

Page 28: Getting Started With ABAQUS

element program may be somewhat new.For computational efficiency ABAQUS/Explicit has a general rigid body capability. Any body or part of a body composed of any element types can be defined as a rigid body. The advantage of rigid bodies over deformable bodies is that the motion of a rigid body is described completely by no more than six degrees of freedom at a reference node. In contrast, deformable elements have many degrees of freedom and require expensive element calculations to determine the deformations. When such deformations are negligible or not of interest, modeling a component as a rigid body produces significant computational savings without affecting the overall results.4.1  Finite elementsThe wide range of elements that are available in ABAQUS may appear intimidating at first. However, the extensive element library provides a powerful set of tools for solving many different problems. This section introduces the five aspects of an element that influence how it behaves. 4.1.1  Characterizing elementsEach element is characterized by the following:텳 amily텱 egrees of freedom (directly related to the element family)텻 umber of nodes텳 ormulation텶 ntegrationEach element in ABAQUS has a unique name, such as T2D2, S4R, or C3D8R. The element name, as you saw in the overhead hoist example in Chapter 2, "ABAQUS Basics," is used as the value of the TYPE parameter on the *ELEMENT option in the input file. The element name identifies each of the five aspects of an element. The naming convention is explained in this chapter.FamilyFigure 4-1   shows the element families most commonly used in a stress analysis. One of the major distinctions between different element families is the geometry type that each family assumes.Figure 4-1  Commonly used element families.The element families that you will use in this guide--continuum, shell, beam, truss, rigid, and special-purpose elements--are discussed in detail in this chapter. The other element families, such as infinite, membrane, and hydrostatic fluid, are not covered in this guide; if you are interested in using them in your models, read about them in the ABAQUS/Explicit User's Manual.The first letter or letters of an element's name indicate to which family the element belongs. For example, S4R is a shell element, C3D8R is a continuum element, and CINPE4 is an infinite element.Degrees of freedomThe degrees of freedom are the fundamental variables calculated during the analysis. For a stress/displacement simulation the degrees of freedom are the translations and, for shell and beam elements, the rotations at each node as well. Coupled temperature-displacement elements also have temperature degrees of freedom; these elements are not discussed in this guide.The following numbering convention is used for the degrees of freedom in two- and three-dimensional models:1Translation in direction 12Translation in direction 23Translation in direction 34Rotation about the 1-axis5Rotation about the 2-axis6Rotation about the 3-axis11TemperatureDirections 1, 2, and 3 correspond to the global 1-, 2-, and 3-directions, respectively, unless a local coordinate system has been defined at the nodes using the *TRANSFORM option.When using axisymmetric elements, the displacement and rotation degrees of freedom are as follows:1Translation in the -direction2Translation in the -direction6Rotation in the - planeDirections  (radial) and  (axial) correspond to the global 1- and 2-directions, respectively, unless a local coordinate system has been defined at the nodes.Order of interpolationDisplacements and rotations are calculated only at the nodes of the element. At any other point in the element, the displacements are obtained by interpolating from the nodal displacements. Elements that have nodes only at their corners, such as the 8-node brick shown in Figure 4-2  , use linear interpolation in each direction and are often called linear elements or first-order elements. Elements with midside nodes are often called quadratic or second-order elements. In ABAQUS/Explicit all elements are first-order except for the quadratic triangle and tetrahedron, which use a modified second-order interpolation.Figure 4-2  Hexahedral or brick element.

Page 29: Getting Started With ABAQUS

Typically, the number of nodes in an element is clearly identified in the element name. The 8-node brick element, as you have seen, is called C3D8R; and the 4-node general shell element is called S4R. The beam element family uses a different convention, wherein the order of interpolation is identified in the name. Thus, a first-order, three-dimensional beam element is called B31.FormulationAn element's formulation refers to the mathematical theory used to define the element's behavior. In the absence of adaptive meshing all of the deformable elements in ABAQUS/Explicit are based on the Lagrangian or material description of behavior: the element deforms with the material. In the alternative Eulerian, or spatial, description elements are fixed in space as the material flows through them. Adaptive meshing in ABAQUS/Explicit combines the features of pure Lagrangian and Eulerian analyses and allows the motion of the element to be independent of the material; it is not discussed in this guide.IntegrationABAQUS uses numerical techniques to integrate various quantities over the volume of each element. For most elements ABAQUS uses Gaussian quadrature to evalresponse at each integration point in each element.ABAQUS uses the letter "R" at the end of the element name to indicate reduced-integration elements. For example, CAX4R is the 4-node, reduced-integration, first-order, axisymmetric solid element.4.1.2  Continuum elementsBetween the different element families, continuum or solid elements can be used to model the widest variety of components. Conceptually, continuum elements simply model small blocks of material in a component. Since they can be connected to other elements on any of their faces, continuum elements, like bricks in a building or tiles in a mosaic, can be used to build models of nearly any shape, subjected to nearly any loading. ABAQUS/Explicit has both stress/displacement and coupled temperature-displacement continuum elements; we will only discuss stress/displacement elements in this guide.Continuum elements in ABAQUS have names that begin with the letter "C." The next two letters indicate the dimensionality and the active degrees of freedom in the element. The letters "3D" indicate a three-dimensional element; "AX," an axisymmetric element; "PE," a plane strain element; and "PS," a plane stress element.Two-dimensional continuum element libraryABAQUS has several classes of two-dimensional continuum elements that differ from each other in their out-of-plane behavior. Two-dimensional elements can be quadrilateral (CPE4R, CPS4R, and CAX4R) or triangular (CPE3, CPE6M, CPS3, CPS6M, CAX3, and CAX6M). Figure 4-3   shows the three classes that are used most commonly.Figure 4-3  Plane strain, plane stress, and axisymmetric elements.Plane strain elements assume that the out-of-plane strain, , is zero; they can be used to model thick structures.Plane stress elements assume that the out-of-plane stress, , is zero; they are suitable for modeling thin structures.Axisymmetric elements, the "CAX" class of elements (CAX3, CAX4R, and CAX6M), model a 360?ring; they are suitable for analyzing structures with axisymmetric geometry subjected to axisymmetric loading.Two-dimensional solid elements must be defined in the 1-2 plane so that the node ordering is counterclockwise around the element perimeter, as shown in Figure 4-4Figure 4-4  Correct nodal connectivity for two-dimensional elements.When using a preprocessor to generate the mesh, ensure that the element normals all point in the same direction as the positive, global 3-axis. Failure to provide the correct element connectivity will cause ABAQUS to issue an error message stating that elements have negative volume.Three-dimensional continuum element libraryThree-dimensional continuum elements can be hexahedra (C3D8R), wedges (C3D6), or tetrahedra (C3D4 and C3D10M).Whenever possible hexahedral elements (C3D8R) or second-order tetrahedral elements (C3D10M) should be used. First-order tetrahedra (C3D4) have a simple, constant-strain formulation and very fine meshes are required for an accurate solution.Degrees of freedomAll of the continuum elements have translational degrees of freedom at each node. Correspondingly, degrees of freedom 1, 2, and 3 are active in three-dimensional elements, while only degrees of freedom 1 and 2 are active in plane strain elements, plane stress elements, and axisymmetric elements.Element propertiesThe *SOLID SECTION option defines the material and any additional geometric data associated with a set of continuum elements. For three-dimensional and axisymmetric elements no additional geometric information is required: the nodal coordinates completely define the element geometry. For plane stress and plane strain elements the thickness of the elements must be specified on the data line. For example, if the elements are 0.2 m thick, the element property definition would be the following:*SOLID SECTION, ELSET=<element set name>, MATERIAL=<material name>0.2,IntegrationEach first-order continuum element in ABAQUS/Explicit has a single integration point. For first-order triangular, tetrahedral, and wedge elements having one integration point is considered to be full integration, while for quadrilateral and hexahedral (brick) elements having one integration point is considered to be reduced integration. The second-order elements in ABAQUS/Explicit have either three or four integration points, depending on whether they are two- or three-dimensional; this is considered to be full integration.Element output variablesBy default, element output variables such as stress and strain reference the global Cartesian coordinate system. Thus, theFigure 4-5  (a) acts in the global 1-direction. Even if the element rotates during a simulation, as shown in Figure 4-5  (b), the default is still to use the global Cartesian system as the basis for defining the element variables.Figure 4-5  Default material directions for continuum elements.However, ABAQUS allows you to define a local coordinate system for element variables, using the *ORIENTATION option. This local coordinate system rotates with the motion of the element in simulations. A local coordinate system can be very useful if the object being modeled has some natural material orientation, such as the fiber directions in a composite material.4.1.3  Shell elementsShell elements are used to model structures in which one dimension (the thickness) is significantly smaller than the other dimensions and the stresses in the thickness direction are negligible.Shell element names in ABAQUS begin with the letter "S." The axisymmetric shell begins with the letters "SAX." The first number in a shell element name indicates the number of

Page 30: Getting Started With ABAQUS

nodes in the element, except for the case of axisymmetric shells, for which the first number indicates the order of interpolation. All shell elements in ABAQUS/Explicit account for finite membrane strains and arbitrarily large rotations with the following exceptions: if the element name ends with the letter "S," the element uses a small-strain formulation and does not consider warping. If the element name ends with the letters "SW," the element uses a small-strain formulation but considers warping.Shell element libraryTriangular and quadrilateral elements are available with linear interpolation and your choice of large-strain and small-strain formulations. A linear axisymmetric shell element is available.For most analyses the standard large-strain shell elements (S4R, S3R, and SAX1) are appropriate. If, however, the analysis involves small membrane strains and arbitrarily large rotations, the small-strain shell elements (S4RS, S3RS, and S4RSW) are more computationally efficient.Degrees of freedomThe three-dimensional shell elements (S3R, S4R, S3RS, S4RS, and S4RSW) have six degrees of freedom at each node (three translations and three rotations).The axisymmetric shell (SAX1) has three degrees of freedom at each node:1Translation in the -direction2Translation in the -direction6Rotation in the - planeElement propertiesUse either the *SHELL GENERAL SECTION or the *SHELL SECTION option to define the thickness and material properties for a set of shell elements. These two options have similar formats:*SHELL SECTION, ELSET=<element set name>, MATERIAL=<material name><thickness>, <number of section points>or*SHELL GENERAL SECTION, ELSET=<element set name>, MATERIAL=<material name><thickness>,If you specify the *SHELL SECTION option, ABAQUS uses numerical integration to calculate the behavior at selected points (called section points) through the thickness of the shell, as shown in Figure 4-6  . The MATERIAL parameter references a material property definition, which may be linear or nonlinear. You can specify any odd number of section points through the shell thickness.Figure 4-6  Section points through the thickness of a shell element.The *SHELL GENERAL SECTION option allows you to define the cross-section behavior in a number of general ways to model linear or nonlinear behavior. Since ABAQUS models the shell's cross-section behavior directly in terms of section engineering quantities (area, moments of inertia, etc.) with this option, there is no need for ABAQUS to integrate any quantities over the element cross-section. Therefore, *SHELL GENERAL SECTION is less expensive computationally than *SHELL SECTION. The response is calculated in terms of force and moment resultants; the stresses and strains are calculated only when they are requested for output.Reference surface offsetsThe reference surface of the shell is defined by the shell element's nodes and normal definitions. When modeling with shell elements, the reference surface is typically coincident with the shell's midsurface. However, many situations arise in which it is more convenient to define the reference surface as offset from the shell's midsurface. For example, surfaces created in CAD packages usually represent either the top or bottom surface of the shell body. In this case it may be easier to define the reference surface to be coincident with the CAD surface and, therefore, offset from the shell's midsurface.Shell offsets can also be used to define a more precise surface geometry for contact problems where shell thickness is important. By default, shell offset and thickness are accounted for in contact constraints in ABAQUS/Explicit. The effect of offset and thickness in contact can be suppressed, if required.Shell offsets can also be useful when modeling a shell with continuously varying thickness. In this case defining the nodes at the shell midplane can be difficult. If one surface is smooth while the other is rough, as in some aircraft structures, it is easiest to use shell offsets to define the nodes at the smooth surface.Offsets can be introduced by using the OFFSET parameter on the *SHELL SECTION and *SHELL GENERAL SECTION options. The offset value is defined as a fraction of the shell thickness measured from the shell's midsurface to the shell's reference surface.The degrees of freedom for the shell are associated with the reference surface. All kinematic quantities, including the element's area, are calculated there. Large offset values for curved shells may lead to a surface integration error, affecting the stiffness, mass, and rotary inertia for the shell section. For stability purposes ABAQUS/Explicit also automatically augments the rotary inertia used for shell elements on the order of the offset squared, which may result in errors in the dynamics for large offsets. When large offsets from the shell's midsurface are necessary, use multi-point constraints or rigid body constraints instead.Element output variablesThe element output variables for shells are defined in terms of local material directions that lie on the surface of each shell element. These axes rotate with the element's deformation.4.1.4  Beam elementsBeam elements are used to model components in which one dimension (the length) is significantly greater than the other two dimensions and only the stress in the direction along the length of the beam is significant.Beam element names in ABAQUS begin with the letter "B." The next character indicates the dimensionality of the element: "2" for two-dimensional beams and "3" for three-dimensional beams. The third character indicates the interpolation used: "1" for linear interpolation. Linear beams (B21 and B31) are available in two and three dimensions.Degrees of freedomThree-dimensional beams have six degrees of freedom at each node: three translational degrees of freedom (1-3) and three rotational degrees of freedom (4-6).Two-dimensional beams have three degrees of freedom at each node: two translational degrees of freedom (1 and 2) and one rotational degree of freedom (6) about the normal to the plane of the model.

Page 31: Getting Started With ABAQUS

Element propertiesUse the *BEAM SECTION option to define the geometry of the beam cross-section; the nodal coordinates define only the length. The beam cross-section is defined geometrically, and the MATERIAL parameter refers to a material property definition. ABAQUS calculates the cross-section behavior of the beam by numerical integration over the cross-section, allowing both linear and nonlinear material behavior.Formulation and integrationThe beams are shear deformable and account for finite axial strains; therefore, they are suitable for modeling both slender and non-slender beams.Element output variablesThe stress components in three-dimensional beam elements are the axial stress () and the shear stress due to torsion (). The shear stress acts about the section wall in a thin-walled section. Corresponding strain measures are also available, as well as estimates of transverse shear forces on the section.The two-dimensional beam uses only axial stress and strain.The axial force, bending moments, and curvatures about the local beam axes can also be requested for output. For details of what components are available with which elements, refer to the ABAQUS/Explicit User's Manual.4.1.5  Truss elementsTruss elements are rods that can carry only tensile or compressive loads. They have no resistance to bending; therefore, they are useful for modeling pin-jointed frames. Moreover, truss elements can be used as an approximation for cables or strings (for example, in a tennis racket). Trusses are also sometimes used to represent reinforcement within other elements.The truss element names begin with the letter "T." The next two characters indicate the dimensionality of the element--"2D" for two-dimensional trusses and "3D" for three-dimensional trusses. The final character represents the number of nodes in the element. Linear truss elements (T2D2 and T3D2) are available in two and three dimensions.Degrees of freedomTruss elements have only translational degrees of freedom at each node. Three-dimensional truss elements have degrees of freedom 1, 2, and 3, while two-dimensional truss elements have degrees of freedom 1 and 2.Element propertiesThe *SOLID SECTION option is used to specify the name of the material property definition associated with the given set of truss elements. The cross-sectional area is given on the data line:*SOLID SECTION, ELSET=<element set>, MATERIAL=<material><cross-sectional area>Element output variablesAxial stress and strain are available as output.4.1.6  Mass and rotary inertia elementsThese elements (MASS and ROTARYI) define mass and rotary inertia at a discrete point.Degrees of freedomMass elements have three translational degrees of freedom at each node. Rotary inertia elements have three rotational degrees of freedom at each node.Element propertiesUse the *MASS option to define the element property for a mass element:*MASS, ELSET=<element set name><mass magnitude>,Use the *ROTARY INERTIA option to define the element properties for a rotary inertia element:*ROTARY INERTIA, ELSET=<element set name><I11>, <I22>, <I33>,<I12>, <I13>, <I23>Element output variablesNo output is available for these elements.4.1.7  Spring and dashpot elementsSpring and dashpot elements (SPRINGA and DASHPOTA) are used to model the effective stiffness or damping between two nodes without modeling the bodies in detail. The line of action remains between the two nodes throughout the deformation.Degrees of freedomSpring and dashpot elements have three translational degrees of freedom at each node.Element propertiesUse the *SPRING option to define the linear or nonlinear element properties for a spring element. To be consistent with SPRINGA and DASHPOTA elements in ABAQUS/Standard, the first data line following *SPRING and *DASHPOT is blank. If defining a linear spring, use the following:*SPRING, ELSET=<element set name><spring stiffness>,If defining a nonlinear spring, use the following, repeating the second data line as often as necessary:*SPRING, ELSET=<element set name>, NONLINEAR<force>, <relative displacement>Use the *DASHPOT option to define the linear or nonlinear element properties for a dashpot element. If defining a linear dashpot, use the following:*DASHPOT, ELSET=<element set name><dashpot coefficient>,If defining a nonlinear dashpot, use the following, repeating the second data line as often as necessary:*DASHPOT, ELSET=<element set name>, NONLINEAR<force>, <relative velocity>Element output variables

Page 32: Getting Started With ABAQUS

For spring elements S11 is the force in the spring, and E11 is the relative displacement across the spring. For dashpot elements S11 is the force in the dashpot, and E11 is the relative displacement across the dashpot.4.2  Rigid bodiesIn ABAQUS/Explicit a rigid body is a collection of nodes and elements whose motion is governed by the motion of a single node, known as the rigid body reference node, as shown in Figure 4-7  . The shape of the rigid body is defined either as an analytical rigid surface obtained by revolving or extruding a two-dimensional geometric profile or as a discrete rigid body obtained by meshing the body with nodes and elements. The shape of the rigid body does not change during a simulation but can undergo large rigid body motions. The mass and inertia of a discrete rigid body can be calculated based on the contributions from its elements, or they can be assigned specifically.Figure 4-7  Elements forming a rigid body.The motion of a rigid body can be prescribed by applying boundary conditions at the rigid body reference node. Loads on a rigid body are generated from concentrated loads applied to nodes and distributed loads applied to elements that are part of the rigid body or from loads applied to the rigid body reference node. Rigid bodies interact with the rest of the model through nodal connections to deformable elements and through contact with deformable elements.4.2.1  Determining when to use a rigid bodyIn dynamic analyses rigid bodies can be used to model very stiff components that are either fixed or undergoing large dynamic motions. They can also be used to model constraints between deformable components, and they provide a convenient method of specifying certain contact interactions. When ABAQUS/Explicit is used for quasi-static forming analyses, rigid bodies are ideally suited for modeling tooling (such as punch, die, drawbead, blank holder, roller, etc.) and may also be effective as a method of constraint.It may be useful to make parts of a model rigid for verification purposes. For example, in complex models where all potential contact conditions cannot be anticipated, elements far away from the impact region could be included as part of a rigid body, resulting in faster run times while developing a model. When the user is satisfied with the model and contact pair definitions, rigid body definitions can be removed and an accurate deformable finite element representation can be incorporated throughout.The principal advantage to representing portions of a model with rigid bodies rather than deformable finite elements is computational efficiency. Element-level calculations are not performed for elements that are part of a discrete rigid body. Although some computational effort is required to update the motion of the nodes of the discrete rigid body and to assemble concentrated and distributed loads, the motion of the rigid body is determined completely by a maximum of six degrees of freedom at the rigid body reference node.Rigid bodies are particularly effective for modeling relatively stiff parts of a model for which tracking waves and stress distributions is not important. Element stable time increment estimates in the stiff region can result in a very small global time increment. Since rigid bodies and elements that are part of a rigid body do not affect the global time increment, using a rigid body instead of a deformable finite element representation in a stiff region can result in a much larger global time increment, without significantly affecting the overall accuracy of the solution.Rigid bodies defined with analytical rigid surfaces are slightly cheaper in terms of computational cost than discrete rigid bodies. Contact with analytical rigid surfaces tends to be less noisy than contact with discrete rigid bodies because analytical rigid surfaces can be smooth, whereas discrete rigid bodies are inherently faceted. However, the shapes that can be defined with analytical rigid surfaces are limited.4.2.2  Creating a rigid bodyTo create a discrete rigid body, use the *RIGID BODY option as the property reference for the elements forming the rigid body. Use the REF NODE parameter to assign a rigid body reference node to the rigid body. A rigid body reference node has both translational and rotational degrees of freedom and must be defined for every rigid body.*RIGID BODY, REF NODE=<node>, ELSET=<element set name>, PIN NSET=<node set name>, TIE NSET=<node set name><thickness>,In addition to the rigid body reference node, discrete rigid bodies consist of a collection of nodes that are generated by assigning elements and nodes to the rigid body. These nodes provide a connection to other elements. Nodes that are part of a rigid body are one of two types:텾 in nodes, which have only translational degrees of freedom.톂 ie nodes, which have both translational and rotational degrees of freedom.The rigid body node type is determined by the type of elements on the rigid body to which the node is attached. The node type also can be specified or modified when assigning nodes directly to a rigid body. For pin nodes only the translational degrees of freedom are part of the rigid body, and the motion of these degrees of freedom is constrained by the motion of the rigid body reference node. For tie nodes both the translational and rotational degrees of freedom are part of the rigid body and are constrained by the motion of the rigid body reference node.4.2.3  Rigid elementsThe rigid body capability in ABAQUS/Explicit allows any elements--not just rigid elements--to be part of a rigid body. For example, shell elements or rigid elements can be used to model the same effect if a *RIGID BODY option refers to the element set that contains the elements forming the rigid body. The rules governing rigid bodies, such as how loads and boundary conditions are applied, pertain to all element types that form the rigid body, including rigid elements. The names of all rigid elements begin with the letter "R." The next characters indicate the dimensionality of the element. For example, "2D" indicates that the element is planar; and "AX," that the element is axisymmetric. The final character represents the number of nodes in the element.Rigid element libraryThe three-dimensional quadrilateral (R3D4) and triangular (R3D3) rigid elements can be used to model the two-dimensional surfaces of a three-dimensional rigid body.Two-node rigid elements are available for plane strain and plane stress (R2D2) as well as axisymmetric models (RAX2).Physical propertiesAll rigid elements must reference a *RIGID BODY option. For the planar and beam elements the cross-sectional area can be defined on the data line. For the axisymmetric and three-dimensional elements the thickness can be defined on the data line. The default thickness is zero. Alternatively, the NODAL THICKNESS parameter defines an average facet thickness based on the thickness at the nodes. These data are required when applying body forces or when the thickness is needed for the contact definition.4.3  Example: hourglassing in a rubber blockUnder certain loading conditions linear reduced-integration elements can experience a pattern of nonphysical deformation called hourglassing. Consider a single first-order, reduced-integration element modeling a small piece of material subjected to pure bending, as shown in Figure 4-8  . Dotted visualization lines are shown passing through the single integration point in the element.Figure 4-8  Deformation of a first-order element with reduced integration subjected to a bending moment.As the element deforms, neither of the dotted visualization lines changes in length, and the angle between them also does not change. Therefore, all components of stress and

Page 33: Getting Started With ABAQUS

strain at the element's single integration point are zero. This deformation mode is, therefore, a zero-energy mode because no strain energy is generated by distorting the element in this manner. The element is unable to resist this type of deformation since it has no stiffness in this mode. In coarse meshes this zero-energy mode can propagate through the mesh, producing incorrect results.ABAQUS/Explicit has first-order, reduced-integration quadrilateral and hexahedral elements that have hourglass modes. Hourglassing can, therefore, sometimes propagate through a mesh. ABAQUS/Explicit includes sophisticated controls to prevent hourglassing from being a problem in most real analyses. However, the hourglass controls work by applying corrective forces and may take a few increments to control hourglassing. In some severe cases hourglassing can propagate through the mesh before the hourglass controls can correct the problem. This example illustrates such a modeling situation.In this example you will consider a thick rubber block as it is slowly compressed along its diagonal by a rigid surface, as shown in Figure 4-9whether or not hourglassing is a problem and, if it is a problem, how to correct the model to prevent the problem from occurring.Figure 4-9  Rubber block being compressed diagonally by a rigid surface.4.3.1  Node and element setsUse your preprocessor to create a two-dimensional model of the rubber block with a 10 ?10 mesh of two-dimensional plane strain elements (CPE4R) or use the commands given in ``Hourglassing in a rubber block,'' Section A.4.The node sets shown in Figure 4-10   are necessary to apply the loads and boundary conditions and to visualize output. Put the block elements in an element set called EALL, and put the rigid element in an element set called ERIGID. You could define the rigid body using either deformable elements, discrete rigid elements, or an analytical rigid surface. For purposes of this example we assume that you are using a single discrete rigid element. The reference node, which you should place in node set NREF, can be positioned anywhere; however, it is convenient to place it close to its rigid body.Figure 4-10  Node sets NBOT, NRHS, and NREF.4.3.2  10 x 10 uniform mesh: reviewing the input file--the model dataWe now review the model data associated with this problem, including the model description, block definition, rigid body definition, material properties, boundary conditions, amplitude definition, and surface definitions.Model descriptionSince you will study several different meshes in this example, choose a model heading that describes the analysis as well as the mesh, such as the following:*HEADINGHourglassing example10 X 10 regular meshSI Units (kg, m, s, N)Defining the blockEnsure that the element type is CPE4R. Use the following section properties to give the block a thickness of 0.10 m and refer to a material named RUBBER:*SOLID SECTION, ELSET=EALL, MATERIAL=RUBBER.10,Defining the rigid bodyUse a single rigid element (element type R2D2) to define the rigid body that compresses the block at a 45?angle. Make the surface large enough to compress the block by the required amount. The rigid element nodes must be separate from the nodes defining the block. Define the rigid element so that its positive normal points toward the rubber block. For two-dimensional rigid elements the positive normal direction is defined by a 90?counterclockwise rotation from the direction going from the first node defining the element to the second. Define a rigid body reference node that will control the motion of the rigid body. Use the following section properties to define the rigid body:*RIGID BODY, ELSET=<element set name>, REF NODE=<node number>Material propertiesThe block in this example is made of rubber and, thus, should be modeled using the hyperelastic material model. The hyperelastic constants are given in Pascals and are typical for a synthetic rubber. Refer to Chapter 5, "Materials," for more information about defining hyperelastic materials.*MATERIAL, NAME=RUBBER** hyperelastic constants in Pa*HYPERELASTIC, POLYNOMIAL, N=13.2E6, .8E6** density is 1500 kg/m^3*DENSITY1500.,Fixed boundary conditionsFixed boundary conditions can be defined in either the model or the history part of the input file. Define roller boundary conditions on the bottom and right-hand side of the block. Fix the rigid body's rotational degree of freedom as well.*BOUNDARYNBOT, 2NRHS, 1NREF, 6Amplitude definitionTo gradually compress the rubber block by prescribing a nodal displacement at the rigid body reference node, you must first define the loading amplitude in the model definition. The prescribed displacements in the history definition will then refer to this loading amplitude. Define a smooth linear loading amplitude that has a value of zero at the start of the step (time 0.0 s) and a value of 1.0 at the end of the step (time 0.1 s), such as the following:*AMPLITUDE, NAME=CRUSH, DEFINITION=SMOOTH STEP0., 0., .1, 1.Since the parameter DEFINITION was set equal to SMOOTH STEP in the above option, the first and second derivatives of the amplitude curve will be zero at the endpoints of the

Page 34: Getting Started With ABAQUS

specified time interval. This promotes a smooth transition from one amplitude level to another. This parameter is commonly used to promote quasi-static response and is discussed further in ``Smooth amplitude curves,'' Section 7.2.1.Surface definitionsDefine surfaces on the side of the rigid element that will contact the block and on the exterior of the block. Since the normal of the rigid element points toward the rubber block, contact will occur on the rigid element's positive (SPOS) face. *SURFACE, NAME=RIGIDERIGID, SPOS*SURFACE, NAME=SOLIDEALL,4.3.3  10 x 10 uniform mesh: reviewing the input file--the history dataThe history data required for this simulation are discussed next, including the step definition, contact definitions, loading, and output requests.Step definitionThe following would be an appropriate heading for this step:*STEPCompress the rubber blockThe goal is to compress the block slowly so that the dynamic effects are not dominant. Since this model is quite small, computer time is not an issue. For this case 0.1 s is a sufficiently large amount of time to compress the block in a nearly static manner. (Quasi-static analyses will be discussed in detail in Chapter 7, "Quasi-Static Analysis.") Therefore, choose 0.1 s as the total time for the step.*DYNAMIC, EXPLICIT, 0.1Contact definitionsContact is discussed in detail in Chapter 6, "Contact." Define the contact between the rigid body and the block using the following:*CONTACT PAIR, INTERACTION=INTERSOLID, RIGID*SURFACE INTERACTION, NAME=INTERLoadingThe loading for this analysis is a displacement boundary condition imposed on the rigid body reference node. As the rigid body moves, it compresses the block. To move the rigid body a distance of 0.017 m at a 45?angle, impose equal displacement boundary conditions of 0.012 m in both the 1-direction and the negative 2-direction.*BOUNDARY, TYPE=DISPLACEMENT, AMPLITUDE=CRUSHNREF, 1, 1, .012NREF, 2, 2, -.012Output requestsYou want to have an output database file created during the analysis so you can use ABAQUS/Viewer to postprocess the results. Write the preselected field data and the model energies as history data to the output database file. Add the following output requests to your input file:*OUTPUT, FIELD, NUMBER INTERVAL=20, VARIABLE=PRESELECT*OUTPUT, HISTORY, FREQUENCY=1*ENERGY OUTPUTALLAE, ALLKE, ALLSE, ALLVD,ALLFD, ALLWK, ETOTALSetting the FREQUENCY parameter on the *OUTPUT, HISTORY option equal to 1 causes history data to be written to the output database file every increment, permitting great detail for postprocessing. However, if many variables are chosen, the price of such detail can be a large output database file.Indicate the end of a step with the option*END STEPMake sure that this input option is the last option in your model.4.3.4  Running the analysisAfter storing your input in a file called hourglass_square.inp, run the analysis using the following command:abaqus job=hourglass_squareIf the analysis does not complete, check the files hourglass_square.dat and hourglass_square.sta for error messages. Modify your input file to remove any error messages. If you still have trouble running the analysis, compare your input file to the one provided in ``Hourglassing in a rubber block,'' Section A.4.4.3.5  PostprocessingStart ABAQUS/Viewer by typingabaqus viewer odb=hourglass_squareat the operating system prompt.Plotting the deformed model shapeTo begin this exercise, plot the deformed model shape.To plot the deformed model shape:1.From the main menu bar, select Plot->Deformed Shape; or use the  tool in the toolbox.The deformed model plot appears in the current viewport as shown in Figure 4-11  .Figure 4-11  Final deformed shape of mesh 1.Looking closely at the deformation, you will notice that much of the mesh has a pattern of alternating trapezoids, which indicates that hourglassing is propagating through the mesh. The problem is most pronounced near the corner that is being pushed in. In this example the hourglassing pattern is severe enough that we can readily see the problem by looking

Page 35: Getting Started With ABAQUS

at the deformed mesh. Usually, hourglassing is not a severe problem if it is not readily visible in the deformed mesh. A more quantitative approach is to look at the history of the artificial strain energy, which is primarily the energy dissipated to control hourglassing deformation. If the artificial strain energy is excessive, too much strain energy may be going into controlling hourglassing deformation.Studying the artificial strain energyTo determine what is an excessive value of artificial strain energy, the most useful approach is to compare the artificial strain energy to the other internal energies. In this example the material is elastic; therefore, a comparison with the elastic strain energy is appropriate.In ABAQUS/Explicit the variable ALLAE is the total energy dissipated as artificial strain energy and the variable ALLSE is the elastic, or recoverable, strain energy. ALLAE contains both viscous and elastic terms; however, since the viscous term is usually predominant, most of the energy that goes into artificial strain energy is non-recoverable. Look at the history of the artificial strain energy and the elastic strain energy in ABAQUS/Viewer to determine whether the amount of artificial strain energy is excessive in this problem.To create history plots of the artificial and elastic strain energies:1.From the main menu bar, select Result->History Output.2.Select the variable ALLAE from the list of available Output Variables in the History Output dialog box.3.Click Plot.ABAQUS/Viewer plots the artificial strain energy history as shown in Figure 4-12  .Figure 4-12  History plot of artificial strain energy (ALLAE) in mesh 1.4.Select the variable ALLSE from the list of available Output Variables in the History Output dialog box.5.Click Plot.ABAQUS/Viewer plots the elastic strain energy history as shown in Figure 4-13  .Figure 4-13  History plot of elastic strain energy (ALLSE) in mesh 1.6.Click Dismiss to close the History Output dialog box.ABAQUS/Viewer allows you to create new X-Y data objects by performing operations on previously saved X-Y data objects. You will use this feature to create an X-Y data object that is the ratio of the artificial strain energy to the elastic strain energy versus time. Then, you will plot the ratio of artificial strain energy to elastic strain energy versus time.To plot the ratio of artificial strain energy to elastic strain energy versus time:1.From the main menu bar, select Tools->XY Data->Manager.The XY Data Manager dialog box appears.2.From this dialog box, click Create.3.From the Create XY Data dialog box that appears, select ODB history output and click Continue.The History Output dialog box appears.4.From the list of available Output Variables in the History Output dialog box, select ALLAE and click Save As.The Save XYData As dialog box appears.5.Name the X-Y data object ALLAE, and click OK.6.Use a similar technique to save a data object containing the elastic strain energy (ALLSE). Name this data object ALLSE.7.Dismiss the History Output dialog box.You are now ready to operate on the X-Y data objects.8.In the XY Data Manager dialog box, click Create.9.From the Create XY Data dialog box that appears, select Operate on XY data and click Continue.The Operate on XY Data dialog box appears.10.From the XY Data field, select ALLAE."ALLAE" appears in the text field at the top of the dialog box.11.From the Operators field, select the division symbol (/).A division symbol appears following "ALLAE" in the text field at the top of the dialog box.12.From the XY Data field, select ALLSE."ALLSE" is appended to the expression in the text field at the top of the dialog box.13.Click Save As.The Save XYData As dialog box appears.14.Name the data object AESE, and click OK.A dialog box may appear warning that ABAQUS/Viewer detected an attempt to divide by zero. In this case the elastic strain energy is zero at time equal to zero, and you can safely click Dismiss. ABAQUS/Viewer sets the corresponding value to zero.15.Dismiss the Operate on XY Data dialog box.You are now ready to plot the ratio of artificial strain energy to elastic strain energy.16.From the XY Data Manager dialog box, select AESE and click Plot.ABAQUS/Viewer plots the ratio of artificial strain energy to elastic strain energy versus time. By default, there is no title on the vertical axis. You will now add a title.17.From the main menu bar, select Options->XY Plot.The XY Plot Options dialog box appears.18.Click the Titles tab. From the Y-Axis options, change the title source to User-specified; then enter AESE for Whole Model for the title text.19.Click OK.ABAQUS/Viewer creates the plot shown in Figure 4-14  .Figure 4-14  History of the artificial strain energy to elastic strain energy ratio.This plot shows that the ratio of artificial to elastic strain energy reaches a maximum of 15.7% early in the analysis. After this point little artificial energy is dissipated while elastic strain energy continues to increase, indicating that the hourglassing problem is not worsening. At the conclusion of the analysis, the ratio drops to approximately 2%. This plot confirm s that for much of the analysis the ratio of energy dissipated as artificial strain energy to actual strain energy is well over 10%, while a general rule is that it is desirable to

Page 36: Getting Started With ABAQUS

keep the ratio well below 5%. With the ratio of 10% we need to think about what is possibly causing the excessive artificial energy and how we can decrease the ratio to improve the results.Understanding what is causing the mesh to hourglass so severelyTo help understand what is causing the mesh to hourglass so severely, consider the deformed model shape near the time when the hourglassing is most severe. You must first determine when this occurs.To determine when hourglassing is most severe:1.From the main menu bar, select Tools->Query.2.In the Query dialog box that appears, click OK.The Probe Values dialog box appears. 3.Move the cursor over the curve, and locate the peak value on the curve.As you move the mouse, notice that ABAQUS/Viewer displays the X-Y coordinates of the point currently under the cursor in the Current Probe Values field of the Probe Values dialog box. The peak value of the ratio of artificial strain energy to elastic strain energy occurs at 0.044 s. 4.Click Cancel to close the Probe Values dialog box.Plot the deformed model shape in the vicinity of 0.044 s into the simulation to gain further insight into the source of the hourglassing.To plot the deformed model shape near the time when hourglassing is most severe:1.From the main menu bar, select Result->Step/Frame.The Step/Frame dialog box appears.2.In the Frame field of the Step/Frame dialog box, select the increment with a step time nearest to 0.044 s.3.Click OK.Subsequent deformed model plots will correspond to the increment you just selected.4.From the main menu bar, select Plot->Deformed Shape; or use the  tool in the toolbox.ABAQUS/Viewer displays the deformed shape of the model. Turn on the display of node symbols.5.From the main menu bar, select Options->Deformed Shape.The Deformed Shape Plot Options dialog box appears.6.Click the Labels tab, and toggle on Show node symbols.7.Click OK.The deformed model plot is updated to reflect the selected deformed plot options.8.Zoom in on the upper left corner of the mesh.From the toolbar, click the  tool and drag the mouse to select a rectangular region that encloses the upper left corner of the mesh.ABAQUS/Viewer zooms in on the selected region of the mesh as shown in Figure 4-15  .Figure 4-15  Hourglassing in the corner region of mesh 1.9.Click mouse button 2 to exit the box zoom mode.The displaced mesh shows the classic hourglassing pattern, in which adjacent elements are alternating trapezoids. Several observations can be made. First, the corner element, which initially contacts the rigid body at a single node, is deformed excessively. Second, the hourglassing pattern is most severe in elements close to the corner element. Third, the hourglassing pattern appears to be more severe in the elements with free edges than in interior elements. Since these observations are based only on the displaced shape, they are somewhat subjective.It appears that the hourglassing is seeded at the corner element, where the contact at a single node is similar to a concentrated force along the diagonal. Hourglassing propagates easily along the unconstrained boundaries of the block and along the diagonal. As the analysis progresses, the free boundaries become further constrained by contact with the rigid body, and the severity of the hourglassing decreases. Table 4-1   lists three common causes of hourglassing and remedies for the problem.Table 4-1  Common causes and remedies of excessive hourglassing.CauseRemedyConcentrated force at a single nodeDistribute the force among several nodes or apply a distributed load.Boundary condition at a single nodeDistribute the boundary constraint among several nodes.Contact at a single nodeDistribute the contact constraint among several nodes.In summary, loads, boundary conditions, or contact constraints at a single node tend to promote hourglassing, as shown in Figure 4-16constraint over two or more nodes greatly reduces hourglassing problems, as shown in Figure 4-17  .Figure 4-16  Concentrated force or constraint seeding hourglassing deformation.Figure 4-17  Improved deformation pattern with distributed force or constraint.There are two specific changes we can make to the rubber block mesh to reduce hourglassing.1.Refine the mesh, as mesh refinement always decreases hourglassing; or2.Round the corner so that contact never occurs at only a single node. Distributing the contact constraint over several nodes removes the "seed" for the hourglassing deformation pattern.4.3.6  Effects of changing the meshTo illustrate the effects of refining the mesh and distributing the contact constraint over several nodes, we have created the three additional meshes shown in Figure 4-18Figure 4-18  From left to right: a coarse, flat-cornered mesh (mesh 2); a fine, square mesh (mesh 3); a fine, flat-cornered mesh (mesh 4).Meshes 2 and 4 incorporate the simplest type of rounded corner: a single triangular element replaces the square element at the contacting corner. With these meshes contact does not occur at a single corner node; instead, contact initially occurs at two nodes, as shown in Figure 4-19  , thereby reducing hourglassing. Changing the mesh in this way clearly

Page 37: Getting Started With ABAQUS

alters the model by removing some of the material at the corner. With mesh refinement, however, the change to the model becomes less significant.Figure 4-19  Initial contact between the rigid body and the fine, flat-cornered mesh (mesh 4).We study the quality of the results from these new meshes in the same manner as before, using X-Y plots of energy and deformed plots of the mesh. Figure 4-20strain energy history using the original mesh and using the three new meshes. Since the block is compressed monotonically, it follows that the strain energy should increase monotonically as well, as the plot confirm s. The maximum strain energy is lower in the models with the flat corner than in the models with the sharp corner because the flat-corner models contain less material at the corner and compressing less material stores less strain energy. With mesh refinement the differences decrease between the flat-corner and square mesh results.Figure 4-20  Elastic strain energy history for all 4 meshes.Figure 4-21   shows the histories of artificial strain energy for the four meshes, for which the trends are clear. Figure 4-21  Artificial strain energy history of all four meshes.Mesh 1 (the coarse, square mesh) has by far the highest artificial strain energy; and mesh 3 (the fine, square mesh) has the next highest artificial strain energy, although its level is much lower than that of the coarse mesh. For each of these cases the artificial strain energy initially dissipates rapidly but eventually reaches a plateau and remains nearly constant. The rapid increase occurs while there is contact at only a single node; after two nodes come into contact, the highest artificial strain energy increases very little. This observation leads to the conclusion that the sooner two or more nodes are in contact, the sooner the hourglassing will diminish. From the beginning the flat-cornered meshes have two nodes in contact; thus, they do not show an initial plateau in the artificial strain energy. Even the coarse, flat-cornered mesh (mesh 2) has a lower artificial strain energy than the fine, square mesh, suggesting that distributing the contact forces between two nodes does more to decrease hourglassing than refining the mesh. Still lower in artificial strain energy is the fine, flat-cornered mesh whose advantages over the square mesh include mesh refinement and distributed contact forces.Figure 4-22   shows how the ratio of the dissipated artificial strain energy to elastic strain energy changes as the analysis progresses.Figure 4-22  History of artificial strain energy to elastic strain energy for all four meshes.The trends are the same as for the artificial strain energy plots alone. The advantage of energy ratios is that they allow us to use a simple approximate rule to determine whether or not hourglassing is a problem. For both the coarse and fine square meshes the ratio, which is between 10% and 15% throughout the analysis, exceeds the 5% rule. Only after the rubber block becomes highly compressed does the ratio drop below 5%. For the flat-cornered meshes the ratio remains below 2% throughout the entire analysis, indicating that hourglassing is insignificant.For this example we showed the most basic way to distribute the corner contact forces by flattening the corner of the rubber block. While this approach clearly illustrates a remedy for excessive hourglassing, a more general approach would be to round the corner with a smooth fillet instead of replacing the corner element with a triangular element. A coarse, filleted mesh and a refined, filleted mesh are shown in Figure 4-23  . Though their behavior is slightly more complicated than that of their flat-cornered counterparts, these meshes alleviate hourglassing problems in the same manner. Once more than one node is in contact at the corner, the hourglassing problem diminishes. The rounded meshes are somewhat more appealing for real engineering simulations because they allow a better representation of the physical problem.Figure 4-23  Left: coarse, filleted mesh (mesh 5); right: fine, filleted mesh (mesh 6).4.4  Summary텮 BAQUS has an extensive library of elements that can be used for a wide range of structural applications. Element type has important consequences affecting the accuracy and efficiency of your simulation.톂 he degrees of freedom active at a node depend on the element types attached to the node.톂 he element name completely identifies the element's family, formulation, number of nodes, and type of integration.텮 ll elements must refer to an element property option. The element property option provides any additional data required to define the geometry of the element and also identifies the associated material property definition.텳 or continuum elements ABAQUS defines the element output variables, such as stress and strain, with respect to the global Cartesian coordinate system. You can change to a local coordinate system by using the *ORIENTATION option.텳 or three-dimensional shell elements ABAQUS defines the element output variables with respect to a coordinate system based on the surface of the shell. You can change the coordinate system by using the *ORIENTATION option.텳 or computational efficiency any part of a model can be defined as a rigid body, which has degrees of freedom only at its reference node.텮 s a method of constraint, rigid bodies are computationally more efficient than multi-point constraints.텵 ourglassing can be caused by concentrated forces, boundary conditions, or contact acting at a single node. Refining the mesh and distributing the forces or constraints between several nodes often can prevent the problem.5.  MaterialsThe material library in ABAQUS/Explicit allows most engineering materials to be modeled, including metals, plastics, rubbers, foams, composites, granular soils, and plain and reinforced concrete. This guide discusses four of the most commonly used material models: linear elasticity, metal plasticity, rubber elasticity, and foam plasticity. All of the material models are discussed in detail in the ABAQUS/Explicit User's Manual.5.1  Defining materials in ABAQUSYou can define any number of materials within an ABAQUS model. Each material definition begins with a *MATERIAL option. The NAME parameter identifies the material's name, which is used to assign the material definition to specific elements in the model.The material definition is one of the few situations in which the position of option blocks in the ABAQUS input file is important. All of the option blocks defining specific aspects of a material's behavior, such as its elastic modulus or density, must follow the *MATERIAL option directly. Furthermore, the material option blocks defining the behavior of a particular material cannot be interrupted by other nonmaterial options. ABAQUS issues an error message if it cannot associate a material behavior option block, such as *ELASTIC, with a prior *MATERIAL option.For example, consider the material description of an elastic-plastic metal, which requires several material behavior options to supply the requisite data. In addition to the elastic and plastic property option blocks, ABAQUS/Explicit always requires a density. Thus, the complete material description would be:A non-material option block between the *PLASTIC and *DENSITY options, as shown below, would cause ABAQUS to terminate the analysis with an error message.5.2  Plasticity in ductile metalsMany metals exhibit approximately linear elastic behavior at low strain levels, as shown in Figure 5-1  .Figure 5-1  Stress-strain behavior for a linear elastic material, such as steel, at small strains.

Page 38: Getting Started With ABAQUS

 A constant stiffness, called the Young's modulus or the elastic modulus, characterizes the material behavior. At higher strain levels metals exhibit nonlinear, plastic behavior, as shown in Figure 5-2  .Figure 5-2  Nominal stress-strain behavior of an elastic-plastic material in a tensile test.5.2.1  Characteristics of plasticity in ductile metalsThe plastic behavior of a material is described by its yield point and its post-yield hardening. Figure 5-2   shows a stress-strain curve for a ductile metal with all the important regions labeled. At a point on the stress-strain curve known as the elastic limit or the yield point, the behavior changes from elastic to plastic. In most metals the stress at the yield point, called the yield stress, is 0.05 to 0.1% of the material's elastic modulus.The deformation of the metal prior to reaching the yield point creates only elastic strains, which are recovered fully if the applied load is removed. However, once the stress in the metal exceeds the yield stress, permanent or plastic deformation begins to occur. Strains associated with plastic deformation are called plastic strains. Even after yielding, the elastic strains continue to increase according to the original elastic modulus, so that any additional straining contains both elastic and plastic components.Once the metal yields, the stiffness for continued loading decreases dramatically, while the Young's modulus still defines the stiffness when unloading. If the material is loaded again after unloading, its stiffness is equal to the Young's modulus until its stress-strain curve on reloading once again intersects the hardening curve, at which point the material yields and continues loading along the hardening curve. Often plastic deformation increases a material's yield stress upon subsequent loadings, a behavior called work hardening.A metal deforming plastically under a tensile load may experience highly localized deformation, called necking, after reaching its ultimate strength. During necking the nominal stress (force per unit original area) drops well below the ultimate strength, as the nominal strain (length change per unit original length) continues to increase. This material behavior is caused by the geometry of the test specimen, the nature of the test itself, and the stress and strain measures used. For example, testing the same material in compression produces a stress-strain curve that does not have a necking region because the specimen does not thin as it deforms in compression. A mathematical model describing the plastic behavior of metals must be able to account for differences in the compressive and tensile behavior independent of the structure's geometry or the nature of the applied loads. Replacing nominal stress, , and nominal strain, , with alternative stress and strain measures allows us to account for the change in area during the finite deformations.5.2.2  Stress and strain measures for finite deformationsStrains in compression and tension are the same only if considered in the limit as ; i.e.,andwhere  is the current length,  is the original length, and  is the true strain or logarithmic strain.The stress measure that is the conjugate to the true strain is called the true stress and is defined aswhere  is the force in the material and  is the current area. A ductile metal subjected to finite deformations will have identical stress-strain behavior in tension and compression if true stress is plotted against true strain.5.2.3  Defining plasticity in ABAQUSWhen defining plasticity data in ABAQUS, you must use true stress and true strain. ABAQUS requires these values to interpret the data in the input file correctly. However, quite often material test data are supplied using values of nominal stress and strain. In such situations you must convert the plastic material data from nominal stress and strain to true stress and strain.The relationship between true strain and nominal strain is established by expressing the nominal strain asAdding unity to both sides of this expression and taking the natural log of both sides provides the relationship between the true strain and the nominal strain:The relationship between true stress and nominal stress is formed by considering the incompressible nature of the plastic deformation and assuming the elastic volumetric deformation is negligible, so The expression relating the current area to the original area isSubstituting this definition of  into the definition of true stress gives where can also be written as Making this final substitution provides the relationship between true stress and nominal stress and strain:Use the *PLASTIC option in ABAQUS to define the post-yield behavior for most metals. The data pairs on the *PLASTIC option define the true stress as a function of true plastic strain. The first data pair defines the initial yield stress and the corresponding initial plastic strain, which must have a value of zero. ABAQUS connects your stress-strain data pairs with a series of straight line segments to form a continuous, piecewise-linear plasticity curve. You can use any number of data pairs to approximate the actual material behavior; therefore, it is possible to get a very close approximation to the actual material behavior.The strains provided in material test data used to define the plastic behavior are not likely to be the plastic strains in the material. Instead, they will probably be the total strains in the material. You must decompose these total strain values into the elastic and plastic strain components. The plastic strain is obtained by subtracting the elastic strain, defined as the value of true stress divided by the Young's modulus, from the value of total strain (see Figure 5-3  ). This relationship is writtenwhereis true plastic strain,is true total strain,is true elastic strain,is true stress, andis Young's modulus.Figure 5-3  Decomposition of the total strain into elastic and plastic components.Example of converting material test data to ABAQUS inputThe stress-strain curve in Figure 5-4   will be used as an example of how to convert the test data defining a material's plastic behavior into the appropriate input format for ABAQUS. The six points shown on the nominal stress-strain curve will be used as the data for the *PLASTIC option.Figure 5-4  Elastic-plastic material behavior and corresponding ABAQUS input data.The first step is to use the equations relating the true stress to the nominal stress and strain and the true strain to the nominal strain to convert the nominal stress and nominal strain to true stress and true strain. Once these values are known, the equation relating the plastic strain to the total and elastic strains (shown earlier) can be used to determine the plastic strains associated with each yield stress value. The converted data are shown in Table 5-1  . Table 5-1  Converting nominal stress and strain to true stress and strain.

Page 39: Getting Started With ABAQUS

Nominal StressNominal StrainTrue StressTrue StrainPlastic Strain200E60.00095200.2E60.000950.0240E60.025246E60.02470.0235280E60.050294E60.04880.0474340E60.100374E60.09530.0935380E60.150437E60.13980.1377400E60.200480E60.18230.1800While there are only slight differences between the nominal and true values at small strains, there are very significant differences at larger strains; therefore, it is important to provide the proper stress-strain data to ABAQUS if the strains in the simulation will be large. The format of the input data defining this material behavior is shown in Figure 5-4Regularization of user-defined dataWhen performing an analysis, ABAQUS/Explicit may not use exactly the material data defined by the user; for efficiency, all material data that are defined in tabular form are automatically regularized. Material data can be functions of temperature, external fields, and internal state variables, such as plastic strain. For each material point calculation, the state of the material must be determined by interpolation, and, for efficiency, ABAQUS/Explicit fits the user-defined curves with curves composed of equally spaced points. These regularized material curves are the material data used during the analysis. It is important to understand the differences that might exist between the regularized material curves used in the analysis and the curves that you specified in your input file.To illustrate the implications of using regularized material data, consider the following two cases. Figure 5-5   shows a case in which the user has defined data that are not regular. In this example ABAQUS/Explicit generates the six regular data points shown, and the user's data are reproduced exactly. Figure 5-6that are difficult to regularize exactly. In this example it is assumed that ABAQUS/Explicit has regularized the data by dividing the range into 10 intervals that do not reproduce the user's data points exactly.Figure 5-5  Example of user data that can be regularized exactly.Figure 5-6  Example of user data that are difficult to regularize.ABAQUS/Explicit attempts to use enough intervals such that the maximum error between the regularized data and the user-defined data is less than 3%. You can change this error tolerance by using the RTOL parameter on the *MATERIAL option. If more than 200 intervals are required to obtain an acceptable regularized curve, the analysis stops during the data checking with an error message. In general, the regularization is more difficult if the smallest interval defined by the user is small compared to the range of the independent variable. In Figure 5-6   the data point for a strain of 1.0 makes the range of strain values large compared to the small intervals defined at low strain levels. Removing this last data point enables the data to be regularized much more easily.Interpolation between data pointsABAQUS/Explicit interpolates linearly between the regularized data points to obtain the material's response and assumes that the response is constant outside the range defined by the input data. Thus, the stress in the material shown in Figure 5-5   and Figure 5-6   will never exceed 300 MPa; when the stress in the material reaches 300 MPa, the slope of the hardening curve is assumed to be zero.5.3  Example: blast loading on a stiffened plateIn this example you will assess the response of a stiffened square plate subjected to a blast loading. The plate is firmly clamped on all four sides and has three equally spaced stiffeners welded to it. The plate is constructed of 25 mm thick steel and is 2 m square. The stiffeners are made from 12.5 mm thick plate and have a depth of 100 mm. Figure 5-7

Page 40: Getting Started With ABAQUS

shows the plate geometry and material properties in more detail.Figure 5-7  Problem description for blast load on a flat plate.The purpose of this example is to determine the response of the plate and to see how it changes as the sophistication of the material model increases. Initially, we analyze the behavior with the standard elastic-plastic material model. Subsequently, we study the effects of including material damping and rate-dependent material properties.5.3.1  Coordinate systemUse the default rectangular coordinate system with the plate lying in the 1-3 plane. Since the plate thickness is significantly smaller than any other global dimensions, you can use shell elements of type S4R for the model.5.3.2  Mesh designCreate your mesh based on the design shown in Figure 5-8  , which is a relatively coarse mesh of 20 ?20 elements in the plate and 2 ?20 elements in each of the stiffeners. This mesh corresponds to the input file shown in ``Blast loading on a stiffened plate,'' Section A.5. It provides moderate accuracy while keeping the solution time to a minimum. Define the mesh so that the element normals for the plate all point in the positive 1-direction. Doing so ensures that the stiffeners lie on the SPOS face of the plate, which will be important when defining the element properties and shell offsets later.Figure 5-8  Mesh design for the stiffened plate.5.3.3  Node and element setsFigure 5-9   shows all the sets necessary to apply the element properties, loads, and boundary conditions. Figure 5-9  Node and element sets.Include all the nodes on the perimeter of the plate in a node set called EDGE. These nodes will have a completely fixed boundary condition. Define a node set for output purposes called NOUT containing the node at the center of the plate. Put the plate elements in an element set called PLATE, and put the stiffener elements in an element set called STIFF. In addition, define an element set for output purposes called STIFFMAX, which contains the four center elements on the central stiffener. These elements will be subject to the maximum bending stress in the stiffeners.5.3.4  Reviewing the input file--the model dataWe now review the model data for this problem, including the model description, node and element definitions, element properties and shell offsets, material properties, boundary conditions, and amplitude definition for the blast load.Model descriptionThe *HEADING option is used to include a title and model description in the input file. The heading is useful for future reference purposes and may contain information on model revisions and the evolution of complex models. It can be several lines long, but only the first line will be printed as a title on the output pages. Below is the *HEADING definition that might be used for this analysis.*HEADINGBlast load on a flat plate with stiffenersS4R elements (20x20 mesh)Normal stiffeners (20x2)SI units (kg, m, s, N)Nodal coordinates and element connectivityUse your preprocessor to generate the mesh shown in Figure 5-8   and the sets shown in Figure 5-9  . Element properties and shell offsetGive each element set the section properties shown below. Include the appropriate MATERIAL parameter on each *SHELL SECTION option so that each set of elements refers to a material definition.*SHELL SECTION, MATERIAL=STEEL, ELSET=PLATE, OFFSET=SPOS0.025,*SHELL SECTION, MATERIAL=STEEL, ELSET=STIFF0.0125,The material named STEEL will be defined in the next section. Setting OFFSET to SPOS offsets the midsurface of the plate one half of the shell thickness away from the nodes. The effect is to make the PLATE nodes lie on the SPOS shell face instead of on the shell midsurface. The purpose of the shell offset in this case is to allow the stiffeners to butt up against the plate without overlapping any material with the plate. Figure 5-10   shows the cross-section of the joint between the stiffener and panel using the OFFSET parameter.Figure 5-10  Stiffener joint in which the plate's midsurface is offset from its nodes.If the stiffener and base plate elements are joined at common nodes at their midsurfaces, an area of material overlaps, as shown in Figure 5-11Figure 5-11  Overlapping material if OFFSET were not used.If the thicknesses of the plate and stiffener is small in comparison to the overall dimensions of the structure, this overlapping material and the extra stiffness it would create has little effect on the analysis results. However, if the stiffener is short in comparison to its width or to the thickness of the base plate, the additional stiffness of the overlapping material could affect the response of the whole structure.Material propertiesAssume that both the plate and stiffeners are made of steel (Young's modulus of 210.0 GPa and Poisson's ratio of 0.3). At this stage we do not know whether there will be any plastic deformation, but we know the value of the yield stress and details of the post-yield behavior for this steel. We will add this information on the *PLASTIC option in the material definition. The initial yield stress is 300 MPa, and the yield stress increases to 400 MPa at a plastic strain of 35%. The plasticity data are shown below, and the plasticity stress-strain curve is shown in Figure 5-12  .*MATERIAL, NAME=STEEL*ELASTIC210.0E9, .3*PLASTIC300.0E6, 0.000350.0E6, 0.025

Page 41: Getting Started With ABAQUS

375.0E6, 0.100394.0E6, 0.200400.0E6, 0.350*DENSITY7800.0,Figure 5-12  Yield stress versus log plastic strain.During the analysis ABAQUS calculates values of yield stress from the current values of plastic strain. As discussed earlier, the process of lookup and interpolation is most efficient when the data are regular--when the stress-strain data are at equally spaced values of plastic strain. To avoid having the user input regular data, ABAQUS/Explicit automatically regularizes the data. In this case the data are regularized by ABAQUS/Explicit by expanding to 15 equally spaced points with increments of 0.025.To illustrate the error message that is produced when ABAQUS/Explicit cannot regularize the material data, try setting the regularization tolerance, RTOL, to 0.001 and include one additional data pair, as shown below:The combination of the low tolerance value (RTOL=0.001) and the small interval in the user-defined data leads to difficulty in regularizing this material definition. The following error message is produced in the status (.sta) file:***ERROR: Failed to regularize material data. Try regularizing the independent variable intervals.Boundary conditionsFully constrain the edges of the plate using the node set EDGE defined previously.*BOUNDARYEDGE, ENCASTRE Alternatively, you could specify the degrees of freedom by number. *BOUNDARYEDGE, 1, 6Amplitude definition for blast loadSince the plate will be subjected to a load that varies with time, you must define an appropriate amplitude curve to describe the variation. Define the amplitude curve shown in Figure 5-13   as follows:*AMPLITUDE, NAME=BLAST0.0, 0.0, 1.0E-3, 7.0E5, 10E-3, 7.0E5, 20E-3, 0.050E-3, 0.0Figure 5-13  Pressure load as a function of time.The pressure increases rapidly from zero at the start of the analysis to its maximum of 7.0 ?105 N in 1 ms, at which point it remains constant for 9 ms before dropping back to zero in another 10 ms. It then remains at zero for the remainder of the analysis.5.3.5  Reviewing the input file--the history dataThe history data begin with the *STEP option, which is followed immediately by a title for the step. After the title, specify the *DYNAMIC, EXPLICIT procedure with a time period of 50 ms.*STEPApply blast loading** Explicit analysis with a time duration of 50 ms*DYNAMIC, EXPLICIT, 50E-03Applying the blast loadUse the *DLOAD option to apply the blast load to the plate. It is important to ensure that the pressure load is being applied in the correct direction. Positive pressure is defined as acting in the direction of the positive shell normal. For shell elements the positive normal direction is obtained using the right-hand rule about the nodes of the element, as shown in Figure 5-14  . Since the magnitude of the load has been defined in the BLAST amplitude definition, you need to apply only a unit pressure under *DLOAD. Apply the pressure so that it pushes against the top of the plate (where the stiffeners are on the bottom of the plate). Such a pressure load will place the outer fibers of the stiffeners in tension. Use the following option in your input file:*DLOAD, AMPLITUDE=BLASTPLATE, P, 1.0 Figure 5-14  Definition of positive pressure load.Output requestsTo check on the progress of the solution, use the *MONITOR option to monitor the deflection at the center node of the plate during the analysis. Monitor the out-of-plane displacement at the center node by adding the following command to your input file:*MONITOR, NODE=<center node number>, DOF=1Set the number of intervals during the step at which preselected field data are written to the output database file (ODB) to 25. This ensures that the selected data outputs are written every 2 ms since the total time for the step is 50 ms. In general, you should try to limit the number of frames written during the analysis to keep the size of the output database file reasonable. In this analysis saving information every 2 ms should provide sufficient detail to study the response of the structure visually.*OUTPUT, FIELD, NUMBER INTERVAL=25, VARIABLE=PRESELECTA more detailed set of output can be saved for selected parts of the model by using the *OUTPUT, HISTORY option. Set the TIME INTERVAL parameter to 1.0E-4 seconds to write the required data at 500 points during the analysis. Write von Mises stress (MISES), equivalent plastic strain (PEEQ), and volumetric strain rate (ERV) for the elements in element set STIFFMAX. Since the nodes that will undergo the maximum displacements are at the center of the plate, use node set NOUT to output displacement and velocity history data for the center of the plate. In addition, save the following energy variables: kinetic energy (ALLKE), recoverable strain energy (ALLSE), work done (ALLWK), energy lost in plastic dissipation

Page 42: Getting Started With ABAQUS

(ALLPD), total internal energy (ALLIE), energy lost in viscous dissipation (ALLVD), artificial energy (ALLAE), and the energy balance (ETOTAL).*OUTPUT, HISTORY, TIME INTERVAL=1.0E-4*ELEMENT OUTPUT, ELSET=STIFFMAXPEEQ, MISES*NODE OUTPUT, NSET=NOUTU, V*ENERGY OUTPUTALLKE, ALLSE, ALLWK, ALLPD, ALLIE, ALLVD, ALLAE, ETOTAL*END STEP Save your input in a file called blast_base.inp since these results will serve as a base state from which to compare subsequent analyses. Run the analysis using the following command:abaqus job=blast_base5.3.6  OutputWe now examine the output information contained in the status (.sta) file.Status fileInformation concerning model information, such as total mass and center of mass, and the initial stable time increment can be found at the top of the status file. The 10 most critical elements (i.e., those resulting in the smallest time increments) in rank order are also shown here. If your model contains a few elements that are much smaller than the rest of the elements in the model, the small elements will be the most critical elements and will control the stable time increment. The stable time increment information in the status file can indicate elements that are adversely affecting the stable time increment, allowing you to change the mesh to improve the situation, if necessary. It is ideal to have a mesh of roughly uniformly sized elements. In this example the mesh is uniform; thus, the 10 most critical elements share the same minimum time increment. The beginning of the status file is shown below. -------------------------------------------------------------------------------  MODEL INFORMATION (IN GLOBAL X-Y COORDINATES) -------------------------------------------------------------------------------      Total mass in model = 838.50    Center of mass of model = ( 3.488360E-03, 9.999977E-01, 9.999990E-01)       Moments of Inertia :                  About Center of Mass              About Origin       I(XX)          5.557794E+02                  2.232779E+03       I(YY)          2.750539E+02                  1.113565E+03       I(ZZ)          2.849024E+02                  1.123411E+03       I(XY)          9.059906E-06                  2.925000E+00       I(YZ)          4.272461E-04                  8.385000E+02       I(ZX)          3.337860E-06                  2.924998E+00   -------------------------------------------------------------------------------  STABLE TIME INCREMENT INFORMATION -------------------------------------------------------------------------------       The stable time increment estimate for each element is based on    linearization about the initial state.        Initial time increment = 6.99621E-06      Statistics for all elements:       Mean = 1.01237E-05       Standard deviation = 1.71465E-06      Most critical elements :     Element number   Rank    Time increment   Increment ratio    ----------------------------------------------------------         1033          1       6.996214E-06      1.000000E+00         1038          2       6.996214E-06      1.000000E+00         2033          3       6.996214E-06      1.000000E+00         2038          4       6.996214E-06      1.000000E+00         3033          5       6.996214E-06      1.000000E+00         3038          6       6.996214E-06      1.000000E+00

Page 43: Getting Started With ABAQUS

         1013          7       6.996215E-06      9.999999E-01         1018          8       6.996215E-06      9.999999E-01         2013          9       6.996215E-06      9.999999E-01         2018         10       6.996215E-06      9.999999E-01During the analysis the status file can be viewed to monitor the progress of the analysis. Shown below is the beginning of the solution progress portion of the status file. Note that many more increments have been carried out than you would expect from an ABAQUS/Standard analysis and that the output database file is being written at intervals of 2 ms. --------------------------------------------------------------------------------  SOLUTION PROGRESS --------------------------------------------------------------------------------    STEP 1  ORIGIN 0.00000E+00     Total memory used for step 1 is approximately 755.2 kilowords   Global time estimation algorithm will be used.   Scaling factor :  1.0000               STEP      TOTAL       CPU     STABLE      CRITICAL  KINETIC  INCREMENT  TIME      TIME        TIME   INCREMENT    ELEMENT   ENERGY    MONITOR         0  0.000E+00 0.000E+00   00:00:00 6.996E-06    1033   0.000E+00 0.000E+00 Results number  0 at increment zero. ODB Field Frame Number    0 of   25 requested intervals at increment zero.       235  2.000E-03 2.000E-03   00:00:12 8.573E-06    2026   4.468E+03 4.192E-03 ODB Field Frame Number    1 of   25 requested intervals at  2.000078E-03       469  4.006E-03 4.006E-03   00:00:25 8.572E-06    2018   1.119E+04 2.519E-02 ODB Field Frame Number    2 of   25 requested intervals at  4.005884E-03       702  6.003E-03 6.003E-03   00:00:38 8.572E-06    2031   6.167E+03 4.584E-02 ODB Field Frame Number    3 of   25 requested intervals at  6.003135E-03       935  8.000E-03 8.000E-03   00:00:50 8.556E-06    2031   1.766E+02 5.033E-02 ODB Field Frame Number    4 of   25 requested intervals at  8.000187E-03      1170  1.001E-02 1.001E-02   00:01:03 8.545E-06    2030   2.308E+03 4.535E-02 ODB Field Frame Number    5 of   25 requested intervals at  1.000848E-02Output for the node referenced on the *MONITOR option is also included in this file.5.3.7  PostprocessingRun ABAQUS/Viewer by entering the commandabaqus viewer odb=blast_baseat the operating system prompt.Plotting the undeformed model shapeYou will begin this exercise by plotting the undeformed model shape of the plate.To plot the undeformed model shape:1.From the main menu bar, select Plot->Undeformed Shape.The undeformed model shape is displayed in the viewport.2.To change the undeformed plot options, select Options->Undeformed Shape from the main menu bar or click Undeformed Shape Plot Options in the prompt area.The Undeformed Shape Plot Options dialog box appears; by default, the Basic tab is selected.3.Choose the Filled render style.4.Click OK.The plot changes to display the current plot settings.Changing the viewThe default view is isometric, which does not provide a particularly clear view of the plate. To improve the viewpoint, rotate the view using the options in the View menu or the view tools in the toolbar. To rotate the view:1.From the main menu bar, select View->Specify.The Specify View dialog box appears.2.From the Specify View dialog box, select the Viewpoint method.Using the Viewpoint method, you enter three values representing the X-, Y-, and Z-position of an observer. You can also specify an up vector. ABAQUS positions your model so that this vector points upward.3.Enter the X-, Y-, and Z-coordinates of the viewpoint vector as 0.5,1,1 and the coordinates of the up vector as 1,0,0.4.Click OK.ABAQUS displays your model in the specified view. You can also specify a view by entering values for rotation angles, zooming, or panning.Viewport annotationsThe default viewport annotations display the triad, title block, and state block in the viewport. You can suppress their display by changing the viewport annotations.To change the viewport annotations:

Page 44: Getting Started With ABAQUS

1.From the main menu bar, select Canvas->Viewport Annotation Options.The Viewport Annotation Options dialog box appears; by default, the Triad tab is selected.2.Toggle off Show Triad.3.Click the Title Block tab, and toggle off Show Title Block.4.Click OK.To fit the undeformed model shape in the viewport, select View->Auto-fit.Animation of resultsAnimating your results will provide a general understanding of the dynamic response of the plate under the blast loading. You will first plot the deformed model shape and then create a time-history animation of the deformed shape.To plot the deformed model shape:1.From the main menu bar, select Plot->Deformed Shape.The deformed model shape is displayed in the viewport. Only feature edges are visible by default.2.To change the deformed plot options, click Deformed Shape Plot Options in the prompt area.The Deformed Shape Plot Options dialog box appears; by default, the Basic tab is selected.3.Choose All visible edges and the Filled render style.4.Click OK.To create the time-history animation:1.From the main menu bar, select Animate->Time History.ABAQUS/Viewer displays the deformed model shape at the beginning of the simulation and cycles through each available frame. The state block indicates the current step and increment throughout the animation. By default, the animation loops through all available frames repeatedly. This can be changed so that the animation loops through the frames only once.ABAQUS/Viewer displays the movie player controls on the left side of the prompt area.From left to right, these controls perform the following functions: play, stop, first image, previous image, next image, last image.2.To change the animation control options, click Animation Options in the prompt area.The Animation Options dialog box appears; by default, the Player tab is selected.3.From the Mode option, choose Play once.4.Click OK.You will see from the animation that as the blast loading is applied, the plate begins to deflect. Over the duration of the load the plate begins to vibrate and continues to vibrate after the blast load has dropped to zero. The maximum displacement occurs at approximately 8 ms, and a displaced plot of that state is shown in Figure 5-15Figure 5-15  Displaced shape at 8 ms.The animation images can be saved to a file for playback at a later time.To save the animation:1.From the main menu bar, select Animate->Save As.The Save Image Animation dialog box appears.2.In the Settings field, enter the file name blast_base.The format of the animation can be specified as either QuickTime or AVI.3.Choose the QuickTime format, and click OK.The animation is saved as blast_base.mov in your current directory. You can play the animation file using the ABAQUS movie player utility.To play an animation file using the movie player:1.From the main menu bar, select Animate->Image Animation.The Open Image Animation dialog box appears.2.Select the file blast_base.mov.3.Click OK.4.The ABAQUS movie player utility appears, and the animation automatically starts to play.To change any of the default options, click Animation Options in the prompt area.5.After the animation has finished, click Dismiss in the prompt area to exit the ABAQUS movie player utility.History outputSince it is not particularly easy to see the deformation of the plate from the deformed plot, it may be better to view the deflection response of the central node (node set NOUT) in the form of a graph. The displacement of the node in the center of the plate is of particular interest since the largest deflection occurs at this node.To generate a history plot of the central node displacement:Use the following commands to display the displacement history of the central node, as shown in Figure 5-16   (with displacements in millimeters).1.From the main menu bar, select Result->History Output.The History Output dialog box appears.2.Plot the spatial displacement, U1, at node 411.3.To save the current X-Y data, click Save As. Name the data DISP.4.Click Dismiss.The units of the displacements in this plot are meters. Modify the data to create a plot of displacement (in millimeters) versus time.5.Select Tools->XY Data->Manager.The DISP data are listed in the XY Data Manager dialog box.To create the plot with the displacement values in millimeters, you need to multiply the DISP X-Y data by 1000.6.Click Create in the XY Data Manager dialog box; then select Operate on XY Data in the Create XY Data dialog box. Click Continue.

Page 45: Getting Started With ABAQUS

The Operate on XY Data dialog box opens.7.Click DISP in the XY Data field; then click * in the Operators field.8.In the text box at the top of the dialog box, enter 1000 following the * symbol so that the expression appears as:"DISP" * 10009.Click Plot Expression to see the modified X-Y data. Save the data as U_BASE2.10.Click Dismiss.11.To change the plot titles, click XY Plot Options in the prompt area.The XY Plot Options dialog box appears. Click the Titles tab.12.Click Title Source for the Y-axis and select User-specified. Change the title to Displacement (mm).13.Click OK. The resulting plot is shown in Figure 5-16  .Figure 5-16  Central displacement as a function of time.The plot shows that the displacement reaches a maximum of 50.1 mm at 7.4 ms and then oscillates after the blast load is removed.The other quantities saved as history output in the output database are the total energies of the model. The energy histories can help identify possible shortcomings in the model as well as highlight significant physical effects. To generate history plots of the model energies:Use the following commands to display the histories of five different energy output variables--ALLKE, ALLSE, ALLPD, ALLIE, and ALLAE.1.From the main menu bar, select Result->History Output.The History Output dialog box appears.2.Select the output variable Artificial strain energy: ALLAE for Whole Model. Click Save As. Name the curve ALLAE.3.Click OK.4.Similarly, save the history results for the ALLKE, ALLSE, ALLPD, and ALLIE output variables as X-Y data.5.Click Dismiss.6.Select Tools->XY Data->Manager.The ALLAE, ALLKE, ALLSE, ALLPD, and ALLIE X-Y data objects are listed in the XY Data Manager.7.In the XY Data Manager dialog box, select ALLAE, ALLKE, ALLSE, ALLPD, and ALLIE using [Ctrl]+Click; and click Plot to plot the energy curves.8.Click Dismiss.To more clearly distinguish between the different curves in the plot, change their line styles.9.Click XY Curve Options in the prompt area.The XY Curve Options dialog box appears.10.For the curve ALLSE, select a dashed line style.For the curve ALLPD, select a dotted line style.For the curve ALLAE, select a chain dashed line style.For the curve ALLIE, select the second thinnest line type.11.Click Dismiss.Customize the appearance of the plot further by changing the plot titles and the position of the legend.12.To change the plot titles, click XY Plot Options in the prompt area.The XY Plot Options dialog box appears. Click the Titles tab.13.Change the title for the Y-axis to Energy.14.Click OK.15.To change the position of the legend, select Canvas->Viewport Annotation Options.16.Click the Legend tab.The position of the upper left corner of the legend is determined by the values specified in the % Viewport X and % Viewport Y boxes.17.Change the % Viewport X value to 65, and the % Viewport Y value to 50.This will position the legend so that the upper left corner is 65% of the way across the viewport from left to right and 50% of the way up the viewport from bottom to top.18.Click OK. The resulting plot is shown in Figure 5-17  .Figure 5-17  Energy terms as a function of time.We can see that once the load has been removed and the plate vibrates freely, the kinetic energy increases as the strain energy decreases. When the plate is at its maximum deflection and, therefore, has its maximum strain energy, it is almost entirely at rest, causing the kinetic energy to be at a minimum.Note that the plastic strain energy rises to a plateau and then rises again. From the plot of kinetic energy we can see that the second rise in plastic strain energy occurs when the plate has rebounded from its maximum displacement and is moving back in the opposite direction. We are, therefore, seeing plastic deformation on the rebound after the blast pulse.Even though there is no indication that hourglassing is a problem in this analysis, study the artificial strain energy to make sure. As discussed in Chapter 4, "Finite Elements and Rigid Bodies," artificial strain energy is the energy used to control hourglass deformation, and the output variable ALLAE is the accumulated artificial strain energy. Since energy is dissipated as plastic deformation as the plate deforms, the total internal energy is much greater than the elastic strain energy alone. Therefore, it is most meaningful in this analysis to compare the artificial strain energy to an energy quantity that includes the dissipated energy as well as the elastic strain energy. Such a variable is the total internal energy, ALLIE, which is a summation of all internal energy quantities. The artificial strain energy is approximately 1% of the total internal energy, indicating that hourglassing is not a problem.One thing we can notice from the deformed shape is that the central stiffener is subject to almost pure in-plane bending. Using only two first-order, reduced-integration elements through the depth of the stiffener is not sufficient to model in-plane bending behavior. While the solution from this coarse mesh appears to be adequate since there is little hourglassing, for completeness we will study how the solution changes when we refine the mesh of the stiffener. Remember that caution must be taken when refining the mesh, since mesh refinement will increase the solution time by increasing the number of elements and decreasing the element size.

Page 46: Getting Started With ABAQUS

An input file for a model with a refined stiffener mesh is included in ``Blast loading on a stiffened plate,'' Section A.5 (blast_refined.inp); four elements through the depth are used to model the stiffener instead of two. This increase in the number of elements increases the solution time by approximately 20%. In addition, the stable time increment decreases by approximately a factor of two as a result of the reduction of the smallest element dimension in the stiffeners. Since the total increase in solution time is a combination of the two effects, the solution time of the refined mesh increases by approximately a factor of 1.2 ?2, or 2.4, over that of the original mesh.Figure 5-18   shows the histories of artificial energy for both the original mesh and the mesh with the refined stiffeners. As anticipated, the artificial energy is lower in the refined mesh. The important question, however, is whether or not the results changed significantly from the original to the refined mesh. Figure 5-19plate's central node is almost identical in both cases, indicating that the original mesh is capturing the overall response adequately. One advantage of the refined mesh, however, is that it better captures the variation of stress and plastic strain through the stiffeners. Figure 5-18  Artificial energy in the original and refined models.Figure 5-19  Central displacement history in original and refined meshes.Contour plotsUse the contour plotting capability of ABAQUS/Viewer to display the von Mises stress and equivalent plastic strain distributions in the plate. Use the model with the refined stiffener mesh to create the plots: from the main menu bar, select File->Open and choose the file blast_refined.odb.To generate contour plots of the von Mises stress and equivalent plastic strain:1.From the main menu bar, select Result->Field Output.The Field Output dialog box appears.2.Select the stress output variable (S) from the Output Variable area. The stress invariants are displayed in the Invariant area.3.Select the Mises stress invariant.4.Click Section Points to select a section point. The Section Points dialog box appears.5.Select shell under Category and the SPOS section point from the list of available section points.6.Click OK.The Select Plot Mode dialog box appears.7.Toggle on Contour, and click OK.ABAQUS/Viewer displays a contour plot of the von Mises stress.The view that you set earlier for the animation exercise should be changed so that the stress distribution is clearer. By default, only feature edges are visible. Change this so that all element edges are visible. You will also need to reposition the legend in the plot.8.From the main menu bar, select View->Views Toolbox to bring up the Views dialog box. Select the isometric view.9.To show all the visible edges, click Contour Options in the prompt area.The Contour Plot Options dialog box appears.10.Choose Exterior visible edges.11.Click OK.12.To change the legend position back to the default position, select Canvas->Viewport Annotation Options from the main menu bar.13.Click the Legend tab in the Viewport Annotation Options dialog box. Click Defaults to reset the legend position to its default location.14.Click OK.Figure 5-20   shows a contour plot of the von Mises stress at the SPOS section point (section point 5).Now contour the equivalent plastic strain.15.From the main menu bar, select Result->Field Output.The Field Output dialog box appears.16.Select the equivalent plastic strain output variable (PEEQ) from the Output Variable area.17.Click OK.Figure 5-21   shows a contour plot of the equivalent plastic strain at the SPOS section point (section point 5).Figure 5-20  Contour plot of von Mises stress.Figure 5-21  Contour plot of equivalent plastic strain.5.3.8  Reviewing the analysisThe objective of this analysis is to study the deformation of the plate and the stress in various parts of the structure when it is subjected to a blast load. To judge the accuracy of the analysis, you will need to consider the assumptions and approximations made and identify some of the limitations of the model.DampingUndamped structures continue to vibrate with constant amplitude. Over the 50 ms of this simulation the frequency of the oscillation can be seen to be approximately 214 Hz. A constant amplitude vibration is not the response that would be expected in practice since the vibrations in this type of structure would tend to die out over time and effectively disappear after 5-10 oscillations. The energy loss typically occurs by a variety of mechanisms including frictional effects at the supports and damping by the air.Consequently, we need to consider the presence of damping in the analysis to model this energy loss. The energy dissipated by viscous effects, ALLVD, is nonzero, indicating that there is already some damping present in the analysis. By default, a bulk viscosity damping (discussed in Chapter 3, "Overview of Explicit Dynamics") is always present and is introduced to improve the modeling of high-speed events.In this shell model only linear damping is present. With the default value the oscillations would eventually die away, but it would take a long time because the bulk viscosity damping is very small. Material damping should be used to introduce a more realistic structural response. Modify the material data block to include damping, setting the mass proportional damping to 50.0. *DAMPING, ALPHA=50.0, BETA=0.0BETA is the parameter that controls stiffness proportional damping, and at this stage we will leave it set to zero.The time period for the oscillation of the plate is approximately 10 ms, so we need to increase the analysis period to allow enough time for the vibration to be damped out. Therefore, increase the analysis period to 150 ms.

Page 47: Getting Started With ABAQUS

The results of the damped analysis clearly show the effect of mass proportional damping. Figure 5-22   shows the displacement history of the central node for both the damped and undamped analyses. (We have extended the analysis time to 150 ms for the undamped model to compare the data more effectively.) The peak response is also reduced due to damping. By the end of the damped analysis the oscillation has decayed to a nearly static condition.Figure 5-22  Damped and undamped displacement histories.Rate dependenceSome materials, such as mild steel, show an increase in the yield stress with increasing strain rate. In this example the loading rate is high, so strain-rate dependence is likely to be important. The *RATE DEPENDENT option is used with the *PLASTIC option to introduce strain-rate dependence.Add the following to the material option block:*RATE DEPENDENT40.0, 5.0 With this definition of rate-dependent behavior, the ratio of the dynamic yield stress to the static yield stress () is given for an equivalent plastic strain rate (), according to the equation , where  and  are material constants (40.0 and 5.0 in this case).When the *RATE DEPENDENT option is included, the yield stress effectively increases as the strain rate increases. Therefore, because the elastic modulus is higher than the plastic modulus, we expect a stiffer response in the analysis with rate dependence. Both the displacement history of the central portion of the plate shown in Figure 5-23of plastic strain shown in Figure 5-24   confirm that the response is indeed stiffer when rate dependence is included. Figure 5-23  Displacement of the central node with and without rate dependence.The results are, of course, sensitive to the material data. In this case the values of  and  are typical of a mild steel, but more precise data would be required for detailed design analyses.Figure 5-24  Plastic strain energy with and without rate dependence.5.4  HyperelasticityThe stress-strain behavior of typical rubber materials, which is shown in Figure 5-25  , is elastic but highly nonlinear. Figure 5-25  Typical stress-strain curve for rubber.This type of material behavior is called hyperelasticity. The deformation of hyperelastic materials, such as rubber, remains elastic up to large strain values (often well over 100%).ABAQUS/Explicit makes the following assumptions when modeling a hyperelastic material:톂 he material behavior is elastic.톂 he material behavior is isotropic.톂 he material is nearly incompressible (Poisson's ratio is 0.475 by default.)Elastomeric foams are another class of highly nonlinear, elastic materials. They differ from rubber materials in that they have a highly compressible behavior when subjected to compressive loads. They are modeled using the hyperfoam model in ABAQUS/Explicit. The hyperfoam model will not be discussed in this guide.5.4.1  Strain energy potentialABAQUS uses a strain energy potential (U), rather than a Young's modulus and Poisson's ratio, to relate stresses to strains in hyperelastic materials. Several different strain energy potentials are available: a polynomial model, the Ogden model, the Arruda-Boyce model, and the van der Waals model. Simpler forms of the polynomial model are also available, including the Mooney-Rivlin, neo-Hookean, reduced polynomial, and Yeoh models. The polynomial form of the strain energy potential is the one that is most commonly used. Its form iswhere  is the strain energy potential;  is the elastic volume ratio;  and  are measures of the distortion in the material; and , , andtemperature. The  parameters describe the shear behavior of the material, and the  parameters introduce compressibility. If the material were fully incompressible (a condition not allowed in ABAQUS/Explicit), all the values of  would be zero, and the second part of the equation shown above could be ignored. If the number of terms, , is one, the initial shear modulus, , and bulk modulus, , are given by and The other hyperelastic material models are similar in concept and are described in the ABAQUS/Explicit User's Manual.You must provide ABAQUS with the relevant material parameters to use a hyperelastic material. For the polynomial form these are , , and . It is possible that you will be supplied with these parameters when modeling hyperelastic materials; however, more likely you will be given test data for the materials that you must model. ABAQUS can accept test data directly and calculate the material parameters for you (using a least squares fit).5.4.2  Defining hyperelastic behavior using test dataA convenient way of defining a hyperelastic material is to supply ABAQUS with experimental test data. ABAQUS then calculates the constants using a least squares method. The experimental tests for which ABAQUS can fit data are:톃 niaxial tension and compression.텲 quibiaxial tension and compression.텾 lanar tension and compression (pure shear).톅 olumetric tension and compression.The deformation modes seen in these tests and the ABAQUS input options used to define the data for each are shown in Figure 5-26hyperelastic materials must be given to ABAQUS as nominal stress and nominal strain values.Figure 5-26  Deformation modes and ABAQUS input options for the various experimental tests for defining hyperelastic material behavior.Achieving the best material model from your dataThe quality of the results from a simulation using hyperelastic materials strongly depends on the material test data that you provide ABAQUS. There are several things that you can do to help ABAQUS calculate the best possible material parameters.Wherever possible, try to obtain experimental test data from more than one deformation state to help ABAQUS form a much more accurate and stable material model. Some of the tests shown in Figure 5-26   produce equivalent deformation modes for incompressible materials. The following are equivalent tests for incompressible materials:톃 niaxial tension ?Equibiaxial compression.톃 niaxial compression ?Equibiaxial tension.텾 lanar tension ?Planar compression.

Page 48: Getting Started With ABAQUS

You do not need to include data from a particular test if you already have data from another test that models the same deformation mode.In addition, the following may improve your hyperelastic material model:텽 btain test data for the deformation modes that are likely to occur in your simulation. For example, if your component is loaded in compression, make sure that your test data include compressive, rather than tensile, loading.텯 oth tension and compression data are allowed, with compressive stresses and strains entered as negative values. If possible, use compression or tension data depending on the application, since the fit of a single material model to both tensile and compressive data will normally be less accurate for each individual test.텾 rovide more data at the strain magnitudes that you expect the material will be subjected to during the simulation. For example, if the material will only have small tensile strains, say under 50%, do not provide much, if any, test data at high strain values (over 100%).텾 erform one-element simulations of the experimental tests, and compare the results ABAQUS calculates to the experimental data. If the computational results are poor for a particular deformation mode that is important to you, try to obtain more experimental data for that deformation mode.These one-element simulations are very easy to perform in ABAQUS/CAE. Please consult the ABAQUS/CAE User's Manual for details.Stability of the material modelIt is possible for the hyperelastic material model determined from the test data to be unstable at certain strain magnitudes. ABAQUS performs a stability check to determine the strain magnitudes where unstable behavior will occur and prints a warning message in the data (.dat) file. You should check this information carefully since your simulation may not be realistic if any part of the model experiences strains beyond the stability limits.See ``Hyperelastic behavior,'' Section 9.3.1 of the ABAQUS/Explicit User's Manual, for suggestions on improving the accuracy and stability of the test data fit.CompressibilityMost solid rubber materials have very little compressibility compared to their shear flexibility. This behavior is not a problem with plane stress, shell, or membrane elements. However, it can be a problem when using other elements, such as plane strain, axisymmetric, and three-dimensional solid elements. For example, in applications where the material is not highly confined, it would be quite satisfactory to assume that the material is fully incompressible: the volume of the material cannot change except for thermal expansion. In cases where the material is highly confined (such as an O-ring used as a seal), the compressibility must be modeled correctly to obtain accurate results.Except for plane stress cases, it is not possible to assume that the material is fully incompressible in ABAQUS/Explicit because the program has no mechanism for imposing such a constraint at each material calculation point. An incompressible material also has an infinite wave speed, resulting in a time step of zero. Therefore, you must provide some compressibility. The difficulty is that, in many cases, the actual material behavior provides too little compressibility for the algorithms to work efficiently. Thus, except for plane stress, the user must provide enough compressibility for an efficient solution, knowing that this makes the bulk behavior of the model softer than that of the actual material. Therefore, some judgement is required to decide whether or not the solution is sufficiently accurate or whether the problem can be modeled at all with ABAQUS/Explicit because of this numerical limitation. We can assess the relative compressibility of a material by the ratio of its initial bulk modulus, , to its initial shear modulus, . Poisson's ratio, , also provides a measure of compressibility since it is defined asTable 5-2   provides some representative values:Table 5-2  Relationship between compressibility and Poisson's ratio.Poisson's ratio100.452200.475500.4901000.4951,0000.499510,0000.49995If no value is given for the material compressibility in the hyperelastic option, by default ABAQUS/Explicit assumes , corresponding to a Poisson's ratio of 0.475. Since typical unfilled elastomers have  ratios in the range of 1,000 to 10,000 ( 0.4995 to  0.49995) and filled elastomers have  ratios in the range of 50 to 200 ( 0.490 tomuch more compressibility than is available in most elastomers. However, if the elastomer is relatively unconfined, this softer modeling of the material's bulk behavior usually provides quite accurate results. However, in cases where the material is highly confined--such as when it is in contact with stiff, metal parts and has a very small amount of free surface, especially when the loading is highly compressive--it may not be feasible to obtain accurate results with ABAQUS/Explicit.If you are defining the compressibility rather than accepting the default value, an upper limit of 100 is suggested for the ratio of . Larger ratios introduce high-frequency noise into the dynamic solution and require the use of excessively small time increments.5.5  Material dampingAn ABAQUS/Explicit model often includes energy dissipation mechanisms--dashpots, inelastic material behavior, and the like--as part of the basic model. In such cases there is usually no need to introduce additional "structural" or general damping, as such damping would be unimportant compared to these other dissipative effects. However, some models do not have such energy dissipation sources, and some models require additional energy dissipation beyond that provided by other parts of the model. In such cases material damping may be desirable. Material damping is also discussed in ``Material damping,'' Section 3.6.3.Material damping in ABAQUS/Explicit is Rayleigh damping, which is defined using the *DAMPING option, a suboption of the *MATERIAL option block. There are two damping factors associated with Rayleigh damping:  for mass proportional damping and  for stiffness proportional damping. Generally, mass proportional damping is used to damp out the low-frequency response, and stiffness proportional damping is used to damp out the high-frequency response (to smooth a noisy solution).Mass proportional dampingThe  factor defines a damping contribution proportional to the mass matrix for an element. The damping forces that are introduced are caused by the absolute velocities of nodes in the model. The resulting effect can be likened to the model moving through a viscous ``ether'' so that any motion of any point in the model triggers damping forces.

Page 49: Getting Started With ABAQUS

Stiffness proportional dampingThe  factor defines damping proportional to the elastic material stiffness. A ``damping stress,'' , proportional to the total strain rate is introduced, using the following formula:where  is the strain rate. For hyperelastic and hyperfoam materials  is defined as the initial elastic stiffness. For all other materialsdamping stress is added to the stress caused by the constitutive response at the integration point when the dynamic equilibrium equations are formed, but it is not included in the stress output. Damping can be introduced for any nonlinear case and provides standard Rayleigh damping for linear cases. For a linear case stiffness proportional damping is exactly the same as defining a damping matrix equal to  times the stiffness matrix. To avoid a dramatic drop in the stable time increment, the stiffness proportional damping factor, , should be less than or of the same order of magnitude as the initial stable time increment without damping.5.6  Summary텮 BAQUS contains an extensive library of material models, including models for metal plasticity and rubber elasticity.톂 he stress-strain data for the metal plasticity model must be defined in terms of true stress and true plastic strain. Nominal stress-strain data can be converted easily into true stress-strain data.톂 he metal plasticity model assumes nearly incompressible behavior once the material has yielded.텳 or efficiency ABAQUS/Explicit regularizes user-defined material curves by fitting them with curves composed of equally spaced points.텾 olynomial, Ogden, Arruda-Boyce, van der Waals, Mooney-Rivlin, neo-Hookean, reduced polynomial, and Yeoh strain energy functions are available for rubber elasticity (hyperelasticity).텵 yperelasticity models allow the material coefficients to be determined directly from experimental test data. The test data must be specified as nominal stress and nominal strain values.톁 tability warnings may indicate that a hyperelastic material model is unsuitable for the strain ranges you wish to analyze.톂 he default Poisson's ratio for hyperelastic materials in ABAQUS/Explicit is 0.475. Some analyses may require increasing Poisson's ratio to model incompressibility more accurately.텴 enerally, mass proportional damping is used to damp low-frequency oscillations, and stiffness proportional damping is used to damp high-frequency oscillations.톂 o avoid a dramatic drop in the stable time increment, the stiffness proportional damping factor, , should be less than or of the same order of magnitude as the initial stable time increment without damping.6.  ContactMany analyses in ABAQUS/Explicit involve contact between separate components. As bodies come into contact, they impose normal pressures and frictional shear tractions on each other. The goal of a contact analysis is to determine the areas of the model that are in contact and the stresses on the bodies due to the contact.Contact is different from most constraints because it is discontinuous, meaning that a contact constraint must be applied only when bodies are in contact. The finite element code must be able to determine whether or not the bodies are in contact and apply the appropriate constraints. If contact is lost, the contact constraint must be removed as well.6.1  Overview of contact capabilitiesContact modeling in ABAQUS/Explicit is based on the concept of surfaces coming into contact with one another. The user must define surfaces based on the elements in the model and then define interactions between the surfaces. The contact capability is very general. Contact can be defined between surfaces of almost any type: a deformable surface can contact another deformable surface, a deformable surface can contact a rigid surface, a deformable surface can contact itself, or a set of nodes can contact a deformable or rigid surface. Once bodies are in contact, the surface interaction properties, such as the coefficient of friction, are defined. Another option is to define ``spot welds'' whose stiffness can degrade and eventually fail, causing surface debonding.6.2  Defining contactThe contact definition in ABAQUS/Explicit has two parts: the definition of the surfaces that may come into contact and the definition of the way the surfaces interact. In ABAQUS/Explicit, as in ABAQUS/Standard, the definition of surfaces is part of the model data. In ABAQUS/Explicit contact is applied as a constraint, somewhat like a boundary condition, and as such it can be applied and removed at will during the history of the simulation.6.2.1  Defining surfacesSurfaces are created using the *SURFACE option. The TYPE parameter on this option dictates the type of surface created:톂 he parameter TYPE=ELEMENT (default) on the *SURFACE option creates a surface by specifying the underlying element faces forming the surface.톂 he parameter TYPE=NODE on the *SURFACE option creates a pure slave surface composed of the specified set of nodes. Nodes on any elements can be part of this node-based surface. For several reasons, including more accurate frictional forces and the ability to use the balanced master-slave approach, it is better to use the *SURFACE option without the parameter TYPE=NODE when possible.The concepts of master and slave surfaces are discussed later in this chapter.톂 he TYPE parameter on the *SURFACE option can also be used to specify the specific form of an analytical rigid surface. The different values that the TYPE parameter can take in this case are discussed later in this chapter.Surfaces on continuum elementsA two-dimensional, first-order continuum element, such as CPE4R, has four faces consisting of the segments defined by nodes 1-2, 2-3, 3-4, and 4-1, respectively, as shown in Figure 6-1  . The face identifiers consist of the letter ``S'' followed by the face number. A surface is defined by specifying the element number and face identifier for all the faces that form the surface. Figure 6-1  Face numbers on a two-dimensional, first-order (4-node) element.For example, use the following option block to include face 2 of the element shown in Figure 6-1   in a surface called FLANGE1:*SURFACE, NAME=FLANGE15, S2As is the case for many options in ABAQUS, both element numbers and element sets can be used; the use of element sets can make the definition of large surfaces much easier. It is valid to specify both element sets and individual elements in the same *SURFACE option block. For example, the surface TOPSURF consists of the element faces shown in Figure 6-2   and is created as follows:*ELSET, ELSET=TOP, GENERATE5, 8*SURFACE, NAME=TOPSURF

Page 50: Getting Started With ABAQUS

TOP, S35, S48, S2Figure 6-2  Face numbers and elements that form the surface TOPSURF.ABAQUS can determine the free faces of two- and three-dimensional continuum elements automatically and use them to create a surface. To use this capability, simply include all of the elements whose free faces compose the surface on the data lines of the *SURFACE option. Element sets as well as individual element numbers can be used. ABAQUS will ignore any elements that do not contain free faces. For example, the surface shown in Figure 6-2   could also be defined as follows:*SURFACE, NAME=TOPSURFTOP,While generally not necessary, surfaces on continuum elements also can be defined by a set of nodes. To define a node-based surface, specify node numbers or node sets on the data lines following the *SURFACE, TYPE=NODE option.Surfaces on shell, membrane, and rigid elementsThere are three ways to define surfaces on shell, membrane, and rigid elements: using single-sided surfaces, double-sided surfaces, and node-based surfaces.Using single-sided contact surfaces, you select one of the two available faces as a contact surface. The face whose normal points in the direction of the positive element normal is called SPOS, while the face whose normal points in the direction of the negative element normal is called SNEG, as shown in Figure 6-3Figure 6-3  Surfaces on two- and three-dimensional shell, membrane, and rigid elements.Using the right-hand rule, the nodal ordering of an element defines the positive element normal. By default, the contact surface is the actual element surface, taking into consideration the current thickness of the element. When using shell elements, you can instead specify the shell reference surface (the surface defined by the nodes) as the contact surface, by using the NO THICK parameter on the *SURFACE option. The following option block defines surface SURF1 as the surface composed of all the SPOS faces of the elements in element set SHELLS:*SURFACE, NAME=SURF1SHELLS, SPOSSingle-sided contact surfaces account for contact only on the face and not on the edge. Using a node-based surface in conjunction with a single-sided surface models contact on both the face and the edge. The following option block defines a node-based surface named EDGE, composed of the edge nodes in a node set called NEDGE, as shown in Figure 6-4:*SURFACE, TYPE=NODE, NAME=EDGENEDGE,Figure 6-4  Node-based surface for contact on a shell edge.Double-sided contact surfaces are more general because both the SPOS and SNEG faces and all free edges are included automatically as part of the contact surface. Contact can occur on either face or on the edges of the elements forming the double-sided surface. For example, a slave node can start on one side of a double-sided surface and then travel around the perimeter to the other side during the course of an analysis. No face identifier is specified when defining double-sided contact because both faces are included automatically. Currently, double-sided surfaces are available only for three-dimensional elements. The following option block defines surface SURF2 as the surface composed of both faces of the elements in element set SHELLS:*SURFACE, NAME=SURF2SHELLS,Rigid surfacesRigid surfaces are the surfaces of rigid bodies. They can be defined as an analytical shape, or they can be based on the underlying surfaces of elements associated with the rigid body.Analytical rigid surfaces are created by defining a series of connected lines, arcs, and parabolas. The parameter ANALYTICAL SURFACE on the *RIGID BODY option binds an analytical rigid surface (defined with the TYPE parameter on the *SURFACE option) with a rigid body. The *RIGID BODY option must be defined in the model definition. The TYPE parameter on the *SURFACE option defines the dimensionality of the surface, and it has three possible values:톃 se TYPE=SEGMENTS to define a two-dimensional analytical rigid surface.톃 se TYPE=CYLINDRICAL to define a three-dimensional analytical rigid surface that is extruded infinitely in the out-of-plane direction.톃 se TYPE=REVOLUTION to define a three-dimensional analytical rigid surface of revolution.The following is an example input for the two-dimensional analytical rigid surface named SRIGID shown in Figure 6-5  :*SURFACE, TYPE=SEGMENTS, NAME=SRIGIDSTART, 5.0, 0.0LINE, 10.0, 0.0CIRCL, 15.0, 5.0, 10.0, 5.0 where the rigid body is defined previously by *RIGID BODY, ANALYTICAL SURFACE=SRIGID, REF NODE=10000Figure 6-5  Analytical rigid surface.Discretized rigid surfaces are based on the underlying elements that make up a rigid body; thus, they can be more geometrically complex than analytical rigid surfaces. Discretized rigid surfaces are defined using the *SURFACE option in exactly the same manner as surfaces on deformable bodies.Surfaces on one-dimensional, deformable elementsContact surfaces on one-dimensional, deformable elements, such as beams and trusses, must be node-based surfaces. To define a node-based surface, simply include the desired node numbers and node sets on the data line following the *SURFACE, TYPE=NODE option, as follows:*SURFACE, TYPE=NODE, NAME=SNODE101, 102, NSET1, NSET26.2.2  Defining the interaction between surfacesTo define an interaction between two surfaces, you must specify the surfaces as a contact pair and the type of interaction between them.

Page 51: Getting Started With ABAQUS

Contact pairsDefine possible contact between two surfaces in an ABAQUS simulation by specifying the surface names on the *CONTACT PAIR option. A surface can appear in any number of contact pairs. When defining a contact pair, you must decide whether to use the small-sliding formulation or the more general finite-sliding formulation. Small sliding is appropriate if the relative motion of the two surfaces is less than a small proportion of the characteristic length of an element face. The small-sliding formulation is selected by including the SMALL SLIDING parameter on the *CONTACT PAIR option. The small-sliding contact search algorithm is much less expensive than the finite-sliding algorithm.Each contact pair must refer to a surface interaction definition, in much the same way that each element must refer to an element property definition. Use the INTERACTION parameter on the *CONTACT PAIR option to refer to a *SURFACE INTERACTION option, through which the different surface interaction models, such as *FRICTION, can be defined.The following example specifies that surfaces FLANGE1 and FLANGE2 can interact with each other and that the amount of relative sliding will be small:*CONTACT PAIR, INTERACTION=FRIC, SMALL SLIDING FLANGE1, FLANGE2A surface may contact itself if only one surface is given on the *CONTACT PAIR option; for example,*CONTACT PAIR, INTERACTION=FRICTUBE,Single-surface contact is much more computationally expensive than two-surface contact. However, single-surface contact is useful if a surface folds over and contacts itself during the analysis. In such cases it is not possible to identify prior to the analysis which parts of the surface will interact.Specifying the interaction modelEach contact pair must refer to a *SURFACE INTERACTION option block, which can specify a model for the interaction between the contacting surfaces. The two possible models are *FRICTION, which defines the frictional properties of the surfaces, and *BOND, which defines a spot weld that can degrade and fail at the specified node. If neither of these options is specified, the default is frictionless contact with no bonding. The friction model is discussed in ``Surface interaction models,'' Section 6.3.3. The following *SURFACE INTERACTION option block defines an interaction named FRIC with a friction coefficient of 0.1:*SURFACE INTERACTION, NAME=FRIC*FRICTION0.1,6.3  Contact algorithmsThe contact search algorithm, the contact constraint, and the surface interaction models available in ABAQUS/Explicit are discussed in the following sections.6.3.1  Contact search algorithmDetermining the parts of the contact surfaces that are in contact at any given time is the most expensive part of the contact analysis.Two-surface contactBecause it is possible for a node on one contact surface to contact any of the facets on the opposite contact surface, ABAQUS/Explicit uses sophisticated search algorithms for tracking the motions of the contact surfaces. While the contact search algorithm is transparent to the user and is rarely a concern, some situations require special consideration and an understanding of the methods. While the balanced master-slave algorithm is used in most cases, for discussion we consider a pure master-slave algorithm. (The difference between the two approaches is that the balanced approach performs the same contact search twice, reversing the master and slave surfaces the second time.)At the beginning of each step an exhaustive, global search is conducted to determine the closest master surface facet for each slave node of each contact pair. Because a global search considers the possibility of contact between every slave node and every master facet, a global search is very expensive and is performed only every 100 increments by default. Figure 6-6   shows the global search to determine which of all of the facets on the master surface is the closest facet to slave node 50. The search determines that the closest master facet is the face of element 10. Node 100 is determined to be the node on that master facet that is closest to slave node 50; therefore, it is designated as the tracked master surface node. The goal of the global search is to determine the closest master facet and a tracked master surface node for each slave node.Figure 6-6  Two-dimensional global contact search.Since the cost of each global search is so high, a less expensive local search is performed in most increments. In a local search a given slave node searches only the facets that are attached to the previous tracked master surface node to determine the closest facet. In Figure 6-7   the slave surface of the model shown in Figure 6-6previous increment. Since the previous tracked master surface node was 100, the nearest master surface facet of those attached to node 100 (facets 9 and 10) is determined.Figure 6-7  Two-dimensional local contact search.In this case facet 10 is the closest to node 50. The next step is to determine the current tracked master surface node from the nodes attached to facet 10. This time node 101 is the closest node on facet 10 to slave node 50. The local search continues until the tracked master surface node remains the same from one iteration of the search to the next. In this case the tracked master surface node changed from 100 to 101, so the local search continues. Again, the closest master facet is determined from the master facets attached to node 101, in this case facets 10 and 11. Facet 11 is determined to be the closest facet, and node 102 is determined to be the new tracked master surface node. Since node 102 is truly the closest master node to slave node 50, further iteration does not change the tracked master surface node, and the local search ends.Since the time increments are very short, for most situations the contacting bodies move a very small amount from one increment to the next, and the local contact search is adequate to track the motion of the contact surfaces. However, there are certain situations that may cause the local contact search to fail. One such situation, illustrated in Figure 6-8  , is a master surface containing a hole. Figure 6-8  Example in which local contact search may fail.The shaded element face has been identified as the closest master facet to the slave node belonging to a separate, contacting body. Thus, ABAQUS/Explicit conducts a local search of the master facet and its neighbors for contact in the next increment. If the slave node later displaces across the hole and reaches the other side before another global search is performed, the local search algorithm will still be checking only the shaded facet and its neighbors. Potential contact between the slave node and master facets across the hole will not be recognized in the local contact search. To overcome the problem, force ABAQUS/Explicit to perform a global contact search more often because a global search will recognize contact across the hole. To force the global contact search more often than the default (every 100 increments), set the GLOBTRKINC parameter on the *CONTACT CONTROLS option equal to the desired number of increments between global contact searches. Use caution when using the GLOBTRKINC parameter because frequent global contact searches are computationally expensive.Single-surface contactAnother option is to allow a single surface to contact itself. For example, the inside of a tube could be defined as a single surface, which contacts itself as the tube is crushed. Due to the generality and complexity of single-surface contact, a global contact search is performed every few increments, making single-surface contact significantly more expensive than

Page 52: Getting Started With ABAQUS

two-surface contact.6.3.2  Applying the normal contact constraintBy default, ABAQUS/Explicit uses a kinematic contact formulation that achieves precise compliance with the contact conditions using a predictor/corrector algorithm. The increment at first proceeds under the assumption that contact does not occur. If at the end of the increment there is an overclosure, iterations are performed to correct the kinematics of the slave node to comply with the contact. The depth of each node's penetration, its mass, and the time increment are used to calculate the resisting force that would have been required to prevent the penetration from occurring.The normal contact constraint can optionally be enforced with a penalty contact algorithm. The penalty contact algorithm results in a less strict enforcement of contact constraints than the kinematic algorithm as it allows small residual penetrations of the slave nodes into the master surface. The penalty stiffness is chosen so that the effect on the time increment is minimal yet the penetration is not significant. The penalty stiffness is chosen automatically by ABAQUS/Explicit but can be overridden by specifying a penalty scale factor or a "softened" contact relationship. The penalty contact algorithm can model some types of contact that the kinematic contact algorithm cannot. For example, the penalty algorithm allows modeling of contact between two rigid surfaces (except when both surfaces are analytical rigid surfaces). To select the penalty algorithm, set the MECHANICAL CONSTRAINT parameter to PENALTY on the *CONTACT PAIR option.Pure master-slave approachIn the pure master-slave approach one of the surfaces is the master surface and the other is the slave surface. As the two bodies come into contact, the resisting forces of the slave nodes are distributed to the nodes on the master surface. When the kinematic contact formulation is used, these forces and the masses of the nodes are used to calculate the acceleration correction for the master surface nodes. The acceleration corrections for the slave nodes are then determined using the predicted penetration for each node, the time increment, and the acceleration corrections for the master surface nodes. These corrections are used to obtain a corrected configuration in which the contact constraints are enforced. Unless the mesh is adequately refined, it is possible for the master surface to penetrate the slave surface, while the slave nodes are strictly constrained against penetrating the master surface. When the penalty contact formulation is used, equal and opposite contact forces (proportional to the penetration distance) are applied to the master and slave nodes at the penetration points. The pure master-slave approach is used by default for shell-to-solid contact, in which the solid is the pure master surface, and for deformable-to-rigid contact, in which the rigid surface is always the pure master. The pure master-slave constraint when kinematic compliance is used is illustrated in Figure 6-9Figure 6-9  Pure master-slave contact constraint with kinematic compliance.Balanced master-slave approachBalanced master-slave contact is more expensive computationally than pure master-slave contact. However, it minimizes the penetration of the contacting bodies and, thus, provides more accurate results in most cases. The balanced approach simply applies the pure master-slave algorithm twice, reversing the surfaces on the second pass. One set of acceleration corrections is obtained with surface 1 as the slave, and another set of corrections is obtained with surface 2 as the slave. The final acceleration corrections are obtained by taking a weighted average of the two acceleration corrections, where the weight of the average is specified by the user using the WEIGHT parameter on the *CONTACT PAIR option. For most element types the default weight is 0.5 so that the same weight is used for each of the acceleration corrections. Setting WEIGHT to 1.0 specifies a pure master-slave relationship with the first surface as the master surface. Conversely, a weight of zero means that the second surface is the master surface. The balanced master-slave contact constraint when kinematic compliance is used is illustrated in Figure 6-10  .Figure 6-10  Balanced master-slave contact constraint with kinematic compliance.6.3.3  Surface interaction modelsThere are several options for surface interaction models to use once contact is established.Friction modelIf the *FRICTION option is used, ABAQUS/Explicit uses a Coulomb friction model to resist relative tangential motion between two contacting surfaces. If the *FRICTION option is not used, the default friction coefficient is zero. The tangential motion is zero until the surface traction reaches a critical shear stress value, which depends on the normal contact pressure, according to the following equation:where  is the coefficient of friction and  is the normal contact stress. Figure 6-11   shows the variation of shear stress with slip, .Figure 6-11  Coulomb friction model.Optionally, a friction stress limit can be specified using the TAUMAX parameter on the *FRICTION option. (TAUMAX cannot be used when one of the surfaces in the contact pair has been defined as a node-based surface)The *FRICTION option is a suboption of the *SURFACE INTERACTION option. In the following example, a coefficient of friction of 0.1 is defined with a friction stress limit of 80 MPa:*SURFACE INTERACTION, NAME=INTER*FRICTION, TAUMAX=80.0E60.1,Often the friction coefficient at the initiation of slipping from a sticking condition is different from the friction coefficient when sliding. The former is typically referred to as the static friction coefficient, and the latter is referred to as the kinetic friction coefficient. In ABAQUS/Explicit an exponential decay law is available to model the transition between static and kinetic friction (see Figure 6-12  ). Figure 6-12  Exponential decay friction model.These friction coefficients are defined when the EXPONENTIAL DECAY parameter is used on the *FRICTION option.*FRICTION, EXPONENTIAL DECAY, , Frictional constraints are imposed using a predictor/corrector algorithm much like that used to apply the normal contact constraint. The force required to maintain a node's position on the opposite surface in the predicted configuration is calculated using the mass associated with the node, the distance the node has slipped, and the time increment. If the shear stress at the node calculated using this force is greater than , the surfaces are slipping, and the force corresponding to corrections tangential to the surface at the slave node and the nodes of the master surface facet that it contacts.Tied contactTied contact bonds together the tangential and normal motions of surfaces initially in contact throughout the analysis. Rotational degrees of freedom are not constrained. Tied contact can be specified only in the first step by using the TIED parameter on the *CONTACT PAIR option. If the surfaces specified under *CONTACT PAIR are not in contact at the start of the analysis, tied contact will not be imposed, and the two surfaces will never interact throughout the analysis. To force the surfaces to be exactly in contact at the start of the analysis, use the required ADJUST parameter on the *CONTACT PAIR option. ADJUST forces any initially overclosed nodes, as well as any open nodes within the specified

Page 53: Getting Started With ABAQUS

distance, to lie exactly on the contact surface. If nodes have to be adjusted by distances that are a large fraction of the length of the side of the element (to which the node is attached), the element can become severely distorted; avoid large adjustments if possible.Tied contact is particularly useful for rapid mesh refinement between dissimilar meshes.Spot welds and debondingNodes can be ``spot welded'' to the nearest point on the master surface using the *BOND option, which is a suboption of *SURFACE INTERACTION. The bond between the slave node and the master surface can yield and degrade until it eventually fails, according to the specified failure criterion. Once the bond has failed, the slave node interacts with the master surface just like a nonbonded slave node in a pure master-slave contact pair. Since a node set is specified under *BOND, the option can be associated only with a pure master-slave contact pair, where the node set is the slave. Use the WEIGHT parameter on the *CONTACT PAIR option to force the pure master-slave relationship. The resulting contact constraint is similar to that applied with tied contact, except that in this case the bond is imperfect and can yield and fail. If the slave nodes are not exactly in contact with the master surface at the start of the analysis, the slave nodes are adjusted in a strain-free manner so that they are in contact.The bond carries a normal force and a shear force, and the yield criterion uses a combination of the two forces. The post-yield behavior is defined in one of two ways: a time-to-failure model or a damaged failure model. The time-to-failure model gradually shrinks the yield surface to zero over a specified time period, while the damaged failure model defines the failure behavior on the basis of the total energy dissipated in the Mode I and Mode II response. For further information, see the ABAQUS/Explicit User's Manual.Other contact interaction optionsOther contact interaction options include adhesive contact behavior, softened contact behavior, and viscous contact damping. These options are not discussed in this guide. Details about them can be found in the ABAQUS/Explicit User's Manual.6.4  Modeling considerationsWe now discuss the following modeling considerations: correct definition of surfaces, possibility of overconstraining the model, and initial overclosures.6.4.1  Correct surface definitionsCertain rules must be followed when defining contact surfaces. All surfaces must be continuous and simply connected, while a valid surface can be either open or closed. The continuity requirement has several implications for what constitutes a valid or invalid surface definition.In two dimensions the surface must be either a simple, nonintersecting curve with two terminal ends or a closed loop. Figure 6-13dimensional surfaces. Figure 6-13  Valid and invalid two-dimensional surfaces.In three dimensions an edge of an element face belonging to a valid surface may be either on the perimeter of the surface or shared by one other face. Two element faces forming a contact surface cannot be joined just at a shared node; they must be joined across a common element edge. An element edge cannot be shared by more than two surface facets. Figure 6-14   illustrates valid and invalid three-dimensional surfaces.In addition, it is possible to define two- or three-dimensional double-sided surfaces. In this case both sides of a shell, membrane, or rigid element are included in the same surface definition, as shown in Figure 6-15  .Extending surfacesABAQUS/Explicit does not extend surfaces automatically beyond the perimeter of the surface defined by the user. Figure 6-14  Valid and invalid three-dimensional surfaces.Figure 6-15  Valid double-sided surface.If a node from one surface is in contact with another surface and it slides along the surface until it reaches an edge, it may ``fall off the edge.'' Such behavior can be troublesome because the node may later reenter from the back side of the surface, thereby violating the kinematic constraint and causing large jumps in acceleration at that node. Therefore, it is good modeling practice to extend surfaces somewhat beyond the regions that will actually contact.Figure 6-16   shows two simple box-like bodies constructed of brick elements. The upper box has a contact surface defined only on the top face of the box. While it is a permissible surface definition in ABAQUS/Explicit, the lack of extensions beyond the ``raw edge'' could be problematic. In the lower box the surface wraps some distance around the side walls, thereby extending beyond the flat, upper surface. If contact is to occur only at the top face of the box, this extended surface definition minimizes contact problems by keeping any contacting nodes from going behind the contact surface.Figure 6-16  Surface perimeters.Mesh seamsDefining two nodes with the same coordinates (double noding) can generate a seam or crack in a valid surface that appears to be continuous, as shown in Figure 6-17sliding along the surface can fall through this crack and slide behind the contact surface. The contact algorithm will cause a large, nonphysical acceleration correction once penetration is detected. Mesh seams can be detected in ABAQUS/Viewer by drawing the free edges of the model. Any seams that are not part of the desired perimeter can be double-noded regions.Figure 6-17  Example of a double-noded mesh.Complete surface definitionFigure 6-18   illustrates a two-dimensional model of a simple connection between two parts. The contact definition shown in the figure is not adequate for modeling this connection because the surfaces do not represent a complete description of the geometry of the bodies. At the beginning of the analysis some of the nodes on surface 3 find that they are ``behind'' surfaces 1 and 2. Figure 6-19   shows an adequate surface definition for this connection. The surfaces are continuous and describe the entire geometry of the contacting bodies.Figure 6-18  Example of an incorrect surface definition.Figure 6-19  Correct surface definition.Consistent surface normalsNormal directions must be consistent for surfaces with underlying shell, membrane, or rigid elements. The face identifier SPOS indicates that the surface is on the face with the positive outward normal, and the face identifier SNEG indicates the reverse. The user must define surfaces on elements of these types so that the normals do not ``flip'' as the surface is traversed. Figure 6-20   shows a mesh of SAX1 elements whose normals are not continuous from one element to the next. If a surface was defined using the SPOS face for all the elements, ABAQUS/Explicit would issue a warning message stating that the surface is not valid. Figure 6-20  Inconsistent surface normals.A valid surface could be defined with this mesh if the surface definition shown in the figure, which uses both SPOS and SNEG face identifiers to accommodate the inconsistent

Page 54: Getting Started With ABAQUS

element normals, is used.Highly warped surfacesWhen a surface is highly warped from one facet to the next, a more expensive search algorithm must be used than the algorithm required when the surface is not highly warped. To keep the solution as efficient as possible, ABAQUS monitors the warpage of the surfaces and issues a warning if surfaces become too warped; if the normal directions of adjacent facets differ by more than 20? ABAQUS issues a warning message. Once a surface is deemed to be highly warped, ABAQUS switches from the more efficient contact search algorithm to a more accurate search algorithm to account for the difficulties posed by the highly warped surface.For the sake of efficiency ABAQUS does not check for highly warped surfaces every increment. Rigid surfaces are checked for high warpage only at the start of the step, since rigid surfaces do not change shape during the analysis. Deformable surfaces are checked for high warpage every 20 increments by default. Some analyses may have surfaces whose warpage increases in severity quite suddenly, making the default 20 increment frequency check inadequate. The user can change the frequency of the warping checks by setting the WARP CHECK PERIOD parameter on the *CONTACT CONTROLS option to the desired number of increments. Some analyses in which the surface warping is less than 20?may also require the more accurate contact search algorithm associated with highly warped surfaces. Use the WARP CUT OFF parameter on the *CONTACT CONTROLS option to redefine the angle that defines high warpage.Rigid element discretizationComplex rigid surface geometries can be modeled using rigid elements. Rigid elements in ABAQUS/Explicit are not smoothed; they remain faceted exactly as defined by the user. The advantage of unsmoothed surfaces is that the surface defined by the user is exactly the same as the surface used by ABAQUS; the disadvantage is that faceted surfaces require much higher mesh refinement to define smooth bodies accurately. In general, using a large number of rigid elements to define a rigid surface does not increase the CPU costs significantly. However, a large number of rigid elements does increase the memory overhead significantly.The user must ensure that the discretization of any curved geometry on rigid bodies is adequate. If the rigid body discretization is too coarse, contacting nodes on the deformable body may ``snag,'' leading to erroneous results, as illustrated in Figure 6-21  . Figure 6-21  Potential effect of coarse rigid body discretization.A node that is snagged on a sharp corner may be trapped from further sliding along the rigid surface for some time. Once enough energy is released to slide beyond the sharp corner, the node will snap dynamically before contacting the adjacent facet. Such motions cause noisy solutions. The more refined the rigid surface, the smoother the motion of the contacting slave nodes.Analytical rigid surfaces are smooth and are computationally efficient. They should normally be used for rigid bodies whose shape is an extruded profile or a surface of revolution.6.4.2  Overconstraining the modelJust as multiple conflicting boundary conditions should not be defined at a given node, multi-point constraints and contact conditions generally should not be defined at the same node because they may generate conflicting kinematic constraints. Unless the constraints are entirely orthogonal to one another, the model will be overconstrained; the resulting solution will be quite noisy, as ABAQUS/Explicit tries to satisfy the conflicting constraints.6.4.3  Mesh refinementFor contact as well as all other types of analyses, the solution improves as the mesh is refined. For contact analyses using a pure master-slave approach, it is especially important that the slave surface is refined adequately so that the master surface facets do not overly penetrate the slave surface. By default, deformable-deformable contact uses a balanced master-slave approach, which does not require high mesh refinement on the slave surface to have adequate contact compliance. Mesh refinement is generally most important with contact between deformable and rigid bodies; in this case the deformable body is always the pure slave surface and, thus, must be refined enough to interact with any feature on the rigid body. Figure 6-22   shows an example of the penetration that can occur if the discretization of the slave surface is poor compared to the dimensions of the features on the master surface. If the deformable surface were more refined, the penetrations of the rigid surface would be much less severe.Figure 6-22  Example of inadequate slave surface discretization.Tied contact for mesh refinementIncluding the TIED parameter on the *CONTACT PAIR option prevents surfaces initially in contact from penetrating, separating, or sliding relative to one another. ``Tied'' contact is, therefore, an easy means of mesh refinement. Since any gaps that exist between the two contact surfaces, however small, will result in nodes that are not tied to the opposite contact boundary, you must use the ADJUST parameter to ensure that the two surfaces are exactly in contact at the start of the analysis.As the tied contact formulation constrains only translational degrees of freedom, any rotational degrees of freedom are left unconstrained. For example, if you use tied contact to attach a stiffener made of shell elements perpendicularly to a plate of shell elements, the stiffener will be free to pivot about its contact edge. Therefore, when using tied contact with structural elements, you must ensure that the unconstrained rotations will not cause problems.6.4.4  Initial contact overclosureABAQUS/Explicit does not allow any initial overclosure of contact surfaces. The undeformed coordinates of nodes on contact surfaces are, therefore, adjusted to remove any initial overclosure. When using the balanced master-slave approach, both surfaces are adjusted; when using the pure master-slave approach, only the slave surface is adjusted. Displacements associated with adjusting the surface to remove overclosures do not cause any initial strain or stress for contact pairs defined in the first step of the analysis. When using the balanced master-slave approach, contact will not always resolve initial overclosures exactly, resulting in stresses even in the first increment. Switching to the pure master-slave approach may reduce the stresses.In subsequent steps any nodal adjustments to remove initial overclosures cause strains that often cause severe mesh distortions because the entire nodal adjustments occur in a single, very brief increment. For example, if the node is overclosed by 1.0 ?10-3 m and the increment time is 1.0 ?10-7 s, the acceleration applied to the node to correct the overclosure is 2.0 ?1011 m/s2. Such a large acceleration applied to a single node typically will cause warnings about deformation speed exceeding the wave speed of the material and warnings about severe mesh distortions a few increments later, once the large acceleration has deformed the associated elements significantly. Even a very slight initial overclosure can induce extremely large accelerations because of the small time increments. Consequently, it is important that in Step 2 and beyond any new contact surfaces that you define are not overclosed.Figure 6-23   shows a common case of initial overclosure of two contact surfaces. All of the nodes on the contact surfaces lie exactly on the same arc of a circle; but since the mesh of the inner surface is finer than that of the outer surface and since the element edges are linear, some nodes on the finer, inner surface initially penetrate the outer surface.Figure 6-23  Original overclosure of two contact surfaces.Assuming that the pure master-slave approach is used, Figure 6-24   shows the initial, strain-free displacements applied to the slave-surface nodes by ABAQUS/Explicit. In the absence of external loads this geometry is stress free. If the default, balanced master-slave approach is used, a different initial set of displacements is obtained, and the resulting mesh is not entirely stress free.

Page 55: Getting Started With ABAQUS

Figure 6-24  Corrected contact surfaces.6.5  Example: circuit board drop testIn this example you will investigate the behavior of a circuit board in protective crushable foam packaging dropped at an angle onto a rigid surface. Your goal is to assess whether the foam packaging is adequate to prevent circuit board damage when the board is dropped from a height of 1 meter. Figure 6-25foam packaging in millimeters and the material properties.Figure 6-25  Dimensions in millimeters and material properties.6.5.1  Coordinate systemWhile the circuit board will be dropped at an angle, it is easiest to use the *SYSTEM option to define the mesh aligned with a local rectangular coordinate system, as shown in Figure 6-25  . The *SYSTEM option transforms nodal coordinates from the local coordinate system to the global coordinate system. This option allows you to define the circuit board in the x-z plane of the local coordinate system, which is rotated by the desired angle relative to the global coordinate system.The *SYSTEM option defines a new coordinate system by specifying three points: a local origin, a point on the local x-axis, and a point in the local x-y plane. Before defining the nodes for the circuit board, use the following option to tilt the mesh so that it lands on its corner:*SYSTEM0., 0., 0., .5, .707, .25-.5, .707, -.5 All subsequent nodal definitions will be in this local coordinate system. To reset the coordinate system to the default, use another *SYSTEM option with no data lines.6.5.2  Mesh designThe overall mesh for this problem is shown in Figure 6-26  . Figure 6-26  Mesh of the circuit board and foam packaging.Define the circuit board so that the shell normals are in the direction indicated. Defining the bottom corner of the foam packaging as the origin of your model will ensure the correct positioning of the circuit board and packaging. Since the ground onto which the board will be dropped is effectively rigid, use a single R3D4 element for this part of the model. The packaging is a three-dimensional solid structure that should be modeled using C3D8R elements. The circuit board itself can be considered as a thin, flat plate with various chips attached to it. Therefore, model the circuit board with S4R elements, and model the chips with MASS elements.Since you will be using shell elements for the circuit board, ABAQUS/Explicit will, by default, use the current shell element thickness when checking for contact. The circuit board and its slot in the foam packaging are both the same thickness (2 mm) so that there is a snug fit between the two bodies. In this example the circuit board is a mesh of 10 ?10 S4R elements, and the foam packaging is a mesh of 6 ?7 ?15 elements, as shown in Figure 6-27  . Figure 6-27  Packaging mesh detail.The MASS elements are positioned as shown in Figure 6-28  . The mesh for the packaging is too coarse near the impacting corner to provide highly accurate results. However, the mesh is adequate for a low-cost preliminary study.6.5.3  Node and element setsFigure 6-28   and Figure 6-29   show all of the sets necessary to apply the element properties, loads, initial conditions, and boundary conditions, as well as to request output for postprocessing.Figure 6-28  Position of mass elements on circuit board. Numbers in parentheses are (x, y) coordinates in millimeters based on a local origin at the bottom left-hand corner of the circuit board.Figure 6-29  Necessary node and element sets.Include the circuit board elements in an element set called BOARD, and include the corresponding circuit board nodes in a node set called BOARD. Similarly, for the foam packaging include the elements in an element set called PACK, and include the nodes in a node set called PACK. The element sets will be used to refer to material properties and to define contact conditions, and the node sets will be used to apply initial conditions. Include the bottom row of elements in the circuit board in an element set called LOWBOARD for use when defining contact. Create an element set called FLOOR containing the floor's rigid element and a node set called REF containing the reference node for the rigid surface modeling the floor. Include the mass elements modeling the chips in an element set called CHIPS.6.5.4  Simulating free fallTwo methods could be used to simulate the circuit board being dropped from a height of 1 meter. You could model the circuit board and foam at a height of 1 meter above the rigid surface and allow ABAQUS/Explicit to calculate the motion under the influence of gravity; however, this method is clearly impractical because of the large number of increments required to complete the ``free-fall'' part of the simulation. The most efficient method is to model the circuit board and packaging in an initial position very close to the surface with an initial velocity to simulate the 1 meter drop (4.439 m/s).6.5.5  Reviewing the input file--the model dataWe now review the model data required for this simulation, including the model description, the node and element definitions, element and material properties, boundary and initial conditions, and surface definitions.Model descriptionUsing the *HEADING option, provide a suitable heading for your model, such as the one shown below. You should use SI units in your model.*HEADINGCircuit board drop test1.0 meter dropSI units (kg, m, s, N)Nodal coordinates and element connectivityUse your preprocessor to generate the mesh in the local coordinate system. Precede the nodal definitions with the *SYSTEM option to transform the nodes into the tilted coordinate system, as described previously. Your nodal definitions for the foam packaging and circuit board will look something like the following:*SYSTEM0., 0., 0., .5, .707, .25-.5, .707, -.5*NODE

Page 56: Getting Started With ABAQUS

1,     0.005, -0.010, 0.01211,    0.005, -0.010, 0.162...**** Reset coordinate system***SYSTEMWhen you have finished defining the nodes in the rotated, local coordinate system, use the *SYSTEM option again without any data lines so that additional node numbers will be given in the global coordinate system. Define the nodes for the rigid surface so that it is large enough to keep the deformable bodies from falling off any of its edges. Use a 0.1 mm vertical clearance from the bottom corner of the foam packaging to ensure that there is no initial overclosure of the contact surfaces.Element propertiesGive each element set appropriate section properties. Include the appropriate MATERIAL parameter on each section option so that each set of elements is linked to a material definition. We have named the foam packaging material FOAM, and we will define it in the next section. *SOLID SECTION, ELSET=PACK, MATERIAL=FOAMFor the circuit board it is most meaningful to output stress results in the longitudinal and lateral directions, aligned with the edges of the board. Therefore, we need to specify local material directions for the circuit board mesh. We can use the same local coordinate system that we previously defined using the *SYSTEM option. The desired material directions can be achieved using the *ORIENTATION option with the DEFINITION=COORDINATES parameter. On the first data line specify the x-, y-, and z-coordinates of two points, a and b, respectively, to define the local coordinate system. On the second data line specify an additional rotation of zero degrees about the local 3- (or z-) axis. The name of the ORIENTATION is then referred to on the *SHELL SECTION option.*SHELL SECTION, ELSET=BOARD, MATERIAL=PCB, ORIENTATION=OR10.002,*ORIENTATION, NAME=OR1, SYSTEM=RECTANGULAR,DEFINITION=COORDINATES0.5, 0.707, 0.25, -0.5, 0.707, -0.53, 0.0Define the mass of each of the chips on the circuit board to be 0.005 kg using the *MASS option.*MASS, ELSET=CHIPS0.005,Define the rigid body by referring to the element set FLOOR and the rigid body reference node on the *RIGID BODY option. You must specify the actual node number of the reference node and not the node set name.*RIGID BODY, ELSET=FLOOR, REF NODE=<reference node number>Material propertiesYou now need to define the material properties for the circuit board and the foam packaging. For the circuit board use a PCB plastic material with a Young's modulus of 45 GPa, a Poisson's ratio of 0.3, and a density of 500 kg/m3.*MATERIAL, NAME=PCB*ELASTIC45.E9, 0.3*DENSITY500.0,Model the foam packaging material using the crushable foam plasticity model. Use the *ELASTIC option to define the Young's modulus as 3 MPa and the Poisson's ratio as 0.0. The material density is 100.0 kg/m3. *MATERIAL, NAME=FOAM*ELASTIC 3.E6, 0.0*DENSITY 100.0,The yield surface of a crushable foam in the p-q (pressure stress-Mises equivalent stress) plane is illustrated in Figure 6-30Figure 6-30  Crushable foam model: yield surface in the p-q plane.The *CRUSHABLE FOAM, HARDENING=VOLUMETRIC option uses two data items to define the initial yield behavior. *CRUSHABLE FOAM, HARDENING=VOLUMETRIC 1.1, 0.1The first data item is the the ratio of initial yield stress in uniaxial compression to initial yield stress in hydrostatic compression, ; we have chosen it to be 1.0. The second data item is the ratio of yield stress in hydrostatic tension to initial yield stress in hydrostatic compression, . This data item is given as a positive value; in this problem we have chosen it to be 0.1.Figure 6-31  Foam hardening material data.Include hardening effects with the *CRUSHABLE FOAM HARDENING option. The first data item on each line is the yield stress in uniaxial compression, given as a positive value; the second data item on each line is the absolute value of the corresponding plastic strain. The crushable foam hardening model follows the curve shown in Figure 6-31*CRUSHABLE FOAM HARDENING0.22000E6, 0.0

Page 57: Getting Started With ABAQUS

0.24651E6, 0.10.27294E6, 0.20.29902E6, 0.30.32455E6, 0.40.34935E6, 0.50.37326E6, 0.60.39617E6, 0.70.41801E6, 0.80.43872E6, 0.90.45827E6, 1.00.49384E6, 1.20.52484E6, 1.40.55153E6, 1.60.57431E6, 1.80.59359E6, 2.00.62936E6, 2.50.65199E6, 3.00.68334E6, 5.00.68833E6, 10.0Boundary conditionsFully constrain the rigid surface representing the floor by applying a fixed boundary condition to the reference node, which you previously defined as node set REF.*BOUNDARYREF, ENCASTREInitial conditionsGive the circuit board and foam packaging an initial velocity of -4.43 m/s in the global 3-direction, corresponding to the velocity at the end of a 1 meter free fall.*INITIAL CONDITIONS, TYPE=VELOCITYBOARD, 3, -4.43PACK, 3, -4.43Surface definitionsDefine the surfaces that will experience contact during the analysis. You should determine not only which surfaces are in initial contact but also which surfaces are likely to come into contact during the analysis. The simplest and most general approach is to define the following surfaces:톂 he bottom portion of the circuit board.톂 he floor.톂 he foam packaging.Both sides of the circuit board can be included in the same double-sided surface definition by simply omitting the face identifier (SPOS or SNEG) from the surface definition. The entire foam packaging can be included in a surface definition by simply specifying the element set PACK and letting ABAQUS determine the free surface. Define the contact surface for the rigid floor so that its normal points toward the foam packaging. Depending on how you defined the rigid element for the floor, either SPOS or SNEG is the correct face identifier. *SURFACE, NAME=LOWBOARDLOWBOARD,*SURFACE, NAME=PACKPACK, *SURFACE, NAME=FLOORFLOOR, <SPOS or SNEG>6.5.6  Reviewing the input file--the history dataUse the *DYNAMIC, EXPLICIT option to select a dynamic stress/displacement analysis using explicit integration, and define the time period of the step as 20 ms using the following commands:*STEP*DYNAMIC, EXPLICIT, 0.02Creating the contact pairsUse the *CONTACT PAIR option to indicate which contact surfaces will interact during the analysis. Each contact pair must refer to a corresponding *SURFACE INTERACTION option through the INTERACTION parameter. Specify a coefficient of friction of 0.3 between each of the contacting surfaces. By default, ABAQUS/Explicit uses a pure master-slave approach for contact between shell elements and continuum elements. For this analysis, however, it is desirable to use the balanced master-slave approach instead by setting the WEIGHT parameter on the *CONTACT PAIR option to 0.5. *CONTACT PAIR, INTERACTION=FRIC, WEIGHT=0.5PACK, LOWBOARD*CONTACT PAIR, INTERACTION=FRICPACK, FLOOR*SURFACE INTERACTION, NAME=FRIC*FRICTION

Page 58: Getting Started With ABAQUS

0.3,Output requestsWrite the preselected field data to the output database file at 20 evenly spaced intervals during the analysis by including the following line in your input file:*OUTPUT, FIELD, VARIABLE=PRESELECT, NUMBER INTERVAL=20Write values of nodal displacement (U), velocity (V), and acceleration (A) for each of the attached chips as history data to the output database file. In addition, write element values of logarithmic strain (LE), stress (S), principal stress (SP), and logarithmic principal strain (LEP) at the surfaces (section points 1 and 5) of the element set BOTPART of the circuit board to which the bottom-most chip is attached. Select an output interval of 0.1 ms.*OUTPUT, HISTORY, TIME INTERVAL=0.1E-3*NODE OUTPUT, NSET=CHIPSU, V, A*ELEMENT OUTPUT, ELSET=BOTPART1, 5LE, S, SP, LEPWrite energy values summed over the entire model. Specifically, write values for kinetic energy (ALLKE), internal energy (ALLIE), elastic strain energy (ALLSE), artificial energy (ALLAE), and the energy dissipated by plastic deformation (ALLPD).*ENERGY OUTPUTALLIE, ALLKE, ALLPD, ALLAE, ALLSEIndicate the end of the step with the *END STEP option.6.5.7  Running the analysisSave your input in a file called circuit.inp. Run the analysis using the following command:abaqus job=circuit analysis This analysis is somewhat more complicated than the previous analyses in this guide, and it may take 45 minutes or more to run to completion, depending on the power of your computer.Status fileInformation concerning the initial stable time increment can be found at the top of the status file. The 10 most critical elements (i.e., those resulting in the smallest time increments) are also shown in rank order.  -------------------------------------------------------------------------------  MODEL INFORMATION (IN GLOBAL X-Y COORDINATES) -------------------------------------------------------------------------------      Total mass in model = 3.49594E-02    Center of mass of model = (-1.076768E-02, 4.948696E-02, 8.492264E-02)       Moments of Inertia :                  About Center of Mass              About Origin       I(XX)          6.655609E-05                  4.042923E-04       I(YY)          9.977436E-05                  3.559498E-04       I(ZZ)          6.921255E-05                  1.588800E-04       I(XY)         -1.344123E-05                  5.187227E-06       I(YZ)         -5.240334E-06                 -1.521594E-04       I(ZX)          3.958669E-05                  7.155425E-05   -------------------------------------------------------------------------------  STABLE TIME INCREMENT INFORMATION -------------------------------------------------------------------------------       The stable time increment estimate for each element is based on    linearization about the initial state.        Initial time increment = 7.11932E-07      Statistics for all elements:       Mean = 1.04549E-05       Standard deviation = 4.05159E-06      Most critical elements :     Element number   Rank    Time increment   Increment ratio    ----------------------------------------------------------           42          1       7.119323E-07      1.000000E+00

Page 59: Getting Started With ABAQUS

           87          2       7.119323E-07      1.000000E+00           64          3       7.119323E-07      9.999999E-01           89          4       7.119323E-07      9.999999E-01            5          5       7.119324E-07      9.999998E-01           21          6       7.119324E-07      9.999998E-01           30          7       7.119324E-07      9.999998E-01           39          8       7.119324E-07      9.999998E-01           47          9       7.119324E-07      9.999998E-01           62         10       7.119324E-07      9.999998E-01     ***WARNING: At least one pair of adjacent slave nodes (2035,2034) on slave              surface PACK are on the opposite sides of double-sided master              surface LOWBOARD.       Maximum overclosure between surface PACK and surface LOWBOARD is 1.00000E-03.       ***WARNING: In contact pair 1, node 452 on the slave surface LOWBOARD has              143.02 times more mass than the mass of node 16064 on the master              surface PACK. Significant contact noise may result with the              kinematic contact algorithm when the slave nodes have              significantly greater mass than the master nodes. Suggested              workarounds include setting the WEIGHT parameter so that surface              PACK is a pure slave surface in the contact pair, using              mass-scaling to adjust the ratio of nodal masses, or using the              penalty contact algorithm.     -------------------------------------------------------------------------------  SOLUTION PROGRESS -------------------------------------------------------------------------------    STEP 1  ORIGIN 0.00000E+00     Total memory used for step 1 is approximately 750.7 kilowords   Global time estimation algorithm will be used.   Scaling factor :  1.0000               STEP      TOTAL       CPU     STABLE      CRITICAL  KINETIC  INCREMENT  TIME      TIME        TIME   INCREMENT    ELEMENT   ENERGY         0  0.000E+00 0.000E+00   00:00:01 7.119E-07      87   3.430E-01 Results number  0 at increment zero. ODB Field Frame Number    0 of   20 requested intervals at increment zero.     ***WARNING: Master surface PACK of contact pair # 1 contains facets with              out-of-plane warping of at least 20.000 degrees in increment 280.              Large warping that develops during an analysis often corresponds              to severe distortion of the underlying elements. It may be              appropriate to rerun the analysis with a refined mesh.        1181  1.000E-03 1.000E-03   00:01:28 8.418E-07      39   3.126E-01 ODB Field Frame Number    1 of   20 requested intervals at  1.000320E-03      2351  2.000E-03 2.000E-03   00:02:55 8.756E-07      50   2.269E-01                                   :                                   :                                   :The status file indicates several warnings were generated during the analysis. As a general rule you should always investigate the source of such warnings to determine whether or

Page 60: Getting Started With ABAQUS

not they are due to modeling errors or whether they can simply be ignored. The first warning states that adjacent slave nodes (on the foam packaging) initially interact with opposite sides of a double-sided master surface (the lower part of the circuit board). This is to be expected since only one element spans the slit at the base of the packaging (see Figure 6-27  ) and the circuit board is positioned in the center of this slit. The location of the offending nodes is visualized easily in ABAQUS/Viewer and confirmwarning. This warning can be ignored.The second warning states that there is a large mass mismatch between a slave node on the circuit board and a master node on the packaging, which may adversely affect the numerical solution when kinematic contact is used. You are not required to eliminate the source of this warning; however, if you choose to ignore it, evalmake sure they are reasonable. In this example we choose to ignore the warning.The final warning concerns out-of-plane warping. This warning is typically issued during impact and postbuckling analyses since very large deformations are common in these types of problems. If contact difficulties develop as a result, it may be necessary to refine your mesh.6.5.8  PostprocessingStart ABAQUS/Viewer by typing the following:abaqus viewer odb=circuitat the operating system prompt.Checking material directionsThe material directions obtained from this orientation definition can be checked with ABAQUS/Viewer. To plot the material orientation:1.First, change the view to a more convenient setting. From the toolbar, click .From the Views dialog box that appears, select the 1-3 setting.2.From the main menu bar, select Plot->Material Orientations.The orientation of the material directions of the circuit board at the end of the simulation are shown. The material directions are drawn in different colors. The material 1-direction is blue, the material 2-direction is yellow, and the 3-direction, if it is present, is red.3.To view the initial material orientation, select Result->Step/Frame. In the Step/Frame dialog box that appears, select Increment 0. Click Apply.ABAQUS/Viewer displays the initial material directions.4.To restore the display to the results at the end of the analysis, select the last increment available in the Step/Frame dialog box; and click OK.Animation of resultsYou will create a time-history animation of the deformation to help you visualize the motion and deformation of the circuit board and foam packaging during impact.To create a time-history animation:1.From the main menu bar, select Plot->Deformed Shape; or click  in the toolbox. The deformed model shape at the end of the analysis appears. The plot shows only the feature edges of the model. Change this so that all element edges are visible.2.Click Deformed Shape Plot Options in the prompt area. The Deformed Shape Plot Options dialog box appears.3.In this dialog box, choose the Hidden render style. Click OK.4.From the main menu bar, select Animate->Time History.The animation controls appear in the prompt area, and the animation of the deformed model shape begins.5.In the prompt area, click  to stop the animation after a full cycle has been completed.Change the animation options so that ABAQUS/Viewer swings through the animation at a faster rate.6.From the main menu bar, select Options->Animation; or click Animation Options in the prompt area to open the Animation Options dialog box.7.Do the following:a.Choose Swing.b.Drag the frame rate slider to Fast.8.Click OK, and replay the animation with these settings.Because you chose the Swing repetition mode, the animation steps backward through each frame when it reaches the end of the analysis instead of jumping back to the beginning of the analysis. ABAQUS/Viewer steps through the animation at a faster rate, because the frame rate has been increased. The deformed state of the foam and board at approximately 4 ms after impact is shown in Figure 6-32  .Figure 6-32  Deformed mesh at 4 ms.Plotting model energy histories Plot graphs of various energy variables versus time. Since accelerations and reaction forces can change significantly from one increment to the next, it is important to plot time histories of these variables with enough data points to provide an accurate representation of the results.To plot energy histories:1.From the main menu bar, select Result->History Output.The History Output dialog box appears.2.Select the ALLAE output variable, and save the data as Artificial Energy.3.Select the ALLIE output variable, and save the data as Internal Energy.4.Select the ALLKE output variable, and save the data as Kinetic Energy.5.Select the ALLPD output variable, and save the data as Plastic Dissipation.6.Select the ALLSE output variable, and save the data as Strain Energy.7.Click Dismiss.8.From the main menu bar, select Tools->XY Data->Manager.The XY Data Manager dialog box appears.9.In this dialog box, select all five curves and click Plot to view the X-Y plot.The selected curves are plotted in the viewport.

Page 61: Getting Started With ABAQUS

10.Click Dismiss to close the dialog box.Customize the appearance of the plot. Change the line styles of the curves, change the number of decimal places displayed on the X-axis, suppress the appearance of minor tick marks, and change the titles of the X- and Y-axes.11.Click XY Curve Options in the prompt area.The XY Curve Options dialog box appears.12.In this dialog box, select different line styles and thicknesses for the curves displayed in the viewport; then click Dismiss.13.Click XY Plot Options in the prompt area.The XY Plot Options dialog box appears.14.In this dialog box:a.Click the Axes tab, and set the number of decimal places to be displayed on the X-axis to zero.b.Click the Tick Marks tab, and set the number of minor tick marks to be displayed on both axes equal to zero.c.Click the Titles tab, and select user-specified title sources for both the X- and Y-axes. Enter an X-axis title of Time and a Y-axis title of Energy.15.Click OK to apply the settings. Now reposition the legend so that it appears inside the plot.16.From the main menu bar, select Canvas->Viewport Annotation Options.The Viewport Annotation Options dialog box appears.17.Click the Legend tab, and enter a relative position of (50,75) for the upper left corner of the legend box in the viewport.The energy histories appear as shown in Figure 6-33  .Figure 6-33  Energy results versus time.First, consider the kinetic energy history. At the beginning of the simulation the components are in free fall, and the kinetic energy is large. The initial impact deforms the foam packaging, thus reducing the kinetic energy. The components then rotate about the impacting corner until the side of the foam packaging impacts the floor at approximately 7 ms, further reducing the kinetic energy. The bodies remain in contact through most of the remainder of the simulation.The deformation of the foam packaging during impact transfers energy from kinetic energy to internal energy in the foam packaging and the circuit board. From Figure 6-33can see that the internal energy increases as the kinetic energy decreases. In fact, the internal energy is composed of elastic energy and plastically dissipated energy, both of which are also plotted in Figure 6-33  . Elastic energy rises to a peak and then falls as the elastic deformation recovers, but the plastically dissipated energy continues to rise as the foam is deformed permanently.Another important energy output variable is the artificial energy, which is a substantial fraction (approximately 15%) of the internal energy in this analysis. By now you should know that the quality of the solution would improve if the artificial energy could be decreased to a smaller fraction of the total internal energy.What causes high artificial strain energy in this problem?In the example in Chapter 4, "Finite Elements and Rigid Bodies," we saw that contact at a single node--such as the corner impact in this example--can cause hourglassing, especially in a coarse mesh. That example posed two methods of reducing the artificial strain energy: refining the mesh or rounding the impacting corner. For the current exercise, however, we shall continue with the original mesh, realizing that improving the mesh would lead to an improved solution.Stresses and strains in the circuit boardThe next result we wish to examine is the stress and strain in the circuit board near the location of the chips. If the stress or strain under the components exceeds a limiting value, the solder securing the chips to the board will fail. Study the lateral and longitudinal stress histories at the top face (SPOS) of the element set BOTPART, which contains an element to which the bottom-most chip is attached. To plot stress histories:1.From the main menu bar, select Result->History Output.The History Output dialog box appears.2.Select the S11 stress component on the SPOS surface of the element in element set BOTPART, and save the data as Lateral.3.Select the S22 stress component on the SPOS surface of the element in element set BOTPART, and save the data as Longitudinal.4.Click Dismiss.5.From the main menu bar, select Tools->XY Data->Manager.The XY Data Manager dialog box appears.6.In this dialog box, select the two curves defined above; and click Plot to view the X-Y plot.7. Click Dismiss to close the dialog box.As before, customize the plot appearance to obtain a plot similar to Figure 6-34  .Figure 6-34  Stress on the top surface of the circuit board.The stress plot shows that the longitudinal stress under the chip varies most of the time between -2 MPa and 2 MPa, with some peaks as large as -4 MPa; and the lateral stress follows a similar trend with less severe peaks. Both the lateral and the longitudinal stresses have peaks at approximately 7 ms. This point has been identified previously from the kinetic energy plot and animation as the instant at which the side of the packaging hits the floor.We wish to identify the peak strain in any direction. Therefore, the maximum and minimum principal logarithmic strains are of interest.To plot logarithmic strain histories:1.From the main menu bar, select Result->History Output.The History Output dialog box appears.2.Select the principal logarithmic strain LEP1 on the SPOS surface of the element in element set BOTPART, and save the data as Minimum.3.Select the principal logarithmic strain LEP2 on the SPOS surface of the element in element set BOTPART, and save the data as Maximum.4.Click Dismiss to close the dialog box.5.From the main menu bar, select Tools->XY Data->Manager.The XY Data Manager dialog box appears.6.In the dialog box, select the two curves defined above; and click Plot to view the X-Y plot.

Page 62: Getting Started With ABAQUS

The settings of the previous plot remain in effect and are inappropriate for this plot. Change the settings to make this X-Y plot more useful, as shown in Figure 6-35Figure 6-35  Principal logarithmic strain values versus time.The strain curves show peak and decay behavior similar to that of the stresses. The peak values are approximately 0.06% compressive and 0.04% tensile.Acceleration and velocity histories at the chipsAnother result that may assist us in determining the desirability of the foam packaging is the acceleration and velocity of the chips attached to the circuit board. Excessive accelerations during impact may damage the chips, even though they may remain attached to the circuit board. Therefore, we need to plot the acceleration histories of the three chips. Since we expect the accelerations to be greatest in the 3-direction, we plot the variable A3.To plot acceleration histories:1.From the main menu bar, select Result->History Output.The History Output dialog box appears.2.Select the acceleration A3 of the nodes in node set Chips, and save the three X-Y data objects as Chip 6001, Chip 6002, and Chip 6003. If you used the input file listed in ``Circuit board drop test,'' Section A.6, these correspond to nodes 60, 357, and 403, respectively.3.Click Dismiss.4.From the main menu bar, select Tools->XY Data->Manager.The XY Data Manager dialog box appears.5.In this dialog box, select the three curves created above; and click Plot.The X-Y plot appears in the viewport. As before, customize the plot appearance to obtain a plot similar to Figure 6-36  .Figure 6-36  Acceleration of the three chips in the z-direction.The acceleration of chip 6001, which is at the top of the board, is smooth compared to the accelerations of the other chips early in the simulation and reaches a peak at approximately 2 ms. However, for chip 6002 the peak acceleration is 2000 m/s2 at approximately 10 ms, while for chip 6003 the peak acceleration is 2500 m/s2 at approximately 7 ms, the instant at which the side of the packaging impacts the floor. This result may be accentuated by the board's rotation following the initial impact.The final plot, Figure 6-37  , shows how the three chips change velocity during impact. Figure 6-37  Velocity of the three chips in the z-direction.At the beginning of the simulation, the chips all have the same downward velocity after the 1 meter drop. The chips all decelerate following the initial impact; but as the board rotates, the velocity profiles diverge rapidly. Only the component near the base of the board, chip 6003, reaches a zero velocity at the end of the analysis.To plot velocity histories:1.From the main menu bar, select Result->History Output.The History Output dialog box appears.2.Select the velocity V3 of the nodes in node set Chips, and save the X-Y data objects as V3 Chip 6001, V3 Chip 6002, and V3 Chip 6003. If you used the input file listed in ``Circuit board drop test,'' Section A.6, these correspond to nodes 60, 357, and 403, respectively.3.Click Dismiss to close the dialog box.4.From the main menu bar, select Tools->XY Data->Manager.The XY Data Manager dialog box appears.5.In this dialog box, select the three curves defined above; and click Plot. The X-Y plot is shown in the viewport. As before, customize the plot appearance to obtain a plot similar to Figure 6-37  .6.6  Example: crushing of a tubeYou have been asked to analyze the crushing of a square, steel box tube between two rigid plates, as shown in Figure 6-38plate with a 500 kg mass at its other end. Both the tube and the rigid plate with mass have an initial velocity of 8.9408 m/s (20 mph) just before the tube's free end impacts a stationary rigid surface. During impact, the tube dissipates a large amount of the initial kinetic energy into plastic deformation, and your primary interest is in evalability to absorb kinetic energy. It is important to model the self-contact in the tube correctly as it folds upon itself while buckling. An application for such an analysis would be the design of energy absorption zones in an automobile frame.Figure 6-38  Problem description: square, steel box tube crushed between two plates.6.6.1  Mesh designFigure 6-39   shows the suggested mesh for this simulation. Figure 6-39  Box tube mesh.Shell elements are appropriate because the thickness (0.001 m) is 1/100th of the smallest planar dimension (0.1 m). While the initial model contains two symmetry planes, it is important to model the entire structure because it is not known whether the lowest buckling modes are symmetric or unsymmetric. Because the tube's deformation will involve buckling, it is necessary to seed the mesh with the lowest buckling modes of the tube to obtain a smooth postbuckling response. You will obtain the first 10 buckling modes by running an eigenvalue buckling analysis of the tube using ABAQUS/Standard and storing these modes in the results (.fil) file. You will then use the *IMPERFECTION option in ABAQUS/Explicit to read the buckling modes, scale them, and use them to perturb the nodal coordinates.6.6.2  Node and element setsAll of the necessary node and element sets are shown in Figure 6-40  . Figure 6-40  Necessary node and element sets.Place the shell elements in an element set called TUBE. Place the top and bottom rigid elements into their own element sets: RIGTOP and RIGBOT. The mass element belongs in an element set called MASS. Place the nodes on the top end of the tube (largest 1-coordinate) in a node set called TOP, and place the nodes on the bottom end of the tube (smallest 1-coordinate) in a node set called BOT. You will use these node sets later when defining interactions with the rigid plates. Create a node set called ALL containing all of the nodes on the tube. You will use this node set when defining the initial velocity of the tube.6.6.3  Preprocessing--creating the modelUse your preprocessor to generate the mesh shown in Figure 6-39  , which is 8 elements wide and 32 elements long. Use S4R elements to model the tube and R3D4 elements to model the rigid plates. Each of the shell elements is 0.0125 m ?0.0125 m, and the rigid elements are 0.2 m ?0.2 m. Define the shell elements such that the normals all point outward. Define a mass element with a mass of 500 kg at the rigid body reference node of the bottom rigid body. In the ABAQUS/Explicit analysis you will give the mass element and

Page 63: Getting Started With ABAQUS

the tube an initial velocity, and its momentum will cause the tube to crush against the top rigid plate. This mass element is not necessary for the ABAQUS/Standard analysis, which is static; however, it does no harm to include the mass in both input files.6.6.4  Reviewing the input file for the ABAQUS/Standard buckling analysis--the model dataBefore creating the input file for the ABAQUS/Explicit analysis, you must create the input file for the ABAQUS/Standard buckling analysis. The buckling analysis should contain as nearly as possible the same mesh and boundary conditions as the crushing analysis. The following would be a suitable description in the *HEADING option for the buckling analysis in ABAQUS/Standard:*HEADINGTube crush (x-direction) -- buckling analysisTube dimensions: 0.4m x 0.1m x 0.1mSI units (kg, m, s, N)Section propertiesAll of the shell elements in the model have the same material and the same 0.001 m (1 mm) thickness. For efficiency use the default Simpson's integration rule with the minimum of three integration points through the shell thickness. While more integration points increases the accuracy of the solution, it also increases its expense. Use the following section property for the shell elements:*SHELL SECTION, ELSET=TUBE, MATERIAL=STEEL0.001, 3The rigid elements also require section properties. Use the following section properties for the two rigid bodies:*RIGID BODY, ELSET=RIGTOP, REF NODE=<top reference node number>*RIGID BODY, ELSET=RIGBOT, REF NODE=<bottom reference node number>The mass element also requires section properties. Use the following section property to define a 500 kg mass attached to the bottom rigid body reference node:*MASS, ELSET=MASS500.,Material propertiesThe tube is made of steel, which will be modeled as an isotropic, elastic-plastic material. Plasticity data and density are not necessary for the buckling analysis, which uses only the linear material properties. However, include the data anyway for consistency with the ABAQUS/Explicit input file. ABAQUS/Standard ignores any material options that are not relevant. Use the following material option block to define the material behavior:*MATERIAL, NAME=STEEL*ELASTIC207.E9, .3*PLASTIC1.587E8, 0.01.631E8, 0.0151.863E8, 0.0331.932E8, 0.0442.020E8, 0.0622.070E8, 1.500*DENSITY7800.,Initial conditionsThere are no initial conditions because you do not need to include the initial velocity in the buckling analysis.Boundary conditionsConstrain the top rigid body completely by constraining its reference node. *BOUNDARYREFTOP, 1, 6Constrain the bottom rigid body in all but the 1-degree of freedom by constraining its reference node. REFBOT, 2, 6Contact definitionsDefine surfaces on the top and bottom rigid elements. The surfaces must be on the side of the elements facing the tube, which may be either the SPOS or the SNEG face, depending on how you defined the rigid elements. *SURFACE, NAME=TOPSURIGTOP, <SPOS or SNEG>*SURFACE, NAME=BOTSURIGBOT, <SPOS or SNEG>Create a node-based surface using the nodes at the top of the tube (contained in node set TOP).*SURFACE, TYPE=NODE, NAME=TOPTOP,Define contact between the nodes at the top of the tube and the top rigid surface. In a linear perturbation step, such as *BUCKLE, the contact conditions at the start of the step remain unchanged throughout the step. Therefore, if you ensure that the top nodes of the tube are in contact with the top rigid surface at the start of the step, the contact constraint will remain in effect throughout the buckling analysis. To ensure the closed contact condition, use the ADJUST parameter, which moves nodes within the specified tolerance (0.01 m) to lie exactly on the contact surface. *CONTACT PAIR, ADJUST=0.01, INTERACTION=TUBE

Page 64: Getting Started With ABAQUS

TOP, TOPSUA contact pair must refer to a *SURFACE INTERACTION option, which may contain additional information regarding the contact interaction, such as a friction model. In this case we assume zero friction between the tube and the top rigid surface. The *SURFACE INTERACTION option block contains only the following keyword line:*SURFACE INTERACTION, NAME=TUBECreate a node-based surface containing the nodes at the bottom of the tube.*SURFACE, TYPE=NODE, NAME=BOTBOT,Tie constraints Use the *TIE option to ``glue'' the slave nodes on the bottom of the tube to the bottom rigid surface. To ensure that the slave nodes are tied to the bottom rigid surface, set the ADJUST parameter equal to YES and the POSITION TOLERANCE parameter to 0.01. Slave nodes of the tube that are within this tolerance are tied to the bottom rigid surface.*TIE, NAME=FIXEDBOTTOM, POSITION TOLERANCE=0.01, ADJUST=YESBOT, BOTSU6.6.5  Reviewing the input file for the ABAQUS/Standard buckling analysis--the history dataStep definitionTo obtain the first 10 buckling modes, use the following step definition:*STEPBuckling analysis of the tube*BUCKLE, EIGENSOLVER=SUBSPACE10,The subspace iteration eigensolver is used since the Lanczos eigensolver is not suitable for solving a buckling problem with contact conditions.LoadingLoad the tube in a manner similar to the actual loading that the tube will experience during the crushing analysis. The actual load magnitude is not critical because ABAQUS/Standard will report the buckling loads as a fraction of the applied load. Apply a concentrated force of 500 N in the positive 1-direction to the bottom rigid surface reference node:*CLOADREFBOT, 1, 500.0Output requestsYou must request results (.fil) file output for the nodal displacements so that you can use the buckling analysis results to seed the ABAQUS/Explicit mesh with imperfections. In addition, request preselected field variable output to the output database (.odb) file and prevent unnecessary results from being printed in the data (.dat) file.*NODE FILEU,*OUTPUT, FIELD, VARIABLE=PRESELECT, FREQUENCY=1*NODE PRINT, FREQUENCY=0*EL PRINT, FREQUENCY=0*END STEP6.6.6  Running the ABAQUS/Standard buckling analysisAfter storing your input in a file called tube_buckle.inp, run the analysis using the following command:abaqus job=tube_buckleIf your analysis does not complete, check tube_buckle.dat for error messages. Modify your input to remove any errors.6.6.7  Results of the buckling analysisAfter running the buckling analysis to completion, look at the eigenvalue output in the data file. The output shows 10 eigenmodes and 10 corresponding eigenvalues. To determine the actual buckling load, multiply the eigenvalue by the applied load; e.g., the buckling load for the first mode is 35.377 ?500.0 N=17689 N.                              E I G E N V A L U E    O U T P U T     BUCKLING LOAD ESTIMATE = ("DEAD" LOADS) + EIGENVALUE * ("LIVE" LOADS).          "DEAD" LOADS = TOTAL LOAD BEFORE  *BUCKLE STEP.          "LIVE" LOADS = INCREMENTAL LOAD IN *BUCKLE STEP

 MODE NO      EIGENVALUE

       1       35.377           2       47.316           3       47.316           4       60.433           5       64.596           6       66.441           7       76.665           8       78.725           9       87.067          10       87.069   Postprocessing with ABAQUS/Viewer

Page 65: Getting Started With ABAQUS

Start ABAQUS/Viewer by entering the command abaqus viewer odb=tube_buckleat the operating system prompt.View the deformed shape of the eigenmodes, and determine whether the deformations in the buckling analysis will provide good imperfection seeds for the crushing analysis in ABAQUS/Explicit. To plot the eigenmodes:1.From the main menu bar, select Tools->Display Group->Create.2.In the dialog box that appears, select element set PART-1-1.TUBE and click Replace.3.Click Dismiss.Observe that the tube alone is now displayed.4.From the main menu bar, select Result->Step/Frame.5.To select the first eigenmode, choose Mode 1 in the dialog box that appears, and click OK.6.Change the plot mode to deformed by selecting Plot->Deformed Shape or by clicking the  tool in the toolbox.The first eigenmode is displayed in the viewport.7.To change the view, click the rotate tool  and drag the cursor to rotate the tube in the viewport.8.Click Deformed Shape Plot Options in the prompt area.The Deformed Shape Plot Options dialog box appears.9.In this dialog box, choose the Hidden render style. Click OK.The eigenmode is displayed with the changed deformed plot options.10.Repeat Step 5 for the second eigenmode.Eigenmodes 1 and 2, which are displayed in Figure 6-41  , show that the eigenmodes are similar to the expected deformation during the crushing analysis. Examination of the remaining eight modes shows that they are relevant as well.Figure 6-41  Eigenmode 1 (left) and eigenmode 2 (right).Now that you have obtained the buckling modes using ABAQUS/Standard, you are ready to create the ABAQUS/Explicit input file.6.6.8  Reviewing the input file for the ABAQUS/Explicit crushing analysis--the model dataMost of the model data are the same for the ABAQUS/Standard buckling analysis and the ABAQUS/Explicit crushing analysis. Specifically, the nodes, elements, material, and section properties are all the same. Also, the tie constraint is the same. One significant difference in the contact definitions is that for ABAQUS/Standard the contact pair definition is part of the model data, whereas in ABAQUS/Explicit the contact pair definition is part of the history data. In addition, the ABAQUS/Explicit input file contains an additional contact pair to model self-contact of the tube as well as an option to read the imperfections from the buckling analysis and to alter the mesh accordingly. The ABAQUS/Explicit model also contains an initial velocity that causes it to impact with the top rigid surface. Copy the buckling input file, tube_buckle.inp, to a file called tube_crush.inp, and then modify tube_crush.inp as described in the next section.Use the buckling eigenmodes to perturb the meshWhen choosing perturbation magnitudes, the goal is to seed the mesh with a deformation pattern that will allow the postbuckling deformation to proceed correctly. Typically, the magnitudes of the perturbations used for the different eigenmodes are a few percent of the relevant structural dimension, such as shell thickness. Since the lowest eigenmodes are most pertinent to a crushing analysis, the magnitude of the perturbation associated with those modes should be greatest. Increasing the imperfection factors causes the crushing to proceed more smoothly. On the other hand, imperfections that are too large are unrealistic.The postbuckling response of a structure with many closely spaced eigenvalues may be highly sensitive to the mesh imperfections that you impose. In such cases slight changes to the mesh imperfections can cause significant changes in postbuckling behavior, requiring a sensitivity study to determine realistic mesh imperfections. In this tube crushing analysis the first eigenvalue is significantly lower than the second, so we can safely assume that the first eigenmode will dominate. Only modes 2 and 3 have closely spaced eigenvalues, but these are far enough away from the lowest eigenvalue that they will not dominate the postbuckling response. A structure such as a short, thin-walled cylinder may have several low eigenvalues that are nearly the same. In such a structure it is not clear whether the lowest eigenmode will dominate.Introduce mesh imperfections that are a maximum of 2% of the shell thickness. Since ABAQUS/Standard scales the eigenvalue output from the buckling analysis so that the maximum deformation in each eigenmode is 1.0 m, choosing an imperfection factor of 1.0 would perturb the mesh by exactly the displacements obtained as output from ABAQUS/Standard. To obtain mesh imperfections for each eigenmode that are a maximum of 2% of the shell thickness (0.001 m ?0.02 = 2.0 ?10-5 m) for the first eigenmode and a decreasing percentage as the eigenmode number increases, use the following imperfection factors: *IMPERFECTION, FILE=tube_buckle, STEP=11, 2.0E-52, 0.8E-53, 0.4E-54, 0.18E-55, 0.16E-56, 0.10E-57, 0.10E-58, 0.08E-59, 0.02E-510, 0.02E-5Initial conditionsThe top rigid body is fixed. The tube and bottom rigid body, including the mass, have an initial velocity of 20 mph, or 8.9408 m/s. Use the following option block to define the initial velocity:*INITIAL CONDITIONS, TYPE=VELOCITY** 1 mph = 0.44701 m/s

Page 66: Getting Started With ABAQUS

** 20 mph = 8.9408 m/sREFBOT, 1, 8.9408ALL, 1, 8.9408Boundary conditionsThe boundary conditions are exactly the same as those used for the buckling analysis.Output node setDefine a node set to use later when requesting output. *NSET, NSET=PRINTOP, REFTOP, BOT, REFBOTSurface definitionsWe will define contact somewhat differently for the crushing analysis than for the buckling analysis, using the self-contact and double-sided contact features in ABAQUS/Explicit. As the tube crushes, it buckles repeatedly so that many regions on the inside and on the outside of the tube contact each other. Since we do not know in advance which specific regions will be in contact with each other, we must allow contact to occur in a very general manner so that any regions can contact any other regions, both on the inside and on the outside of the tube. Self-contact allows the generality of a single body, such as the tube, contacting itself in any regions of the contact surface.Delete the surface TOP, the contact pair between surfaces TOP and TOPSU, and the surface interaction TUBE. Define the entire inside and outside surfaces of the tube to be in one double-sided contact surface by defining a shell surface on the element set, TUBE, without specifying a face identifier. *SURFACE, NAME=TUBETUBE, 6.6.9  Reviewing the input file for the ABAQUS/Explicit crushing analysis--the history dataWe now discuss the history data required for this problem, including the step definition, contact definitions, and output requests.Step definitionRun the explicit dynamics analysis for a total of 0.03 seconds.*STEPImpact of square tube with free deceleration Initial velocity=8.9408m/s (20mph)*DYNAMIC, EXPLICIT, 0.03Contact definitionsTo specify self-contact for the inside and outside of the tube, define a contact pair with the double-sided surface, TUBE, as the only surface.*CONTACT PAIR, INTERACTION=SELFTUBE, In addition, define the surface interaction, SELF, with a friction coefficient of 0.1.*SURFACE INTERACTION, NAME=SELF*FRICTION0.1, Initially, the contact will occur only at the nodes along the top edge of the tube; but as the tube crushes, more of the tube surface could contact the rigid plate. We can define this contact situation by specifying contact between the double-sided surface, TUBE, and the top rigid plate surface, TOPSU. Since a double-sided surface automatically includes the edge in the surface definition, the contact pair is defined as follows:*CONTACT PAIR, INTERACTION=IMPACTTUBE, TOPSUIn addition, define the surface interaction, IMPACT, with zero friction.*SURFACE INTERACTION, NAME=IMPACTOutput requestsSince the primary goal of this analysis is to determine the amount of energy absorbed by the tube as it is crushed, the most important output is the energy history output. Request the following history output to the output database:*OUTPUT, HISTORY, TIME INTERVAL=0.00008*ENERGY OUTPUTALLWK, ALLKE, ETOTAL, ALLPD, ALLIE, ALLVD, ALLAE, ALLSENodal histories and a monitor node, as well as output of the preselected field variables to the output database, are also useful in studying the behavior of the tube.*NODE OUTPUT, NSET=PRINU, V, A, RF1, RF2, RF3*MONITOR, NODE=<bottom rigid reference node number>, DOF=1*OUTPUT, FIELD, VARIABLE=PRESELECT, NUMBER INTERVAL=20*END STEP6.6.10  Running the ABAQUS/Explicit crushing analysisAfter storing your input in a file called tube_crush.inp, run the analysis using the following command:abaqus job=tube_crush analysisAs with the circuit board drop test, this analysis will take a while to complete. If your analysis does not complete, check the data file, tube_crush.dat, and the status file, tube_crush.sta, for error messages. Modify your input to remove any errors.6.6.11  Results of the crushing analysis

Page 67: Getting Started With ABAQUS

After running the simulation successfully, visually display the deformation history of the tube with an animation using the same procedure that you used to animate the circuit board problem. The animation will show the deformed mesh for each of the 20 states stored in the output database file. Viewing the deformation history enables you to determine whether or not the tube appears to be deforming correctly as it is crushed. The final deformed mesh is shown in Figure 6-42  . As you view the displaced mesh, notice that ABAQUS/Explicit includes the thickness of the shell in the contact calculations. The regions that are in contact appear with a slight gap between contacting regions.Figure 6-42  Final deformed mesh.To underscore the importance of perturbing the mesh prior to performing a postbuckling analysis, Figure 6-43   shows the final deformed mesh of an analysis that includes no initial imperfections. Figure 6-43  Deformed mesh when no initial imperfections are imposed.In contrast to the smoothly buckled shape of the perturbed mesh, this unperturbed mesh deforms into sharp folds; the shape is clearly not physically correct. Even the small imperfections introduced in the perturbed mesh are enough to make the postbuckling behavior proceed smoothly.Status fileThe status file issues several warnings regarding high out-of-plane warping in some surfaces. Such warnings are not surprising considering the severe deformation of the mesh in Figure 6-42  . The nature of this crushing analysis is such that a highly refined mesh would be required to eliminate the large warping of some elements. Without further refining the mesh for this exercise, we can simply accept the results as an approximate solution.  STEP 1  ORIGIN 0.00000E+00     Total memory used for step 1 is approximately 1.6 megawords   Global time estimation algorithm will be used.   Scaling factor :  1.0000               STEP      TOTAL       CPU     STABLE      CRITICAL  KINETIC  INCREMENT  TIME      TIME        TIME   INCREMENT    ELEMENT   ENERGY    MONITOR         0  0.000E+00 0.000E+00   00:00:02 1.392E-06     101   2.003E+04 0.000E+00 Results number  0 at increment zero. ODB Field Frame Number    0 of   20 requested intervals at increment zero.     ***WARNING: Master surface TUBE of contact pair # 1 contains facets with              out-of-plane warping of at least 20.000 degrees in increment 320.              Large warping that develops during an analysis often corresponds              to severe distortion of the underlying elements. It may be              appropriate to rerun the analysis with a refined mesh.Postprocessing with ABAQUS/ViewerStart ABAQUS/Viewer by entering the command abaqus viewer odb=tube_crushat the operating system prompt.One way to determine the energy absorption of the tube is to look at a history plot of the pertinent energies. Since most of the energy is dissipated in the form of plastic deformation, plot a history of plastic dissipation, ALLPD. To show how the total kinetic energy of the model changes as the tube deforms, also plot kinetic energy, ALLKE. It is also useful to plot the artificial strain energy, ALLAE, as an indication of the mesh quality.To plot the energy histories:1.From the main menu bar, select Result->History Output.The History Output dialog box appears.2.Select the artificial energy, ALLAE, and save the data as ALLAE.3.Select the kinetic energy, ALLKE, and save the data as ALLKE.4.Select the plastic dissipation, ALLPD, and save the data as ALLPD.5.Click Dismiss to close the dialog box.6.From the main menu bar, select Tools->XY Data->Manager.The XY Data Manager dialog box appears.7.In this dialog box, select the three curves defined above and click Plot.Customize the appearance of the plot by changing the curve styles and the axis titles, as shown in Figure 6-44  .Figure 6-44  History plot of ALLPD and ALLKE.By the end of the analysis 3600 J of energy has been dissipated as plastic deformation, and there is a corresponding decrease of 4400 J in the total kinetic energy of the model. The artificial strain energy at the end of the analysis is 800 J, or 18% of the plastic dissipation. Ideally the artificial strain energy should be a much smaller percentage of the internal energy or plastic dissipation. (In previous examples we introduced 5% as a general rule.) The high percentage in this analysis indicates that the mesh should be refined to improve the results. Since the deformations by the end of the analysis are so severe, a highly refined mesh would be required to minimize the effect of hourglassing on the results. Again, without further refining the mesh, we can accept the results as an approximate solution.6.7  Summary텰 ontact is defined in the history definition part of the input file.톂 he contact definition in ABAQUS/Explicit has two parts: definition of the surface that may come into contact and definition of the interactions between the surfaces.톁 urfaces are defined using the *SURFACE option. Individual nodes can be included in a contact pair by using the TYPE=NODE parameter on the *SURFACE option. Analytical rigid surfaces are assigned to a rigid body by using the ANALYTICAL SURFACE parameter on the *RIGID BODY option. The parameters TYPE=SEGMENTS, CYLINDRICAL, or REVOLUTION on

Page 68: Getting Started With ABAQUS

the *SURFACE option specify the type of analytical rigid surface.텰 ontact can be defined between two surfaces or between a single surface and itself.텮 ll surfaces must be continuous and simply connected. A shell or membrane surface may span both sides of the element.톁 urface normals for shells, membranes, or rigid elements must be consistent from one element to the next within a surface if it is a single-sided surface. The normals must not "flip" as the surface is traversed.텮 BAQUS/Explicit does not smooth rigid surfaces; they are faceted like the underlying elements. Coarse meshing of discrete rigid surfaces can produce noisy solutions.톂 ied contact is a useful means of mesh refinement.텮 BAQUS/Explicit adjusts the nodal coordinates without strain to remove any initial overclosures prior to the first step. If the adjustments are large with respect to the element dimensions, elements can become severely distorted.텶 n subsequent steps any nodal adjustments to remove initial overclosures induce strains that can potentially cause severe mesh distortions.7.  Quasi-Static AnalysisThe explicit solution method is a true dynamic procedure originally developed to model high-speed impact events in which inertia plays a dominant role in the solution. Out-of-balance forces are propagated as stress waves between neighboring elements while solving for a state of dynamic equilibrium. Since the minimum stable time increment is usually quite small, most problems require a large number of increments.The explicit solution method has proven valuable in solving static problems as well--ABAQUS/Explicit solves certain types of static problems more readily than ABAQUS/Standard does. One advantage of the explicit procedure over the implicit procedure is the greater ease with which it resolves complicated contact problems. In addition, as models become very large, the explicit procedure requires less system resources than the implicit procedure. Refer to Chapter 3, "Overview of Explicit Dynamics," for a detailed comparison of the implicit and explicit procedures.Applying the explicit dynamic procedure to quasi-static problems requires some special considerations. Since a static solution is, by definition, a long-time solution, it is often computationally impractical to analyze the simulation in its natural time scale, which would require an excessive number of small time increments. To obtain an economical solution, the event must be accelerated in some way. The problem is that as the event is accelerated, the state of static equilibrium evolves into a state of dynamic equilibrium in which inertial forces become more dominant. The goal is to model the process in the shortest time period in which inertial forces remain insignificant.7.1  Analogy for explicit dynamicsTo provide you with a more intuitive understanding of the differences between a slow, quasi-static loading case and a rapid loading case, we use the analogy illustrated in Figure 7-1  . Figure 7-1  Analogy for slow and fast loading cases.The figure shows two cases of an elevator full of passengers. In the slow case the door opens and you walk in. To make room, the occupants adjacent to the door slowly push their neighbors, who push their neighbors, and so on. This disturbance passes through the elevator until the people next to the walls indicate that they cannot move. A series of waves pass through the elevator until everyone has reached a new equilibrium position. If you increase your speed slightly, you will shove your neighbors more forcefully than before, but in the end everyone will end up in the same position as in the slow case.In the fast case the door opens and you run into the elevator at high speed, permitting the occupants no time to rearrange themselves to accommodate you. You will injure the two people directly in front of the door, while the other occupants will be unaffected.The same thinking is true for quasi-static analyses. The speed of the analysis often can be increased substantially without severely degrading the quality of the quasi-static solution; the end result of the slow case and a somewhat accelerated case are nearly the same. However, if the analysis speed is increased to a point at which inertial effects dominate, the solution tends to localize, and the results are quite different from the quasi-static solution.7.2  Loading ratesThe actual time taken for a physical process is called its natural time. Generally, it is safe to assume that performing an analysis in the natural time for a quasi-static process will produce accurate static results. After all, if the real-life event actually occurs in a natural time scale in which velocities are zero at the conclusion, a dynamic analysis should be able to capture the fact that the analysis has, in fact, achieved a steady state. You can increase the loading rate so that the same physical event occurs in less time as long as the solution remains nearly the same as the true static solution and dynamic effects remain insignificant.7.2.1  Smooth amplitude curvesFor accuracy and efficiency quasi-static analyses require the application of loading that is as smooth as possible. Sudden, jerky movements cause stress waves, which can induce noisy or inaccurate solutions. Applying the load in the smoothest possible manner requires that the acceleration changes only a small amount from one increment to the next. If the acceleration is smooth, it follows that the changes in velocity and displacement are also smooth.ABAQUS has a simple, built-in type of amplitude called SMOOTH STEP that automatically creates a smooth loading amplitude. When you define time-amplitude data pairs using *AMPLITUDE, DEFINITION=SMOOTH STEP, ABAQUS/Explicit automatically connects each of your data pairs with curves whose first and second derivatives are smooth and whose slopes are zero at each of your data points. Since both of these derivatives are smooth, you can apply a displacement loading with SMOOTH STEP using only the initial and final data points, and the intervening motion will be smooth. Using this type of loading amplitude allows you to perform a quasi-static analysis without generating waves due to discontinuity in the rate of applied loading. For example, for the following amplitude definition ABAQUS/Explicit creates the amplitude curve shown in Figure 7-2*AMPLITUDE, DEFINITION=SMOOTH STEP0.0, 0.0, 1.0E-5, 1.0 Figure 7-2  Amplitude definition using *AMPLITUDE, DEFINITION=SMOOTH STEP.7.2.2  Structural problemsIn a static analysis the lowest mode of the structure usually dominates the response. Knowing the frequency and, correspondingly, the period of the lowest mode, you can estimate the time required to obtain the proper static response. To illustrate the problem of determining the proper loading rate, consider the deformation of a side intrusion beam in a car door by a rigid cylinder, as shown in Figure 7-3  . The actual test is quasi-static. Figure 7-3  Rigid cylinder impacting beam.The response of the beam varies greatly with the loading rate. At an extremely high impact velocity of 400 m/s, the deformation in the beam is highly localized, as shown in Figure 7-4  . To obtain a better quasi-static solution, consider the lowest mode. Figure 7-4  Impact velocity of 400 m/s.

Page 69: Getting Started With ABAQUS

The frequency of the lowest mode is approximately 250 Hz, which corresponds to a period of 4 milliseconds. The natural frequencies can easily be calculated using the *FREQUENCY procedure in ABAQUS/Standard. To deform the beam by the desired 0.2 m in 4 milliseconds, the velocity of the cylinder is 50 m/s. While 50 m/s still seems like a high, impact velocity, the inertial forces become secondary to the overall stiffness of the structure, and the deformed shape--shown in Figure 7-5Figure 7-5  Impact velocity of 50 m/s.While the overall structural response appears to be what we expect as a quasi-static solution, it is usually desirable to increase the loading time to 10 times the period of the lowest mode to be certain that the solution is truly quasi-static. To improve the results even further, the velocity of the rigid cylinder could be ramped up gradually--for example, using a SMOOTH STEP amplitude definition--thereby easing the initial impact.7.2.3  Metal forming problemsArtificially increasing the speed of forming events is necessary to obtain an economical solution, but how large a speed-up can we impose and still obtain an acceptable static solution? If the deformation of the sheet metal blank corresponds to the deformed shape of the lowest mode, the time period of the lowest structural mode can be used as a guideline for forming speed. However, in forming processes the rigid dies and punches can constrain the punch in such a way that its deformation may not relate to the structural modes. In such cases a general recommendation is to limit punch speeds to less than 1% of the sheet metal wave speed. For typical processes the punch speed is on the order of 1 m/s, while the wave speed of steel is approximately 5000 m/s. This recommendation, therefore, suggests a factor of 50 as an upper bound on the speed-up of the punch velocity.The suggested approach to determining an acceptable punch velocity involves running a series of analyses at various punch speeds in the range of 3 to 50 m/s. Perform the analyses in the order of fastest to slowest since the solution time is inversely proportional to the punch velocity. Examine the results of the analyses, and get a feel for how the deformed shapes, stresses, and strains vary with punch speed. Some indications of excessive punch speeds are unrealistic, localized stretching and thinning as well as the suppression of wrinkling. If you begin with a punch speed of, for example, 50 m/s, and decrease it from there, at some point the solutions will become similar from one punch speed to the next--an indication that the solutions are converging on a steady-state solution. As inertial effects become less significant, differences in simulation results also become less significant.As the loading rate is increased artificially, it becomes more and more important to apply the loads in a gradual and smooth manner. For example, the simplest way to load the punch is to impose a constant velocity throughout the forming step. Such a loading causes a sudden impact load onto the sheet metal blank at the start of the analysis, which propagates stress waves through the blank and may produce undesired results. The effect of any impact load on the results becomes more pronounced as the loading rate is increased. Ramping up the punch velocity from zero using a SMOOTH STEP amplitude minimizes these adverse effects.SpringbackSpringback is often an important part of a forming analysis because the springback analysis determines the shape of the final, unloaded part. While ABAQUS/Explicit is well-suited for forming simulations, springback poses some special difficulties. The main problem with performing springback simulations within ABAQUS/Explicit is the amount of time required to obtain a steady-state solution. Typically, the loads must be removed very carefully, and damping must be introduced to make the solution time reasonable. Fortunately, the close relationship between ABAQUS/Explicit and ABAQUS/Standard allows a much more efficient approach.Since springback involves no contact and usually includes only mild nonlinearities, ABAQUS/Standard can solve springback problems much faster than ABAQUS/Explicit can. Therefore, the preferred approach to springback analyses is to import the completed forming model from ABAQUS/Explicit into ABAQUS/Standard. You must create an ABAQUS/Standard input file that will import the forming results and perform the springback analysis. Using the *IMPORT option within the ABAQUS/Standard input file, you specify the element sets that you wish to import. Usually, the entire deformable mesh is imported. The nodes, elements, and section properties are imported automatically, but you must redefine the materials and boundary conditions. Once the springback analysis is complete, you can import the model back into ABAQUS/Explicit to continue with another forming stage.7.3  Mass scalingMass scaling enables an analysis to be performed economically without artificially increasing the loading rate. Mass scaling is the only option for reducing the solution time in simulations involving a rate-dependent material or rate-dependent damping, such as dashpots. In such simulations increasing the loading rate is not an option because material strain rates increase by the same factor as the loading rate. When the properties of the model change with the strain rate, artificially increasing the loading rate artificially changes the process.The following equations show how the stable time increment is related to the material density. As discussed in Chapter 3, "Overview of Explicit Dynamics," the stability limit for the model is the minimum stable time increment of all elements. It can be expressed aswhere  is the characteristic element length and  is the dilatational wave speed of the material. The dilatational wave speed for a linear elastic material with Poisson's ratio equal to zero is given bywhere  is the material density.According to the above equations, artificially increasing the material density, , by a factor of  decreases the wave speed by a factor offactor of . Remember that when the global stability limit is increased, fewer increments are required to perform the same analysis, which is the goal of mass scaling. Scaling the mass, however, has exactly the same influence on inertial effects as artificially increasing the loading rate. Therefore, excessive mass scaling, just like excessive loading rates, can lead to erroneous solutions. The suggested approach to determining an acceptable mass scaling factor, then, is similar to the approach to determining an acceptable loading rate scaling factor. The only difference to the approach is that the speedup associated with mass scaling is the square root of the mass scaling factor, whereas the speedup associated with loading rate scaling is proportional to the loading rate scaling factor. For example, a mass scaling factor of 100 corresponds exactly to a loading rate scaling factor of 10.There are several ways to implement mass scaling in your model using the *FIXED MASS SCALING or *VARIABLE MASS SCALING option in the history definition of the input file. Since the option is part of the history definition, it can be changed from step to step, allowing great flexibility. Refer to the ABAQUS/Explicit User's Manual for details.7.4  Energy balanceThe most general means of eval uating whether or not a simulation is producing an appropriate quasi-static response involves studying the various model energies. The following is the energy balance equation in ABAQUS/Explicit:where  is the internal energy (both elastic and plastic strain energy),  is the energy absorbed by viscous dissipation,  is the kinetic energy,dissipation,  is the work of external forces, and  is the total energy in the system.To illustrate energy balance with a simple example, consider the uniaxial tensile test shown in Figure 7-6  . Figure 7-6  Uniaxial tensile test.The energy history for the quasi-static test would appear as shown in Figure 7-7  . Figure 7-7  Energy history for quasi-static tensile test.

Page 70: Getting Started With ABAQUS

If a simulation is quasi-static, the work applied by the external forces is nearly equal to the internal energy of the system. The viscously dissipated energy is generally small unless viscoelastic materials, discrete dashpots, or material damping are used. We have already established that the inertial forces are negligible in a quasi-static analysis because the velocity of the material in the model is very small. The corollary to both of these conditions is that the kinetic energy is also small. As a general rule the kinetic energy of the deforming material should not exceed a small fraction (typically 5% to 10%) of its internal energy throughout most of the process.When comparing the energies, remember that ABAQUS/Explicit reports a global energy balance, which includes the kinetic energy of any rigid bodies with mass. Since only the deformable bodies are of interest when eval uating the results, the kinetic energy of the rigid bodies should be subtracted fromFor example, if you are simulating a transport problem with rolling rigid dies, the kinetic energy of the rigid bodies may be a significant portion of the total kinetic energy of the model. In such cases you must subtract the kinetic energy associated with rigid body motions before a meaningful comparison with internal energy can be made.7.5  Example: deep drawing of a can bottomYou have been asked to simulate the deep drawing of a can bottom. Analyze this two-stage metal forming process as a quasi-static event, assuming that inertial effects are insignificant compared to stiffness effects. Figure 7-8  , Figure 7-9  , and Figure 7-10   provide the detailed model description necessary for you to build this model. Since the process is axisymmetric, you can use axisymmetric shell elements to model the blank and axisymmetric rigid surfaces to model the tools. The consequence of using axisymmetric elements instead of the more general three-dimensional shell elements is that an axisymmetric simulation cannot predict wrinkling in the circumferential direction if there are significant circumferential compressive stresses.Figure 7-8  Detailed model description of forming stage 1. (All dimensions are in meters.)Figure 7-9  Detailed forming description of forming stage 2. (All dimensions are in meters.)Figure 7-10  Material properties for the blank.Creating the final desired shape of the can bottom requires two separate forming stages. In the first forming stage a thin disk of metal--the blank--is drawn 0.015 m between a punch and a stationary die into the shape of a cup. Once the cup has been formed, the blank is removed from the first set of tools so that it can ``spring back'' to an unloaded configuration. It is then annealed to relieve the cold-working plastic strains generated during the first forming stage.After annealing, the blank is placed into a second set of rigid tools, and it is drawn another 0.010 m into the final shape of the bottom of a can. In this forming stage the die, die 2, rests on a spring and dashpot; thus, it is allowed to move in the axial, or 2-, direction. As the punch moves downward, it pinches the blank against die 2 and pushes both the blank and die 2 downward. As the blank moves downward, it contacts the fixed "domer" die, which forms the dome shape in the can bottom. After the second forming stage, the blank is again removed from the tools to spring back to its final, unloaded configuration. 7.5.1  Coordinate systemThe orientation of the model in the global coordinate system is shown in Figure 7-8   and Figure 7-9  . Since the physical process is axisymmetric and is modeled as such, the global 1-, 2-, and 3-directions correspond to radial, axial, and circumferential directions, respectively. 7.5.2  Mesh designThe blankSince the blank is initially a flat disk, model it with axisymmetric shell elements (SAX1) as a straight line starting at the symmetry axis. The only question, to which there is no definitive answer, is how many elements you should use. Examine the forming processes, and consider the deformations the blank will experience during the analysis. The mesh should be adequate to capture all of the features of the rigid forms accurately.When using a uniform mesh--as we are in this example--the element size must be small enough to capture the smallest feature of the rigid forms, which is the 0.002 m radius of the punch in forming stage 2. The general rule that we will use is that there should be 10 elements to model that radius, making the maximum element size 0.00125 m. If we use 50 elements in the blank, which is a disk with a radius of 0.045 m, the element length is 0.0009 m, which is adequate. Both dies and punches are composed of straight segments connected by fairly gradual radii. Since there are no sharp bends, there is no need for a terribly fine mesh; no area of the blank is subjected to severe crimping. Assume that 50 elements in the blank is adequate.The rigid dies and punchesModel the rigid dies and punches with analytical rigid surfaces in forming stage 1 and axisymmetric rigid elements (RAX2) in forming stage 2. An analytical rigid surface provides a smooth representation of the surface as opposed to the piecewise linear representation offered by rigid elements. In this example, it would be straightforward to model the rigid parts in the second forming stage with analytical rigid surfaces. However, most three-dimensional dies and punches require the generality of a rigid surface meshed with rigid elements. In forming stage 2, you must mesh the rigid surfaces finely enough so that they are accurate representations of the actual rigid tools. Mesh each straight segment with a single element, and mesh each radius with 30 rigid elements.The rigid surfaces should be as close as possible to the blank without any overclosure at the start of the forming step. Remember that ABAQUS/Explicit includes the thickness of shell elements when determining contact; therefore, the midplane of the blank must be at least one-half of the shell thickness away from the rigid tools above and below it. Prior to the first step ABAQUS/Explicit will attempt to resolve overclosures in a strain-free manner, and the resulting nodal location changes may distort the elements. In this example initial overclosures could change the initial shape of the blank if the overclosures are great enough.7.5.3  Node and element setsFigure 7-11   shows all of the sets necessary to apply the element properties, loads, and boundary conditions, as well as to request output for postprocessing. The sheet metal blank belongs in an element set called BLANK. Create separate node sets for each of the rigid body reference nodes. Give the name REFP1 to the node set containing the reference node for punch 1, and give the name REFD1 to the node set containing the reference node for die 1. Create a node set called BSYM containing the node of the blank that lies on the symmetry axis, and create a node set called BEND containing the node at the free end of the blank.Figure 7-11  Necessary node and element sets.In addition, create a node set called NHIST containing two nodes for postprocessing. These nodes are selected to provide a detailed velocity history at one point in the bottom flat part and the free end of the blank. Studying the velocity history for typical points in the blank will help to design the loading definition and to debug the analysis. For a mesh of 50 elements, select the 21st node from the symmetry axis and the node at the free end to be in node set NHIST.The second forming stage requires the rigid tools PUNCH2, DIE2, and DOMER to be in element sets with the same names. The node sets containing the corresponding reference nodes are REFP2, REFD2, and REFDOMER. Create element sets SPRING and DASHPOT containing the spring and dashpot elements, respectively.7.5.4  Determining an appropriate step time``Loading rates,'' Section 7.2, discusses the procedures for determining the appropriate step time for a quasi-static process. We can determine an approximate lower bound on step time duration if we know the lowest natural frequency, the fundamental frequency, of the blank. One way to obtain such information is to run a frequency analysis in

Page 71: Getting Started With ABAQUS

ABAQUS/Standard. In this forming analysis the punch deforms the blank into a shape similar to the lowest mode. Therefore, it is important that the time for the first forming stage is greater than the time period for the lowest mode if you wish to model structural, as opposed to localized, deformation.Create an ABAQUS/Standard input file called draw_freq_std.inp. The only elements necessary for the frequency analysis are the elements in the blank, which are defined exactly as they are for the forming analysis. The node and element sets are also the same. Create the mesh in your preprocessor based on the mesh components provided in ``Mesh design,'' Section 7.5.2, and ``Node and element sets,'' Section 7.5.3.The following is an appropriate heading for the analysis:*HEADINGDeep drawing of a can bottom -- frequency analysisABAQUS/StandardSI units (kg, m, s, N)Element propertiesGive each element set appropriate section properties. Create shell section properties for the blank so that it refers to a material called STEEL (to be defined later), uses five-point Gauss integration, and has a thickness of 0.5 mm.*SHELL SECTION, ELSET=BLANK, MATERIAL=STEEL,SECTION INTEGRATION=GAUSS.0005, 5Material propertiesThe blank is modeled using only the elastic material model since a *FREQUENCY analysis is a linear perturbation step and, thus, ignores nonlinear material properties. Use the following data to define the elastic and mass properties of the steel:*MATERIAL, NAME=STEEL*ELASTIC210.0E9, 0.3*DENSITY7800.,Boundary conditionsApply symmetry boundary conditions to node set BSYM, and fix node set BEND in the axial, or 2-, direction. *BOUNDARYBSYM, 1BSYM, 6BEND, 2History definitionThe history definition defines the *FREQUENCY procedure type to extract the first eigenmode. Request *RESTART output and the nodal displacements of the blank as field output to the output database file, and suppress other output.*STEP*FREQUENCY1,*RESTART, WRITE*OUTPUT, FIELD*NODE OUTPUT, NSET=BLANKU,*EL PRINT, FREQUENCY=0*NODE PRINT, FREQUENCY=0*END STEPRun the *FREQUENCY analysisSave your frequency analysis input in a file named draw_freq_std.inp, and run the analysis using the following command:abaqus job=draw_freq_stdPostprocessingWhen the analysis has completed, use ABAQUS/Viewer to plot the shape of mode 1. Start ABAQUS/Viewer by typingabaqus viewer odb=draw_freq_std at the operating system prompt.To plot the mode shape:1.From the main menu bar, select Result->Step/Frame.The Step/Frame dialog box appears. Select mode 1, and click OK.2.From the main menu bar, select Plot->Deformed Shape; or use the  tool in the toolbox.ABAQUS/Viewer displays the deformed model shape for the first buckling mode. Superimpose the undeformed model shape on the deformed model shape.3.From the main menu bar, select Options->Deformed Shape.The Deformed Shape Plot Options dialog box appears.4.Toggle on Superimpose undeformed plot.5.Click OK. ABAQUS/Viewer displays an image of the deformed model of the blank superimposed upon the undeformed model of the blank.The frequency analysis shows that the blank has a fundamental frequency of 304 Hz, corresponding to a period of 0.0033 s. Figure 7-12

Page 72: Getting Started With ABAQUS

mode. We now know that the lower bound on the step time for the first forming stage is 0.0033 s.Figure 7-12  Displaced shape of mode 1 from the ABAQUS/Standard frequency analysis.7.5.5  Reviewing the input file for the ABAQUS/Explicit forming stage 1 analysis--the model dataThe first forming input file, draw_stage1_attempt.inp, will model only the first forming stage; thus, it requires only the components involved in the first forming stage. Use the same mesh for the blank as you used in the frequency extraction input file, draw_freq_std.inp. Create the additional mesh components provided in ``Mesh design,'' Section 7.5.2, and ``Node and element sets,'' Section 7.5.3, using your preprocessor. In this section we will review your model definition, make any corrections, and include additional information.Model descriptionThe following would be a suitable description for the simulation:*HEADINGDeep drawing of a can bottom -- stage 1, attempt 1SI units (kg, m, s, N) This description clearly labels the input data and indicates the units.Element propertiesGive each element set appropriate section properties. Create shell section properties for the blank so that it refers to a material called STEEL (to be defined later), uses five-point Gauss integration, and has a thickness of 0.5 mm. Five section points through the shell thickness should provide accurate results for a body that will incur significant plasticity.*SHELL SECTION, ELSET=BLANK, MATERIAL=STEEL,SECTION INTEGRATION=GAUSS.0005, 5Material propertiesThe blank, which is the only deformable body in this simulation, is modeled using an elastic-plastic material model. Use the following data to define the elastic and mass properties of the steel:*MATERIAL, NAME=STEEL*ELASTIC210.0E9, 0.3*DENSITY7800., Include the plasticity data under the *PLASTIC option.*PLASTIC0.912E8, 0.00.131E9, 0.159E-020.171E9, 0.649E-020.211E9, 0.177E-010.251E9, 0.395E-010.291E9, 0.776E-010.331E9, 0.1390.391E9, 0.295Figure 7-13   shows that the plasticity curve for this example is quite smooth. Figure 7-13  Stress versus plastic strain material curve.Because smoothness is desired for all aspects of a quasi-static problem, it is advantageous to have as smooth a plasticity curve as possible. With a smooth plasticity curve the material stiffness changes only slightly from one increment to the next as plastic straining occurs, thus helping to produce a solution with less noise.Surface definitionsUse the *SURFACE option to define the analytical surfaces of the rigid tools.*SURFACE, TYPE=SEGMENTS, NAME=PUNCH1START,0.032,0.03025LINE,0.032,0.00625CIRCL,0.026,0.00025,0.026,0.00625LINE,0.,0.00025*SURFACE, TYPE=SEGMENTS, NAME=DIE1START,0.0326,-0.02825LINE,0.0326,-0.00425CIRCL,0.0366,-0.00025,0.0366,-0.00425LINE,0.050,-0.00025To bind an analytical surface to a rigid body, assign the name of the analytical surface to the ANALYTICAL SURFACE parameter on the *RIGID BODY option. Use the REF NODE parameter to specify the rigid body reference node that will control the motion of the rigid body.*RIGID BODY, ANALYTICAL SURFCE=PUNCH1,REF NODE=<reference node number>*RIGID BODY, ANALYTICAL SURFACE=DIE1,REF NODE=<reference node number>Define the surfaces on the top and bottom of the blank. The surfaces on the top and bottom of the blank must face PUNCH1 and DIE1, respectively.*SURFACE, NAME=BLANK_TOPBLANK, <SPOS or SNEG>

Page 73: Getting Started With ABAQUS

*SURFACE, NAME=BLANK_BOTBLANK, <SPOS or SNEG>Two surface definitions (one on the top and the other on the bottom of the blank) are required because double-sided surfaces can be defined only on three-dimensional shell, membrane, or rigid elements.Initial fixed boundary conditionsThe initial fixed boundary conditions can be part of the model definition or history definition. Since the model is axisymmetric, you must constrain each of the bodies--the blank, punch 1, and die 1--from motion in the radial, or 1-, direction and from in-plane rotation (degree of freedom 6). In addition, constrain die 1 from motion in the axial, or 2-, direction.*BOUNDARYREFP1, 1REFP1, 6REFD1, 1, 6BSYM, 1 BSYM, 67.5.6  Designing the history definitionSeveral aspects of the loading history are not clearly defined from the model description. Therefore, the analysis will include some amount of trial and error to help determine what produces acceptable results and what does not. Unlike the other example problems in this manual, we will discuss this forming problem one step at a time, becoming satisfied with the results from one step before continuing to the next step.7.5.7  General approach to forming stage 1The goal of the first forming stage is to form a cup with a depth of 0.015 m using punch 1 and die 1. We intentionally did not provide a punch velocity in the problem description because an appropriate punch velocity for a quasi-static analysis is not necessarily the same as the actual punch velocity. Typical punch velocities are on the order of 0.1-1.0 m/s, although actual velocities vary.To analyze the first forming stage successfully, we must consider the following questions:1.What is an appropriate step time?2.How should we move the punch?3.How many increments and how much computer time will the analysis require?4.What output should we request?Determining an appropriate step timeIn ``Determining an appropriate step time,'' Section 7.5.4, we performed a frequency analysis, which showed that the blank has a fundamental frequency of 304 Hz, corresponding to a time period of 0.0033 s. This time period provides a lower bound on the step time for the first forming stage. Choosing the step time to be 10 times the time period of the fundamental natural frequency, or 0.033 s, should ensure a quality quasi-static solution. This time period corresponds to a constant punch velocity of 0.45 m/s, which is typical for metal forming.Moving the punchEven if the punch actually moves at a nearly constant velocity, it is desirable to use a different amplitude curve that allows the blank to accelerate more smoothly. When considering what type of loading amplitude to use, remember that smoothness is important in all aspects of a quasi-static analysis. The preferred approach is to move the punch as smoothly as possible the desired distance in the desired amount of time. We will analyze the first forming stage using both approaches--a constant punch velocity of 0.45 m/s and a smoothly ramped punch velocity using a SMOOTH STEP amplitude--and will compare the results.Computer timeBefore you run the forming analysis, you may wish to know how many increments the analysis will take and, consequently, how much computer time the analysis requires. You can run a datacheck analysis to obtain the approximate value for the initial stable time increment, or you can estimate it using the relations in ``Mass scaling,'' Section 7.3. Knowing the stable time increment, which in this case does not change much from increment to increment, you can determine how many increments are required to complete the forming stage. Once the analysis begins, you can get an idea of how much CPU time is required per increment and, consequently, how much CPU time the step requires.Using the relations stated in ``Mass scaling,'' Section 7.3, the stable time increment for this analysis is approximately 1 ?10-7 s. Therefore, the forming stage requires approximately 330,000 increments for a step time of 0.033 s.OutputTo help determine how closely the analysis approximates the quasi-static assumption, the various energy histories are useful. Especially useful is comparing the kinetic energy to the internal strain energy. Another useful history plot is that of the velocities at typical nodes. Earlier you created the node set, NHIST, containing nodes at which you will obtain velocity histories. Such output gives you an idea of the severity of any velocity spikes in the solution. Write these energy and velocity histories as history data to the output database file. Write the section forces, shell thicknesses, and nodal displacements to the output database as field data for postprocessing with ABAQUS/Viewer. You should also have ABAQUS save the state information so that you can restart the analysis. For your first attempt request state information at 20 intervals. Once you are more confident with the first forming stage, you can decrease this value. Define the reference node for the rigid surface PUNCH1 as the monitor node.7.5.8  Overview of forming stage 1 attemptsFor the first forming stage we present a progression of three attempts to obtain an acceptable solution. In the first attempt we move the punch with a constant velocity. Seeking to diminish the severe oscillations of the first attempt, in the second attempt we smooth the punch velocity amplitude by setting the DEFINITION parameter on the *AMPLITUDE option equal to SMOOTH STEP. To further remove high-frequency oscillations, in the third attempt we introduce stiffness proportional damping. The results of the third attempt are acceptable, and they are subsequently used as a basis of comparison for analyses with varying degrees of mass scaling. If you do not wish to run analyses that do not produce acceptable results, read the discussions for attempts 1 and 2 but run only attempt 3.The history definition for each of the attempts contains the same contact definitions and output requests. The history definition begins with the *STEP option; the *DYNAMIC, EXPLICIT procedure; and a total step time of 10 times the fundamental natural frequency, or 0.033 s.*STEP*DYNAMIC, EXPLICIT, .033

Page 74: Getting Started With ABAQUS

Define contact between the top of the blank and the punch and between the bottom of the blank and the die.*CONTACT PAIR, INTERACTION=INTERPUNCH1, BLANK_TOPDIE1, BLANK_BOTDefine a friction coefficient of 0.1 between all contacting surfaces.*SURFACE INTERACTION, NAME=INTER*FRICTION.1,Write the restart information at 10 evenly spaced intervals during the analysis by including the following line in your input file:*RESTART, WRITE, NUMBER INTERVAL=10Request velocity and displacement history output for node set NHIST and energy history output every 1 ?10-5 s.*OUTPUT, HISTORY, TIME INTERVAL=1.E-5 *NODE OUTPUT, NSET=NHIST U,V*ENERGY OUTPUTALLKE,ALLIE,ALLWK,ALLVD,ALLAE,ALLPD,ETOTALRequest section force and shell thickness field output for element set BLANK and displacement output at 4 intervals during the step.*OUTPUT, FIELD, NUMBER INTERVAL=4*ELEMENT OUTPUT, ELSET=BLANKSTH, SF*NODE OUTPUTU,RF *END STEP7.5.9  Forming stage 1--attempt 1Add the following amplitude to the model definition to simulate the punch moving at a constant velocity of 0.45 m/s:*AMPLITUDE, NAME=FORM10., 0., .033, 1. and add the following prescribed displacement boundary condition to the history definition:*BOUNDARY, TYPE=DISPLACEMENT, AMPLITUDE=FORM1REFP1, 2, 2, -0.015Save your input in a file named draw_stage1_attempt1.inp, and run the analysis. Thirty minutes or more may be required to run this analysis to completion.Strategy for eval uating the resultsBefore looking at the results that are ultimately of interest, such as stresses and deformed shapes, we need to determine whether or not the solution is close enough to being quasi-static to be acceptable. One good approach is to compare the kinetic energy history to the internal energy history. In a metal forming analysis most of the internal energy is due to plastic deformation. Since punch 1 has no mass, the blank is the only body with mass; and the kinetic energy is solely due to the motion of the blank. To indicate an acceptable quasi-static solution, the kinetic energy of the blank should be no greater than a few percent of the internal energy. For greater accuracy, especially when springback stresses are of interest, the kinetic energy should be lower. This approach is very useful because it is general for all types of metal forming processes and does not require any intuitive understanding of the stresses in the model; many forming processes may be too complex to permit an intuitive feel for the results.While a good primary indication of the caliber of a quasi-static analysis, the ratio of kinetic energy to internal energy alone is not adequate to confirmeval uate the two energies independently to determine whether they are reasonable. This part of the eval uation takes on increased importance when accurate springback stress results are needed because an accurate springback stress solution is highly dependent on accurate plasticity results. Even if the kinetic energy is fairly small, if it is highly oscillatory, the model could be experiencing significant plasticity. Generally, we expect smooth loading to produce smooth results; if the loading is smooth but the energy results are oscillatory, the results may be inadequate. Since an energy ratio is incapable of showing such behavior, you should also study the kinetic energy history itself to see whether it is smooth or noisy.If the kinetic energy does not indicate quasi-static behavior, it can be useful to look at velocity histories at some nodes to get an understanding of the model's behavior in various regions. Such velocity histories can indicate which regions of the model are oscillating and causing the high kinetic energies.Eval uating the results for attempt 1In ABAQUS/Viewer, select File->Open from the main menu bar; or use the  tool from the toolbar to open the output database draw_stage1_attempt1.odb. Plot the kinetic energy and the internal energy.To create an energy history plot:1.From the main menu bar, select Plot->History Output.A history plot of the external work for the whole model appears.2.From the main menu bar, select Result->History Output.The History Output dialog box appears.3.From the list of available variables, select Kinetic energy: ALLKE for Whole Model.4.Skipping frames between reads keeps any high frequency oscillation from becoming simply a blackened region on the graph. Skip 7 frames between reads.5.Click Plot to create a history plot of ALLKE.A history plot of the kinetic energy for the whole model appears (see Figure 7-14  ).Figure 7-14  Kinetic energy history for forming stage 1, attempt 1.6.Click Dismiss to close the dialog box.Similarly, create a history plot of the model internal energy, ALLIE (see Figure 7-15  ).

Page 75: Getting Started With ABAQUS

Figure 7-15  Internal energy history for forming stage 1, attempt 1.Figure 7-14   shows the kinetic energy history, which is very noisy through the first half of the step before becoming smooth. That the kinetic energy history has no clear relation to the forming of the blank is an indication of the inadequacy of this analysis. In this analysis the punch velocity remains constant, while the kinetic energy--which is due to the blank entirely since the punch has no mass--is far from constant.Figure 7-15   shows the internal energy history. Without anything further to which to compare the internal energy, it appears reasonable, although it is not clear why the slope changes at 8 ms.Comparing Figure 7-14   and Figure 7-15   shows that the kinetic energy is a small fraction (less than 1%) of the internal energy through all but the very beginning of the analysis. The criterion that kinetic energy must be small relative to internal energy has been satisfied, even for this severe loading case.Since the kinetic energy history is very noisy, it is useful to look at the velocity history of a node in the model to gain an understanding of the blank's motion. Plot the vertical velocity (V2) history of the first node in node set NHIST, which is a node in the central region of the blank (Figure 7-16  ).Figure 7-16  Velocity history of the first node in NHIST for forming stage 1, attempt 1.To create a history plot of the velocity:1.From the main menu bar, select Result->History Output.2.From the list of available variables in the History Output dialog box, select Spatial velocity: V2 at Node 521 in NSET NHIST.3.Click Plot to create a history plot of V2.The velocity of the node oscillates between values as great as ?0 m/s, while the punch velocity remains constant. Such noisy behavior has a strong effect on the results in this case, since the material includes plasticity. These results indicate that we must change the simulation in some way to obtain a smoother response.7.5.10  Forming stage 1--attempt 2For attempt 2 smooth the velocity amplitude of the punch. Instead of moving the punch with a constant velocity, use the SMOOTH STEP amplitude definition. Refer to ``Smooth amplitude curves,'' Section 7.2.1, for an explanation of this amplitude definition. By specifying an amplitude of 0.0 at the beginning of the step and an amplitude of 1.0 at the end of the step, ABAQUS/Explicit creates an amplitude definition that is smooth in both its first and second derivatives. Therefore, using SMOOTH STEP for the displacement control also assures us that the velocity and acceleration are smooth. Change the amplitude definition to*AMPLITUDE, NAME=FORM1, DEFINITION=SMOOTH STEP0., 0., .033, 1.Save your modified input in a file named draw_stage1_attempt2.inp, and run the analysis. Thirty minutes or more may be required to run this analysis to completion.Eval uating the results for attempt 2The kinetic energy history shown in Figure 7-17   is still quite noisy, although somewhat different from that of attempt 1. The noise dies out by 20 ms, and the kinetic energy drops to zero. Near the end of the analysis it again becomes noisy.Figure 7-17  Kinetic energy history for forming stage 1, attempt 2.The internal energy for attempt 2, shown in Figure 7-18  , is similar to that of attempt 1. The internal energy history has a few unexplained bumps, rather than the expected smooth increase. Again, the ratio of kinetic energy to internal energy is quite small and appears to be acceptable.Figure 7-18  Internal energy history for forming stage 1, attempt 2.For many forming analyses a smooth loading velocity, such as that used in attempt 2, is adequate to produce a quasi-static forming step. However, this particular forming process is somewhat less well-behaved than many because of the lack of a blank holder. Figure 7-19   shows the velocity history of node set BEND, which contains the node at the free end of the blank. Figure 7-19  Velocity history of node set BEND for forming stage 1, attempt 2.The node oscillates greatly because the end of the blank is unconstrained. If this forming process had a blank holder, attempt 2 would most likely provide acceptable results. However, since this process lacks such a constraint, we must make additional changes to produce an acceptable quasi-static solution.7.5.11  Forming stage 1--attempt 3To decrease the high-frequency noise caused primarily by the oscillations of the blank's free end, add stiffness proportional damping to the material definition of the blank. It is best to use the smallest amount of damping possible to obtain the desired solution since increasing the stiffness damping decreases the stable time increment and, thus, increases the computer time. (Another available type of material damping is mass proportional damping, which generally is used to decrease the low-frequency oscillations. Adding mass damping is akin to executing the forming process in a viscous fluid. The problem with mass proportional damping in metal forming analyses is the difficulty in determining whether or not the mass proportional damping has adversely influenced the solution. Therefore, we discourage the use of mass proportional damping in forming analyses unless it is absolutely necessary.)To avoid a dramatic drop in the stable time increment, the stiffness proportional damping factor, , should be less than, or of the same order of magnitude as, the initial stable time increment without damping. Since the initial stable time increment for attempt 2 reported in the status file is 1.05 ?10-7, use the following stiffness proportional damping for attempt 3: *DAMPING, BETA=1.E-7 The *DAMPING option should form part of the material definition of the problem.Save your modified input in a file, draw_stage1_attempt3.inp, and run the analysis.Eval uating the results for attempt 3The kinetic energy history shown in Figure 7-20   is much smoother and corresponds to the punch velocity much better than the previous attempts, though there is still some high frequency oscillation.The internal energy history, shown in Figure 7-21  , shows a smooth increase from zero up to the final value. Most of the internal energy is dissipated by plasticity. Again, the kinetic energy is small relative to the internal energy. These results appear to be acceptable.Figure 7-20  Kinetic energy history for forming stage 1, attempt 3.Figure 7-21  Internal energy history for forming stage 1, attempt 3.History plots of the other energy variables reveal that the energy absorbed by viscous dissipation is small relative to the internal energy. This confirmproportional damping included in this model has not adversely affected the results. In addition, the amount of energy used to control hourglassing is zero; thus, hourglassing is not a problem in this analysis.

Page 76: Getting Started With ABAQUS

7.5.12  Discussion of the three forming attemptsBefore continuing the forming process with the springback analysis, we will discuss what we have learned from the three attempts at forming stage 1.Our initial criteria for eval uating the acceptability of the results was that the kinetic energy should be small compared to the internal energy. What we found was that even for the most severe case, attempt 1, this condition seems to have been met adequately. For many forming analyses that are better constrained--for example, with a blank holder--keeping the kinetic energy to internal energy ratio small may be an adequate condition to obtain a good solution to the forming problem. However, in this simulation the high frequency oscillations proved to have a strong effect on the solution, doubling the internal energy of the blank, as shown in Figure 7-22quasi-static.Figure 7-22  Comparison of internal energies for the three attempts of forming stage 1.The additional requirements--that the histories of kinetic energy and internal energy must be appropriate and reasonable--are very useful and necessary, but they also increase the subjectivity of eval uating the results. Enforcing these requirements in general for more complex forming processes may be difficult because these requirements demand some intuition regarding the behavior of the forming process.Results of forming stage 1Now that we are satisfied that the quasi-static solution for the first forming stage is adequate, study some of the other results of interest. Figure 7-23which is the force summation through the entire thickness of the element in the radial direction, or the local 1-direction. The axisymmetric model has been swept 90?for visualization purposes.Figure 7-23  Contour plot of SF1 (section force in the radial direction) for forming stage 1, attempt 3 (swept model for visualization purposes only).To contour the section force:1.First, restrict the display group to the elements representing the blank. From the main menu bar, select Tools->Display Group->Create.The Create Display Group dialog box appears.2.Select the element set PART-1-1.BLANK, and click Replace to replace the current model display with the element set PART-1-1.BLANK.Now, the element set PART-1-1.BLANK is the only member of the display group.3.From the main menu bar, select Result->Field Output.The Field Output dialog box appears.4.Select SF from the Output Variable list.5.From the list of available components, select SF1.6.Click OK to apply these settings.The Select Plot Mode dialog box appears.7.Toggle on Contour, and click OK.To better visualize contours in axisymmetric models, sweep the shell elements to construct the equivalent three-dimensional view. You can extrude two-dimensional elements in a similar fashion.8.From the main menu bar, select View->ODB Display Options.The ODB Display Options dialog box appears.9.Click the Sweep & Extrude tab.10.In the General Sweep region, toggle on Sweep elements and set the sweep range from 0 to 90 degrees.11.Click OK to apply these settings.The view shown in Figure 7-23   can be specified.12.From the main menu bar, select View->Specify.The Specify View dialog box appears.13.Using the Rotation Angles method, enter the X-, Y-, and Z- angles as 45, 0, 0.14.Click OK.ABAQUS displays your model in the specified view.The plot shows that SF1 is nearly constant at a value of approximately 3.274 ?104 in the flat region near the symmetry line. We would expect SF1 to be fairly high and positive in this region because of the uniform stretching. Since the blank is formed in a smooth manner, we would expect SF1 to vary smoothly, as it does. It also is reasonable that SF1 drops to a lower value toward the free end of the blank.Figure 7-24   shows a contour plot of the shell thickness, STH. At the start of the analysis the blank had a uniform shell thickness of 0.5 mm.Figure 7-24  Contour plot of STH (shell thickness) for forming stage 1, and attempt 3 (swept model for visualization purposes only).By the end of forming stage 1 the blank has thinned somewhat in the filleted region, which makes sense since this region has stretched the greatest amount. The flat region has very little change in thickness because there was little drawing in that region. It is interesting that the shell actually became thicker in the vertical region of the blank. Such behavior is reasonable, since the free end of the blank moved substantially toward the symmetry line during forming, resulting in compressive stresses in the hoop direction. This behavior can be seen by looking at SF2, the resultant force in the hoop direction. If this force is strongly compressive, it is possible that a full three-dimensional solution would predict wrinkling. Figure 7-25   shows that the hoop force at the free end of the blank is strongly compressive with a value of 2.05 ?105 N, indicating that there may be wrinkling near the free end.Figure 7-25  Contour plot of SF2 (section force in the hoop direction) for forming stage 1, attempt 3 (swept model for visualization purposes only).7.5.13  Methods of speeding up the analysisNow that we have obtained an acceptable solution to the first forming stage, we can try to obtain similar acceptable results using less computer time. Most forming analyses require too much computer time to be run in their physical time scale because the actual time period of forming events is large by explicit dynamics standards; running in an acceptable amount of computer time often requires making changes to the input file to reduce the computer cost of the analysis. There are two ways to reduce the cost of the analysis:1.Artificially increase the punch velocity so that the same forming process occurs in a shorter step time. This method is called load-rate scaling.2.Artificially increase the mass density of the elements so that the stability limit increases, allowing the analysis to take fewer increments. This method is called mass scaling.Unless the model has rate-dependent materials or damping, these two methods effectively do the same thing. Our model has no rate-dependent materials but does contain rate-dependent damping due to the dashpot in the second forming stage. Since scaling the loading rate would change the velocities and, hence, the force in the dashpot, we will use

Page 77: Getting Started With ABAQUS

mass scaling instead, which will not affect the force in the dashpot.Determining acceptable mass scaling``Loading rates,'' Section 7.2, and ``Metal forming problems,'' Section 7.2.3, discuss how to determine acceptable scaling of the loading rate or mass to accelerate the time scale of a quasi-static analysis. The goal is to model the process in the shortest time period in which inertial forces remain insignificant. There are bounds on how much the solution time can be increased while still obtaining a meaningful quasi-static solution.As discussed in ``Loading rates,'' Section 7.2, we can use the same methods to determine an appropriate mass scaling factor as we would use to determine an appropriate load-rate scaling factor. The difference between the two methods is that a load-rate scaling factor of f has the same effect as a mass scaling factor of . Originally, we assumed that a step time of 10 times the period of the fundamental frequency of the blank would be adequate to produce quasi-static results. By studying the model energies and other results, we were satisfied that these results were acceptable. This technique produced a punch velocity of approximately 0.5 m/s, which is typical of actual punch velocities. Now we will accelerate the solution time using mass scaling and compare the results against our unscaled solution to determine whether the scaled results are acceptable. We assume that scaling can only diminish, not improve, the quality of the results. The objective is to use scaling to decrease the computer time and still produce acceptable results.Our goal is to determine what scaling values still produce acceptable results and at what point the scaled results become unacceptable. To see the effects of both acceptable and unacceptable scaling factors, we investigate a range of scaling factors on the stable time increment size from  to 30; specifically, we choose , 10, and 30. These speedup factors translate into mass scaling factors of 10, 100, and 900, respectively.To apply mass scaling of 10, add the following option to the history definition,*FIXED MASS SCALING, FACTOR=10and save the modified input in a file named draw_stage1_attempt3_sqrt10.inp; run draw_stage1_attempt3_10.inp and draw_stage1_attempt3_30.inp, which have mass scaling factors of 100 and 900, respectively.First we will look at the effect of mass scaling on the section forces and the displaced shape. We will then see whether the energy histories provide a general indication of the analysis quality.Eval uating the results with mass scalingOne of the results of interest in this analysis is the radial section force, SF1. Since we have already seen the contour plot of SF1 at the completion of the unscaled analysis in Figure 7-23  , we can compare the results from each of the scaled analyses with the unscaled analysis results. These contour plots display the results in the form of bands on the displaced mesh. Therefore, these SF1 contour plots also provide the displaced shape of the mesh. Figure 7-26   shows SF1 for a speedup ofspeedup of 10 (mass scaling of 100), and Figure 7-28   shows SF1 for a speedup of 30 (mass scaling of 900). These plots indicate that a speedup ofsimilar to the unscaled results. For a speedup of 10 the results are similar, but the section force at the symmetry axis drops noticeably. For a speedup of 30 the section force results are quite different, indicating that this level of speedup is clearly too high. Figure 7-26  Section force SF1 for speedup of  (mass scaling of 10; swept model for visualization purposes only).Figure 7-27  Section force SF1 for speedup of 10 (mass scaling of 100; swept model for visualization purposes only).Figure 7-28  Section force SF1 for speedup of 30 (mass scaling of 900; swept model for visualization purposes only).Now that we have seen how mass scaling has affected some of the section force results, we will see whether the energy histories provide the same indication of analysis quality. Figure 7-29   shows the histories of kinetic energy and internal energy for all of the scaled analyses. The internal energy is almost identical for all three cases, whereas the kinetic energy increases from nearly zero for a speedup of  to a maximum of approximately 7.0 for a speedup of 30. Figure 7-29  Kinetic and internal energy histories for speedups of , 10, and 30, corresponding to mass scaling factors of 10, 100, and 900, respectively.Discussion of speedup methodsAs the mass scaling increases, the solution time decreases. The quality of the results also decreases because dynamic effects become more prominent, but there is usually some level of scaling that improves the solution time without sacrificing the results. Clearly, a speedup of 30 is too great to produce quasi-static results for this analysis.A smaller speedup, such as , does not alter the results significantly. These results would be adequate for most applications, including springback analyses. With a scaling factor of 10 the quality of the results begins to diminish, while the general magnitudes and trends of the results remain intact. Correspondingly, the ratio of kinetic energy to internal energy increases noticeably. The results for this case would be adequate for many applications but not for accurate springback analysis.7.5.14  Springback after forming stage 1 in ABAQUS/StandardWhile it is possible to perform springback analyses within ABAQUS/Explicit, ABAQUS/Standard is much more efficient at solving springback analyses. Since springback analyses are simply static simulations without external loading or contact, ABAQUS/Standard can obtain a springback solution in just a few increments. Conversely, ABAQUS/Explicit must obtain a dynamic solution over a time period that is long enough for the solution to reach a steady state. For efficiency ABAQUS has the capability to import results back and forth between ABAQUS/Explicit and ABAQUS/Standard, allowing us to perform forming analyses in ABAQUS/Explicit and springback analyses in ABAQUS/Standard.We will create a new input file that imports the results from the analysis with a speedup of  (mass scaling of 10, draw_stage1_attempt3_sqrt10.inp) and perform a springback analysis.Model definitionThe first option following *HEADING is the *IMPORT option, which reads the element definitions and the state from the corresponding ABAQUS/Explicit analysis. Your import input file should begin with the following:*HEADINGDeep drawing of a can bottom -- first springbackABAQUS/Standard springback followingdraw_stage1_attempt3_sqrt10.inpSI units (kg, m, s, N)*IMPORT, STEP=1, INTERVAL=10, STATE=YES, UPDATE=NOBLANK,*IMPORT ELSETBLANK,*IMPORT NSETBSYM, NHIST

Page 78: Getting Started With ABAQUS

Setting the STATE parameter equal to YES causes the state of the model--stresses, strains, etc.--to be imported. Setting the UPDATE parameter equal to NO causes the strains and displacements to be imported as well instead of being reset to zero. The data line following the *IMPORT option supplies the name of the element set containing the elements that are to be imported. The data line following the *IMPORT ELSET option lists element set names to be imported; the *IMPORT NSET option likewise identifies node set names to be imported.History definitionYou must redefine the boundary conditions, which are not imported. Impose the same symmetry boundary conditions as were imposed in the ABAQUS/Explicit input file.*BOUNDARYBSYM, 1BSYM, 6For output, write the final state of the model to the restart file.*RESTART, WRITE, FREQUENCY=999The history definition is quite straightforward since no loads are applied. Use the following history definition:*STEP, NLGEOM*STATIC.1, 1.*BOUNDARY, FIXEDBSYM, 2, 2*OUTPUT, FIELD, FREQUENCY=10*ELEMENT OUTPUT, ELSET=BLANKSTH, SF*NODE OUTPUTU,*END STEPThe NLGEOM parameter is used on the *STEP option since the ABAQUS/Explicit analysis used it (this is the default setting in ABAQUS/Explicit). In general, it is safer to include the NLGEOM parameter because we do not always know whether or not geometric nonlinearities will affect the results. To remove rigid body motion, it is necessary to fix the blank in the 2-direction. Fix the blank at just a single point, such as node set BSYM, so that you impose no unnecessary constraints. It is important to use the FIXED parameter on the *BOUNDARY option so that BSYM is fixed at its final position at the end of forming stage 1. If you were to omit the FIXED parameter, BSYM would return to its original location prior to deformation. Either fixing BSYM at its final position from the previous stage or moving it back to its undeformed location will produce the same springback results; however, fixing BSYM at its final position retains the necessary continuity in the blank location through the stages of this simulation.Save your input in a file named draw_spring1_std.inp, and run the analysis using the following command:abaqus job=draw_spring1_std oldjob=draw_stage1_attempt3_sqrt10Results of the springback analysisFigure 7-30   shows a contour plot of SF1 at the end of the springback analysis in ABAQUS/Standard. These results are necessarily dependent on the accuracy of the forming stage preceding it. In fact, springback results are highly sensitive to errors in the forming stage, more sensitive than the results of the forming stage itself.Figure 7-30  Contour plot of SF1 following springback in ABAQUS/Standard (swept model for visualization purposes only).7.5.15  Annealing and forming stage 2Now that we are satisfied with the results for forming stage 1 with a speedup of  (mass scaling of 10) and its corresponding springback, we continue the simulation with annealing and forming stage 2 using ABAQUS/Explicit. We will create a new input file that imports the final springback condition from ABAQUS/Standard and continue the analysis from that point.Model definitionImport the model from the final increment of the springback analysis. Set the STATE parameter equal to YES so that the stress and strain state of the model is imported. Set the UPDATE parameter equal to NO so that the displacements are continuous. Begin your restart input file with the following *HEADING and *IMPORT option blocks:*HEADINGDeep drawing of a can bottom -- stage 2ABAQUS/Explicit annealing and forming stage 2 followingdraw_spring1_std.inpSI units (kg, m, s, N)*IMPORT, STATE=YES, UPDATE=NOBLANK,Since you are importing only the blank from the ABAQUS/Standard analysis, you must define the rigid tooling needed for forming stage 2 and the necessary node and element sets as shown in Figure 7-11  .*RIGID BODY, ELSET=PUNCH2, REF NODE=<reference node number>*RIGID BODY, ELSET=DIE2, REF NODE=<reference node number>*RIGID BODY, ELSET=DOMER, REF NODE=<reference node number>Define the surfaces on the blank and the rigid tools.*SURFACE, NAME=BLANK_TOPBLANK, <SPOS or SNEG>*SURFACE, NAME=BLANK_BOTBLANK, <SPOS or SNEG>*SURFACE, NAME=PUNCH2PUNCH2, <SPOS or SNEG>

Page 79: Getting Started With ABAQUS

*SURFACE, NAME=DIE2DIE2, <SPOS or SNEG>*SURFACE, NAME=DOMERDOMER, <SPOS or SNEG>You must also define the spring and dashpot on which die 2 sits. These are defined as a SPRINGA and a DASHPOTA element, each with one end attached to the reference node for die 2 (node set REFD2) and one end attached to ground (node set SPEND). *ELEMENT, TYPE=SPRINGA, ELSET=SPRING<element number>,<node # of REFD2>,<node # of SPEND>*SPRING, ELSET=SPRING2,6.3E6,*ELEMENT, TYPE=DASHPOTA, ELSET=DASHPOT<element number>,<node # of REFD2>,<node # of SPEND>*DASHPOT, ELSET=DASHPOT2,1.E4,Define the 10 kg mass associated with die 2.*ELEMENT, TYPE=MASS, ELSET=MASS<element number>,<node # of REFD2>*MASS, ELSET=MASS10.,You must define any desired sets for postprocessing.*NSET, NSET=REFREFP2, REFD2, REFDOMER, SPENDBefore proceeding, you must make certain that the rigid tools are positioned properly by defining a brief step that includes only the rigid body motion of the tools. Since only rigid body motion occurs in this first step, the time period for the step can be very short. We have chosen 1 ?10-6 s as the step time. Include the following amplitude definition in the model definition part of your input file:*AMPLITUDE, NAME=RIGID, DEFINITION=SMOOTH STEP0., 0., 1.E-6, 1. In addition, define an amplitude for the forming stage.*AMPLITUDE, NAME=FORM2, DEFINITION=SMOOTH STEP0., 0., .033, 1.History definitionSince an *ANNEAL step cannot be the first step in an ABAQUS/Explicit import analysis, begin the history by moving the rigid tooling into position. Moving the tooling into position is quite straightforward; the difficulty in this case is positioning the tools properly, given the unknown shape of the blank following springback. At the end of the first forming stage the position of the blank is known: the blank has been drawn to a depth of 0.015 m, and it is clamped between two rigid tools whose positions are known. However, during springback the blank is no longer constrained by the rigid tools, and it deforms freely to minimize its internal strain energy. The changes in shape during springback make it necessary to view the displaced shape following springback in ABAQUS/Viewer before positioning the rigid tools for the second forming stage.After the first step it is imperative that there be no overclosure of contact pairs because, if such overclosure exists, it is resolved in a single increment. Resolving the overclosure results in a large velocity being imposed on an overclosed node, possibly distorting the associated elements and drastically increasing the kinetic energy. On the other hand, computer time is wasted if the rigid bodies are far away from the blank at the start of the step because the analysis runs while no deformation occurs in the blank.Use Tools->Query from the main menu bar in ABAQUS/Viewer to determine the coordinates of some nodes on the blank at the end of springback. The goal is to position the rigid bodies for the second forming stage as close as possible to the deformed blank without any overclosure. Even the slightest overclosure will cause analysis problems. Remember that you must consider the thickness of the shell when positioning the rigid bodies, since ABAQUS/Explicit considers the current shell thickness when performing contact calculations. The forming process is designed so that the curved parts of punch 2 and die 2 form concentric arcs with the blank in between. Punch 2 has a radius of 0.006 m, and it contacts the inner radius of the blank, which also has a radius of approximately 0.006 m after springback. Die 2 has a radius of 0.0065 m, and it contacts the outer radius of the blank, which--given its thickness of approximately 0.0005--also has a radius of approximately 0.0065 m. Include the *DIAGNOSTICS option with the CONTACT INITIAL OVERCLOSURE=DETAIL and DEFORMATION SPEED CHECK=DETAIL parameters to provide detailed information about possible initial overclosures and resulting excessive deformation speeds.Use the amplitude definition named "RIGID" with the displacement boundary condition to move the rigid bodies into position. It is important that the velocity is zero at the end of the positioning step since the final velocity in the positioning step is the initial velocity in the second forming stage. Use the following step to position the rigid bodies for forming stage 2:*STEP*DYNAMIC, EXPLICIT, 1.E-6*RESTART, WRITE, NUMBER INTERVAL=1*BOUNDARY, TYPE=VELOCITYBSYM, 1, 2, 0.BSYM, 6, 6, 0.REFDOMER, 1, 1, 0.REFDOMER, 6, 6, 0.REFD2, 1, 1, 0.

Page 80: Getting Started With ABAQUS

REFD2, 6, 6, 0.SPEND, 1, 1, 0.REFP2, 1, 1, 0.REFP2, 6, 6, 0.*BOUNDARY, AMPLITUDE=RIGIDREFDOMER, 2, 2, <user-determined value>REFD2, 2, 2, <user-determined value>SPEND, 2, 2, <user-determined value>REFP2, 2, 2, <user-determined value>*DIAGNOSTICS, CONTACT INITIAL OVERCLOSURE=DETAIL,DEFORMATION SPEED CHECK=DETAIL*OUTPUT, HISTORY, TIME INTERVAL=1.E-5*NODE OUTPUT, NSET=NHISTU, V*NODE OUTPUT, NSET=REFU, RF*ENERGY OUTPUTALLKE, ALLIE, ALLWK, ALLVD, ALLAE, ALLPD, ETOTAL*OUTPUT, FIELD, NUMBER INTERVAL=4*ELEMENT OUTPUT, ELSET=BLANKSTH, SF, S*NODE OUTPUTU,*END STEPPhysically, annealing is the process of heating a metal part to a high temperature to allow the microstructure to recrystallize, removing dislocations caused by cold working of the material. The *ANNEAL procedure removes stresses and plastic strains from all deformable elements in the model without changing the shell thickness or deformed shape. The material properties are assumed to be the same before and after annealing. The *ANNEAL step is quite simple because there are no loadings or output requests permitted. The entire *ANNEAL step is as follows:*STEP*ANNEAL*END STEPIn the second forming stage the deformed blank is clamped between punch 2 and die 2, which sits on a spring and dashpot. As punch 2 is moved 0.010 m in the negative 2-direction, the blank is forced to move in the negative 2-direction, pressing against the stationary domer in the flat region of the blank. At the end of the second forming stage the blank takes on a dome shape in the previously flat region, while retaining the vertically drawn region from the first forming stage. Since the analysis is similar to the first forming stage, assume that the step time, damping, and mass scaling are the same as for the first forming stage. The loading rate in this stage of the forming simulation is actually slower than that in the first stage because the distance swept by the second punch is shorter while the step time remains the same.Add the following to your input file for forming stage 2:*STEP*DYNAMIC, EXPLICIT, .033*FIXED MASS SCALING, FACTOR=10*DIAGNOSTICS, CONTACT INITIAL OVERCLOSURE=DETAIL, DEFORMATION SPEED CHECK=DETAIL*CONTACT PAIR, INTERACTION=INTERPUNCH2, BLANK_TOPDIE2, BLANK_BOTDOMER, BLANK_BOT*SURFACE INTERACTION, NAME=INTER*FRICTION.1,*BOUNDARY, TYPE=DISPLACEMENT, AMPLITUDE=FORM2, OP=NEWREFP2, 2, 2, -0.010*BOUNDARY, TYPE=VELOCITY, OP=NEWREFP2, 1, 1, 0.REFP2, 6, 6, 0.REFD2, 1, 1, 0.REFD2, 6, 6, 0.SPEND, 1, 2, 0.REFDOMER, 1, 6, 0.BSYM, 1, 1, 0.BSYM, 6, 6, 0.

Page 81: Getting Started With ABAQUS

*MONITOR, NODE=<node # for REFD2>, DOF=2*RESTART, WRITE, NUMBER INTERVAL=10*END STEPSave your input data in a file called draw_stage2.inp. Run the analysis using the following command:abaqus job=draw_stage2 oldjob=draw_spring1_stdEval uating the results for forming stage 2Again you must eval uate the quality of the results as you did following the first forming stage to make certain that there are no severe dynamic effects to damage the analysis. We will not discuss the details of checking the results again because the procedures are the same as were used to check the results from the first forming stage. Some of the things to check are the histories of the kinetic energy, ALLKE, and the velocity of the reference node for die 2.Die 2 moves as it is pushed by the blank, which is pushed by punch 2. Since the bodies may not be exactly in contact at the start of the step, some impact may occur as the bodies interact. When the blank impacts die 2, even with a small velocity, die 2 will oscillate somewhat since it sits on a spring and dashpot. Although it is best to avoid these oscillations as much as possible, they have little effect on the solution because the predominant forming is occurring in the dome region. The deformed model following the second forming stage is shown in Figure 7-31  .Figure 7-31  Displaced model following forming stage 2.7.5.16  Springback after forming stage 2 in ABAQUS/StandardContinue with another springback analysis in ABAQUS/Standard. Perform the springback analysis in ABAQUS/Standard just as you did the first springback analysis. In fact, you must only change the *IMPORT option block to the following: *IMPORT, STATE=YES, UPDATE=NOBLANK,Save the springback input in a file called draw_spring2_std.inp, and run the springback analysis using the following command:abaqus job=draw_spring2_std oldjob=draw_stage2Figure 7-32   shows a contour plot of SF1 following the final springback in ABAQUS/Standard. Figure 7-32  Contour plot of SF1 following final springback in ABAQUS/Standard (swept model for visualization purposes only).Figure 7-33   shows the final shape of the can bottom following the final springback in ABAQUS/Standard.Figure 7-33  Final deformed shape of can bottom (swept model for visualization purposes only).7.6  Summary텶 f a quasi-static analysis is performed in its natural time scale, the solution should be nearly the same as a truly static solution.텶 t is often necessary to use load rate scaling or mass scaling to obtain a quasi-static solution using less CPU time.톂 he loading rate often can be increased somewhat, as long as the solution does not localize. If the loading rate is increased too much, inertial forces adversely affect the solution.텺 ass scaling is an alternative to increasing the loading rate. When using rate-dependent materials, mass scaling is preferable because increasing the loading rate artificially changes the material properties.텶 n a static analysis the lowest modes of the structure dominate the response. Knowing the lowest natural frequency and, correspondingly, the period of the lowest mode, you can estimate the time required to obtain the proper static response.텶 t may be necessary to run a series of analyses at varying loading rates to determine an acceptable loading rate.톂 he kinetic energy of the deforming material should not exceed a small fraction (typically 5% to 10%) of the internal energy throughout most of the simulation.톃 sing the *AMPLITUDE option with the DEFINITION=SMOOTH STEP parameter is the most efficient way to prescribe displacements in a quasi-static analysis.텶 f contact overclosures exist at the beginning of any step other than the first step, the contact overclosure is corrected in a single increment. The correction may cause large velocities and severe element distortions. 텶 mport the model from ABAQUS/Explicit to ABAQUS/Standard to perform an efficient springback analysis.텶 mport the model from ABAQUS/Standard to ABAQUS/Explicit to perform another forming stage following the springback analysis.Appendix A:  Example Input FilesThis appendix provides complete input file listings for the examples contained in this guide. You can get a copy of any of these input files with the commandabaqus fetch job=<file name>where <file name> does not include the extension .inp.A.1  Overhead hoist frameframe_xpl.inp   *HEADINGTwo-dimensional overhead hoist frameSI units (kg, m, s, N)*PREPRINT, ECHO=YES, MODEL=YES, HISTORY=YES**** Model definition***NODE, NSET=NALL101, 0., 0., 0.102, 1., 0., 0.103, 2., 0., 0.104, 0.5, 0.866, 0.105, 1.5, 0.866, 0.*ELEMENT, TYPE=T2D2, ELSET=FRAME11, 101,102

Page 82: Getting Started With ABAQUS

12, 102,10313, 101,10414, 102,10415, 102,10516, 103,10517, 104,105*SOLID SECTION, ELSET=FRAME, MATERIAL=STEEL** diameter = 5mm --> area = 1.963E-5 m^21.963E-5,*MATERIAL, NAME=STEEL*ELASTIC200.E9, 0.3*DENSITY7800.,**** History definition***STEP10kN central load*DYNAMIC, EXPLICIT,0.01*BOUNDARY101, ENCASTRE103, 2*CLOAD102, 2, -10.E3************************************ OUTPUT FOR HKS QA PURPOSES***********************************FILE OUTPUT, NUMBER INTERVAL=20*NODE FILE, NSET=NALLU, RF*EL FILE, ELSET=FRAMES, *END STEPA.2  Stress wave propagation in a barwave_50x10x10.inp   *HEADINGStress wave propagation in a bar -- 50x10x10 elementsSI units (kg, m, s, N)*NODE,NSET=FLHS1,0.,0.21,0.,.2*NGEN,NSET=FLHS1,21,1*NODE,NSET=FRHS5001,1.,0.5021,1.,.2*NGEN,NSET=FRHS5001,5021,1*NFILL,NSET=NFRONTFLHS,FRHS,50,100*NODE,NSET=BLHS200001,0.,0.,-.2200021,0.,.2,-.2*NGEN,NSET=BLHS200001,200021,1*NODE,NSET=BRHS205001,1.,0.,-.2205021,1.,.2,-.2*NGEN,NSET=BRHS

Page 83: Getting Started With ABAQUS

205001,205021,1*NFILL,NSET=NBACKBLHS,BRHS,50,100*NFILL,NSET=NALLNFRONT,NBACK,10,20000*ELEMENT,TYPE=C3D8R,ELSET=BAR1,1,3,103,101,20001,20003,20103,20101*ELGEN,ELSET=BAR1,10,2,2,50,100,100,10,20000,20000*ELGEN,ELSET=ELOAD1,10,2,2,10,20000,20000*ELSET,ELSET=EOUT81209,82509,83709*NFILL,NSET=NLHSFLHS,BLHS,10,20000*NFILL,NSET=NFIXFRHS,BRHS,10,20000*NGEN,NSET=LBOT1,200001,20000*NGEN,NSET=RBOT5001,205001,20000*NFILL,NSET=NBOTLBOT,RBOT,50,100*NGEN,NSET=LTOP21,200021,20000*NGEN,NSET=RTOP5021,205021,20000*NFILL,NSET=NTOPLTOP,RTOP,50,100*SOLID SECTION,ELSET=BAR,MATERIAL=STEEL*MATERIAL,NAME=STEEL*ELASTIC207.0E9,0.3*DENSITY7800.0,*BOUNDARYNFIX,1,3NFRONT,3,3NBACK,3,3NTOP,2,2NBOT,2,2*AMPLITUDE,NAME=BLAST0.,1.,3.88E-5,1.,3.89E-5,0.,3.90E-5,0.*STEPBlast loading*DYNAMIC,EXPLICIT,2.0E-4*BULK VISCOSITY,0.0*DLOAD,AMPLITUDE=BLASTELOAD,P3,1.0E5*OUTPUT, FIELD, VARIABLE=PRESELECT, NUMBER INTERVAL=4*OUTPUT, HISTORY, TIME INTERVAL=1.0E-6*ELEMENT OUTPUT, ELSET=EOUT S,************************************ OUTPUT FOR HKS QA PURPOSES***********************************NSET,NSET=QA_TEST_NLHSNLHS,*OUTPUT, FIELD, NUMBER INTERVAL=2, TIMEMARKS=YES

Page 84: Getting Started With ABAQUS

*NODE OUTPUT, NSET=QA_TEST_NLHSU,*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=5.0E-5***FILE OUTPUT,NUMBER INTERVAL=2,TIMEMARKS=YES*NODE FILE,NSET=NLHSU,*END STEPwave_25x5x5.inp   *HEADINGStress wave propagation in a bar -- 25x5x5 elementsSI units (kg, m, s, N)*NODE,NSET=FLHS1,0.,0.21,0.,.2*NGEN,NSET=FLHS1,21,1*NODE,NSET=FRHS5001,1.,0.5021,1.,.2*NGEN,NSET=FRHS5001,5021,1*NFILL,NSET=NFRONTFLHS,FRHS,50,100*NODE,NSET=BLHS200001,0.,0.,-.2200021,0.,.2,-.2*NGEN,NSET=BLHS200001,200021,1*NODE,NSET=BRHS205001,1.,0.,-.2205021,1.,.2,-.2*NGEN,NSET=BRHS205001,205021,1*NFILL,NSET=NBACKBLHS,BRHS,50,100*NFILL,NSET=NALLNFRONT,NBACK,10,20000*ELEMENT,TYPE=C3D8R,ELSET=BAR1,1,5,205,201,40001,40005,40205,40201*ELGEN,ELSET=BAR1,5,4,4,25,200,200,5,40000,40000*ELGEN,ELSET=ELOAD1,5,4,4,5,40000,40000*NFILL,NSET=NLHSFLHS,BLHS,10,20000*NFILL,NSET=NFIXFRHS,BRHS,10,20000*NGEN,NSET=LBOT1,200001,20000*NGEN,NSET=RBOT5001,205001,20000*NFILL,NSET=NBOTLBOT,RBOT,50,100*NGEN,NSET=LTOP21,200021,20000*NGEN,NSET=RTOP5021,205021,20000*NFILL,NSET=NTOPLTOP,RTOP,50,100*SOLID SECTION,ELSET=BAR,MATERIAL=STEEL

Page 85: Getting Started With ABAQUS

*MATERIAL,NAME=STEEL*ELASTIC207.0E9,0.3*DENSITY7800.0,*BOUNDARYNFIX,1,3NFRONT,3,3NBACK,3,3NTOP,2,2NBOT,2,2*AMPLITUDE,NAME=BLAST0.,1.,3.88E-5,1.,3.89E-5,0.,3.90E-5,0.*STEPBlast loading*DYNAMIC,EXPLICIT,2.0E-4*BULK VISCOSITY,0.0*DLOAD,AMPLITUDE=BLASTELOAD,P3,1.0E5*OUTPUT, FIELD, VARIABLE=PRESELECT, NUMBER INTERVAL=10*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=1.0E-6************************************ OUTPUT FOR HKS QA PURPOSES***********************************NSET,NSET=QA_TEST_NLHSNLHS,*OUTPUT, FIELD, NUMBER INTERVAL=4, TIMEMARKS=YES*NODE OUTPUT, NSET=QA_TEST_NLHSU,*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=5.0E-5***FILE OUTPUT,NUMBER INTERVAL=4,TIMEMARKS=YES*NODE FILE,NSET=NLHSU,*END STEPwave_50x5x5.inp   *HEADINGStress wave propagation in a bar -- 25x5x5 elementsSI units (kg, m, s, N)*NODE,NSET=FLHS1,0.,0.21,0.,.2*NGEN,NSET=FLHS1,21,1*NODE,NSET=FRHS5001,1.,0.5021,1.,.2*NGEN,NSET=FRHS5001,5021,1*NFILL,NSET=NFRONTFLHS,FRHS,50,100*NODE,NSET=BLHS200001,0.,0.,-.2200021,0.,.2,-.2*NGEN,NSET=BLHS200001,200021,1*NODE,NSET=BRHS205001,1.,0.,-.2205021,1.,.2,-.2

Page 86: Getting Started With ABAQUS

*NGEN,NSET=BRHS205001,205021,1*NFILL,NSET=NBACKBLHS,BRHS,50,100*NFILL,NSET=NALLNFRONT,NBACK,10,20000*ELEMENT,TYPE=C3D8R,ELSET=BAR1,1,5,105,101,40001,40005,40105,40101*ELGEN,ELSET=BAR1,5,4,4,50,100,100,5,40000,40000*ELGEN,ELSET=ELOAD1,5,4,4,5,40000,40000*NFILL,NSET=NLHSFLHS,BLHS,10,20000*NFILL,NSET=NFIXFRHS,BRHS,10,20000*NGEN,NSET=LBOT1,200001,20000*NGEN,NSET=RBOT5001,205001,20000*NFILL,NSET=NBOTLBOT,RBOT,50,100*NGEN,NSET=LTOP21,200021,20000*NGEN,NSET=RTOP5021,205021,20000*NFILL,NSET=NTOPLTOP,RTOP,50,100*SOLID SECTION,ELSET=BAR,MATERIAL=STEEL*MATERIAL,NAME=STEEL*ELASTIC207.0E9,0.3*DENSITY7800.0,*BOUNDARYNFIX,1,3NFRONT,3,3NBACK,3,3NTOP,2,2NBOT,2,2*AMPLITUDE,NAME=BLAST0.,1.,3.88E-5,1.,3.89E-5,0.,3.90E-5,0.*STEPBlast loading*DYNAMIC,EXPLICIT,2.0E-4*BULK VISCOSITY,0.0*DLOAD,AMPLITUDE=BLASTELOAD,P3,1.0E5*OUTPUT, FIELD, VARIABLE=PRESELECT, NUMBER INTERVAL=10*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=1.0E-6************************************ OUTPUT FOR HKS QA PURPOSES***********************************NSET,NSET=QA_TEST_NLHSNLHS,*OUTPUT, FIELD, NUMBER INTERVAL=4, TIMEMARKS=YES*NODE OUTPUT, NSET=QA_TEST_NLHSU,*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=5.0E-5

Page 87: Getting Started With ABAQUS

***FILE OUTPUT,NUMBER INTERVAL=4,TIMEMARKS=YES*NODE FILE,NSET=NLHSU,*END STEPwave_50x10x5.inp   *HEADINGStress wave propagation in a bar -- 50x10x5 elementsSI units (kg, m, s, N)*NODE,NSET=FLHS1,0.,0.21,0.,.2*NGEN,NSET=FLHS1,21,1*NODE,NSET=FRHS5001,1.,0.5021,1.,.2*NGEN,NSET=FRHS5001,5021,1*NFILL,NSET=NFRONTFLHS,FRHS,50,100*NODE,NSET=BLHS200001,0.,0.,-.2200021,0.,.2,-.2*NGEN,NSET=BLHS200001,200021,1*NODE,NSET=BRHS205001,1.,0.,-.2205021,1.,.2,-.2*NGEN,NSET=BRHS205001,205021,1*NFILL,NSET=NBACKBLHS,BRHS,50,100*NFILL,NSET=NALLNFRONT,NBACK,10,20000*ELEMENT,TYPE=C3D8R,ELSET=BAR1,1,3,103,101,40001,40003,40103,40101*ELGEN,ELSET=BAR1,10,2,2,50,100,100,5,40000,40000*ELGEN,ELSET=ELOAD1,10,2,2,5,40000,40000*NFILL,NSET=NLHSFLHS,BLHS,10,20000*NFILL,NSET=NFIXFRHS,BRHS,10,20000*NGEN,NSET=LBOT1,200001,20000*NGEN,NSET=RBOT5001,205001,20000*NFILL,NSET=NBOTLBOT,RBOT,50,100*NGEN,NSET=LTOP21,200021,20000*NGEN,NSET=RTOP5021,205021,20000*NFILL,NSET=NTOPLTOP,RTOP,50,100*SOLID SECTION,ELSET=BAR,MATERIAL=STEEL*MATERIAL,NAME=STEEL*ELASTIC207.0E9,0.3

Page 88: Getting Started With ABAQUS

*DENSITY7800.0,*BOUNDARYNFIX,1,3NFRONT,3,3NBACK,3,3NTOP,2,2NBOT,2,2*AMPLITUDE,NAME=BLAST0.,1.,3.88E-5,1.,3.89E-5,0.,3.90E-5,0.*STEPBlast loading*DYNAMIC,EXPLICIT,2.0E-4*BULK VISCOSITY,0.0*DLOAD,AMPLITUDE=BLASTELOAD,P3,1.0E5*OUTPUT, FIELD, VARIABLE=PRESELECT, NUMBER INTERVAL=10*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=1.0E-6************************************ OUTPUT FOR HKS QA PURPOSES***********************************NSET,NSET=QA_TEST_NLHSNLHS,*OUTPUT, FIELD, NUMBER INTERVAL=4, TIMEMARKS=YES*NODE OUTPUT, NSET=QA_TEST_NLHSU,*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=5.0E-5***FILE OUTPUT,NUMBER INTERVAL=4,TIMEMARKS=YES*NODE FILE,NSET=NLHSU,*END STEPA.3  Potential instabilities with springs and dashpotsstability.inp   *HEADINGSpring instabilitySI units (kg, m, s, N)*NODE,NSET=NALL1, 0.0, 0.02, 1.0, 0.03, 0.0, 1.04, 0.1, 1.0*ELEMENT,TYPE=SPRINGA,ELSET=SPRING1,1,2*SPRING,ELSET=SPRING1.0E5,*ELEMENT,TYPE=MASS,ELSET=MASS2,2*MASS,ELSET=MASS  5.0,*ELEMENT,TYPE=T2D2,ELSET=TRUSS3,3,4*SOLID SECTION,ELSET=TRUSS,MATERIAL=MAT11.0,*MATERIAL,NAME=MAT1*DENSITY 10.,*ELASTIC 1.0E4,0.0

Page 89: Getting Started With ABAQUS

*NSET,NSET=N22,***STEPLoad the truss with constant velocityLoad the spring/mass with constant force*DYNAMIC,EXPLICIT,2.0*BOUNDARY, TYPE=DISPLACEMENTNALL,2,21,1,33,1,1*BOUNDARY, TYPE=VELOCITY4,1,1,1*CLOAD2,1,1.0E3*BULK VISCOSITY0.0,*MONITOR,DOF=1,NODE=2*OUTPUT, FIELD, VARIABLE=PRESELECT, NUMBER INTERVAL=1*OUTPUT, HISTORY, TIME INTERVAL=1.0E-3*NODE OUTPUT,NSET=N2U,*ENERGY OUTPUTETOTAL, ALLKE, ALLIE, ALLWK************************************ OUTPUT FOR HKS QA PURPOSES***********************************FILE OUTPUT,NUMBER INTERVAL=5*NODE FILEU,*END STEPstability_addmass.inp   *HEADINGSpring instability*NODE,NSET=NALL1, 0.0, 0.02, 1.0, 0.03, 0.0, 1.04, 0.1, 1.0*ELEMENT,TYPE=SPRINGA,ELSET=SPRING1,1,2*SPRING,ELSET=SPRING1.0E5,*ELEMENT,TYPE=MASS,ELSET=MASS2,2*MASS,ELSET=MASS1760.0,*ELEMENT,TYPE=T2D2,ELSET=TRUSS3,3,4*SOLID SECTION,ELSET=TRUSS,MATERIAL=MAT11.0,*MATERIAL,NAME=MAT1*DENSITY 10.,*ELASTIC 1.0E4,0.0*NSET,NSET=N22, ****

Page 90: Getting Started With ABAQUS

*NSET, NSET=QA_TEST_ALLNODESNALL, N2***STEPLoad the truss with constant velocityLoad the spring/mass with constant force*DYNAMIC,EXPLICIT,2.0*BOUNDARY, TYPE=DISPLACEMENTNALL,2,21,1,33,1,1*BOUNDARY, TYPE=VELOCITY4,1,1,1*CLOAD2,1,1.0E3*BULK VISCOSITY0.0,*MONITOR,DOF=1,NODE=2*OUTPUT, FIELD, VARIABLE=PRESELECT, NUMBER INTERVAL=1*OUTPUT, HISTORY, TIME INTERVAL=1.0E-3*NODE OUTPUT,NSET=N2U,*ENERGY OUTPUTETOTAL, ALLKE, ALLIE, ALLWK************************************ OUTPUT FOR HKS QA PURPOSES***********************************FILE OUTPUT,NUMBER INTERVAL=5*NODE FILEU,*OUTPUT, FIELD, NUMBER INTERVAL=5*NODE OUTPUT, NSET=QA_TEST_ALLNODESU,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIMEINT=0.4***OUTPUT,HISTORY,VARIABLE=PRESELECT*END STEPA.4  Hourglassing in a rubber blockhourglass_square.inp   *HEADINGHourglassing example10 x 10 regular meshSI units (kg, m, s, N)*NODE,NSET=NALL1,0.,0.21,.10,0.1001,0.,.101021,.10,.10*NGEN,NSET=NBOT1,21,1*NGEN,NSET=NTOP1001,1021,1*NFILL,NSET=NALLNBOT,NTOP,20,50*NSET,NSET=NRHS,GENERATE21,1021,50*ELEMENT,TYPE=CPE4R,ELSET=EALL1,1,3,103,101*ELGEN,ELSET=EALL1,10,2,2,10,100,100*SOLID SECTION,ELSET=EALL,MATERIAL=RUBBER

Page 91: Getting Started With ABAQUS

.10,*MATERIAL,NAME=RUBBER** hyperelastic constants in Pa*HYPERELASTIC,POLYNOMIAL,N=13.2E6,.8E6** density is 1500 kg/m^3*DENSITY1500.,**** RIGID ELEMENT USED TO COMPRESS THE BLOCK***NODE, NSET=NRIGID20001,-.10,0.20002,.10,.2020003,-.02,.12*NSET,NSET=NREF20003,*ELEMENT,TYPE=R2D2,ELSET=ERIGID20001,20002,20001*AMPLITUDE,NAME=CRUSH,DEFINITION=SMOOTH STEP0.,0.,.1,1.*BOUNDARYNBOT,2NRHS,1NREF,6***SURFACE,NAME=RIGIDERIGID,SPOS*SURFACE,NAME=SOLIDEALL,*RIGID BODY,ELSET=ERIGID,REFNODE=20003***ELSET,ELSET=QA_TEST_ALLELEMSEALL,***NSET, NSET=QA_TEST_ALLNODESNALL, NBOT, NTOP, NALLNRHS, NRIGID, NREF***STEPCompress the rubber block*DYNAMIC,EXPLICIT,0.1*CONTACT PAIR,INTERACTION=INTERSOLID,RIGID*SURFACE INTERACTION,NAME=INTER** displace a total distance of .012 in both directions*BOUNDARY,TYPE=DISPLACEMENT,AMPLITUDE=CRUSHNREF,1,1,.012NREF,2,2,-.012***OUTPUT, FIELD, NUMBER INTERVAL=20, VARIABLE=PRESELECT*OUTPUT, HISTORY, FREQUENCY=1*ENERGY OUTPUTALLAE, ALLKE, ALLSE, ALLVD,ALLFD, ALLWK, ETOTAL************************************ OUTPUT FOR HKS QA PURPOSES***********************************OUTPUT, FIELD, NUMBER INTERVAL=1, TIMEMARKS=YES*NODE OUTPUT, NSET=QA_TEST_ALLNODES

Page 92: Getting Started With ABAQUS

U,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIMEINT=0.1***FILE OUTPUT,NUMBER INTERVAL=1*NODE FILEU,*END STEPhourglass_square_fine.inp   *HEADINGHourglassing example20 x 20 regular meshSI units (kg, m, s, N)*NODE,NSET=NALL1,0.,0.21,.10,0.1001,0.,.101021,.10,.10*NGEN,NSET=NBOT1,21,1*NGEN,NSET=NTOP1001,1021,1*NFILL,NSET=NALLNBOT,NTOP,20,50*NSET,NSET=NRHS,GEN21,1021,50*ELEMENT,TYPE=CPE4R,ELSET=EALL1,1,2,52,51*ELGEN,ELSET=EALL1,20,1,1,20,50,50*SOLID SECTION,ELSET=EALL,MATERIAL=RUBBER.10,*MATERIAL,NAME=RUBBER** hyperelastic constants in Pa*HYPERELASTIC,POLYNOMIAL,N=13.2E6,.8E6** density is 1500 kg/m^3*DENSITY1500.,**** RIGID ELEMENT USED TO COMPRESS THE BLOCK***NODE, NSET=NRIGID20001,-.10,0.20002,.10,.2020003,-.02,.12*NSET,NSET=NREF20003,*ELEMENT,TYPE=R2D2,ELSET=ERIGID20001,20002,20001*AMPLITUDE,NAME=CRUSH,DEFINITION=SMOOTH STEP0.,0.,.1,1.*BOUNDARYNBOT,2NRHS,1NREF,6***SURFACE,NAME=RIGIDERIGID,SPOS*SURFACE,NAME=SOLIDEALL,*RIGID BODY,ELSET=ERIGID,REFNODE=20003

Page 93: Getting Started With ABAQUS

***ELSET,ELSET=QA_TEST_ALLELEMSEALL,***NSET, NSET=QA_TEST_ALLNODESNALL, NBOT, NTOP, NALLNRHS, NRIGID, NREF***STEPCompress the rubber block*DYNAMIC,EXPLICIT,0.1*CONTACT PAIR,INTERACTION=INTERSOLID,RIGID*SURFACE INTERACTION,NAME=INTER** displace a total distance of .012 in both directions*BOUNDARY,TYPE=DISPLACEMENT,AMPLITUDE=CRUSHNREF,1,1,.012NREF,2,2,-.012***OUTPUT, FIELD, NUMBER INTERVAL=20, VARIABLE=PRESELECT*OUTPUT, HISTORY, FREQUENCY=1*ENERGY OUTPUTALLAE, ALLKE, ALLSE, ALLVD,ALLFD, ALLWK, ETOTAL************************************ OUTPUT FOR HKS QA PURPOSES***********************************OUTPUT, FIELD, NUMBER INTERVAL=1, TIMEMARKS=YES*NODE OUTPUT, NSET=QA_TEST_ALLNODESU,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIMEINT=0.1***FILE OUTPUT,NUMBER INTERVAL=1*NODE FILEU,*END STEPhourglass_flat_corner.inp   *HEADINGHourglassing example10 x 10 regular mesh with triangular cornerSI units (kg, m, s, N)*NODE,NSET=NALL1,0.,0.21,.10,0.1001,0.,.101021,.10,.10*NGEN,NSET=NBOT1,21,1*NGEN,NSET=NTOP1001,1021,1*NFILL,NSET=NALLNBOT,NTOP,20,50*NSET,NSET=NRHS,GENERATE21,1021,50*ELEMENT,TYPE=CPE4R,ELSET=EALL1,1,3,103,101*ELGEN,ELSET=EALL1,10,2,2,9,100,100*ELEMENT,TYPE=CPE4R,ELSET=EALL903,903,905,1005,1003

Page 94: Getting Started With ABAQUS

*ELGEN,ELSET=EALL903,9,2,2*ELEMENT,TYPE=CPE3,ELSET=EALL901,901,903,1003*SOLID SECTION,ELSET=EALL,MATERIAL=RUBBER.10,*MATERIAL,NAME=RUBBER** hyperelastic constants in Pa*HYPERELASTIC,POLYNOMIAL,N=13.2E6,.8E6** density is 1500 kg/m^3*DENSITY1500.,**** RIGID ELEMENT USED TO COMPRESS THE BLOCK***NODE, NSET=NRIGID20001,-.095,-.00520002,.105,.19520003,-.02,.12*NSET,NSET=NREF20003,*ELEMENT,TYPE=R2D2,ELSET=ERIGID20001,20002,20001*AMPLITUDE,NAME=CRUSH,DEFINITION=SMOOTH STEP0.,0.,.081,1.*BOUNDARYNBOT,2NRHS,1NREF,6***SURFACE,NAME=RIGIDERIGID,SPOS*SURFACE,NAME=SOLIDEALL,*RIGID BODY,ELSET=ERIGID,REFNODE=20003*STEPCompress the rubber block*DYNAMIC,EXPLICIT,.081*CONTACT PAIR,INTERACTION=INTERSOLID,RIGID*SURFACE INTERACTION,NAME=INTER** displace a total distance of .012 in both directions*BOUNDARY,TYPE=DISPLACEMENT,AMPLITUDE=CRUSHNREF,1,1,.007NREF,2,2,-.007***OUTPUT, FIELD, NUMBER INTERVAL=20, VARIABLE=PRESELECT*OUTPUT, HISTORY, FREQUENCY=1*ENERGY OUTPUTALLAE, ALLKE, ALLSE, ALLVD,ALLFD, ALLWK, ETOTAL************************************ OUTPUT FOR HKS QA PURPOSES***********************************NSET,NSET=QA_TEST_ALLNODESNALL,*OUTPUT, FIELD, NUMBER INTERVAL=1, TIMEMARKS=YES*NODE OUTPUT,NSET=QA_TEST_ALLNODESU,

Page 95: Getting Started With ABAQUS

*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=.081***FILE OUTPUT,NUMBER INTERVAL=1*NODE FILEU,*END STEPhourglass_flat_corner_fine.inp   *HEADINGHourglassing example20 x 20 regular mesh with triangular cornerSI units (kg, m, s, N)*NODE,NSET=NALL1,0.,0.21,.10,0.1001,0.,.101021,.10,.10*NGEN,NSET=NBOT1,21,1*NGEN,NSET=NTOP1001,1021,1*NFILL,NSET=NALLNBOT,NTOP,20,50*NSET,NSET=NRHS,GENERATE21,1021,50*ELEMENT,TYPE=CPE4R,ELSET=EALL1,1,2,52,51*ELGEN,ELSET=EALL1,20,1,1,19,50,50*ELEMENT,TYPE=CPE4R,ELSET=EALL952,952,953,1003,1002*ELGEN,ELSET=EALL952,19,1,1*ELEMENT,TYPE=CPE3,ELSET=EALL951,951,952,1002*SOLID SECTION,ELSET=EALL,MATERIAL=RUBBER.10,*MATERIAL,NAME=RUBBER** hyperelastic constants in Pa*HYPERELASTIC,POLYNOMIAL,N=13.2E6,.8E6** density is 1500 kg/m^3*DENSITY1500.,**** RIGID ELEMENT USED TO COMPRESS THE BLOCK***NODE, NSET=NRIGID20001,-.0975,-.002520002,.1025,.197520003,-.02,.12*NSET,NSET=NREF20003,*ELEMENT,TYPE=R2D2,ELSET=ERIGID20001,20002,20001*AMPLITUDE,NAME=CRUSH, DEFINITION=SMOOTH STEP0.,0.,.095,1.*BOUNDARYNBOT,2NRHS,1NREF,6**

Page 96: Getting Started With ABAQUS

*SURFACE,NAME=RIGIDERIGID,SPOS*SURFACE,NAME=SOLIDEALL,*RIGID BODY,ELSET=ERIGID,REFNODE=20003*STEPCompress the rubber block*DYNAMIC,EXPLICIT,.095*CONTACT PAIR,INTERACTION=INTERSOLID,RIGID*SURFACE INTERACTION,NAME=INTER** displace a total distance of .012 in both directions*BOUNDARY,TYPE=DISPLACEMENT,AMPLITUDE=CRUSHNREF,1,1,.0095NREF,2,2,-.0095***OUTPUT, FIELD, NUMBER INTERVAL=20, VARIABLE=PRESELECT*OUTPUT, HISTORY, FREQUENCY=1*ENERGY OUTPUTALLAE, ALLKE, ALLSE, ALLVD,ALLFD, ALLWK, ETOTAL************************************ OUTPUT FOR HKS QA PURPOSES***********************************NSET,NSET=QA_TEST_ALLNODESNALL,*OUTPUT, FIELD, NUMBER INTERVAL=1, TIMEMARKS=YES*NODE OUTPUT,NSET=QA_TEST_ALLNODESU,*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=.081***FILE OUTPUT,NUMBER INTERVAL=1*NODE FILEU,*END STEPhourglass_rounded.inp   *HEADINGHourglassing exampleCoarse rounded meshSI units (kg, m, s, N)***NODE, NSET=QA_TEST_ALLNODES  1,5.78316e-10 ,  0.0  2,0.1 ,         0.0  3,0.01 ,        -8.17963e-09      4,0.02 ,        -1.77636e-17      5,0.03 ,        0.0               6,0.04 ,        -8.88178e-18      7,0.05 ,        0.0               8,0.06 ,        0.0               9,0.07 ,        0.0              10,0.08 ,        0.0              11,0.09 ,        1.77636e-17      12,0.1 ,         0.1              13,0.1 ,         0.01             14,0.1 ,         0.02             15,0.1 ,         0.03             16,0.1 ,         0.04             17,0.1 ,         0.05             18,0.1 ,         0.06            

Page 97: Getting Started With ABAQUS

 19,0.1 ,         0.07             20,0.1 ,         0.08             21,0.1 ,         0.09             22,0.01 ,        0.1              23,0.09 ,        0.1              24,0.08 ,        0.1              25,0.07 ,        0.1              26,0.06 ,        0.1              27,0.05 ,        0.1              28,0.04 ,        0.1              29,0.03 ,        0.1              30,0.02 ,        0.1              31,-8.88178e-18 ,0.09             32,0.00292893 ,  0.0970711        33,0.0 ,         0.08             34,8.88178e-18 , 0.07             35,-3.55271e-17 ,0.06             36,1.77636e-17 , 0.05             37,-1.77636e-17 ,0.04             38,1.77636e-17 , 0.03             39,-1.77636e-17 ,0.02             40,8.88178e-18 , 0.01             41,0.01 ,        0.01             42,0.02 ,        0.01             43,0.03 ,        0.01             44,0.04 ,        0.01             45,0.05 ,        0.01             46,0.06 ,        0.01             47,0.07 ,        0.01             48,0.08 ,        0.01             49,0.09 ,        0.01             50,0.09 ,        0.02             51,0.09 ,        0.03             52,0.09 ,        0.04             53,0.09 ,        0.05             54,0.09 ,        0.06             55,0.09 ,        0.07             56,0.09 ,        0.08             57,0.09 ,        0.09             58,0.08 ,        0.09             59,0.07 ,        0.09             60,0.06 ,        0.09             61,0.0503229 ,   0.0904665        62,0.0409745 ,   0.0908973        63,0.0316622 ,   0.0910528        64,0.0227124 ,   0.0916174        65,0.0146448 ,   0.0916235        66,0.00792875 ,  0.0912914        67,0.00647801 ,  0.0859062        68,0.00714392 ,  0.0773471        69,0.00770258 ,  0.068442         70,0.00838407 ,  0.0594883        71,0.00909115 ,  0.0499915        72,0.00948701 ,  0.0399975        73,0.00971194 ,  0.0299992        74,0.00986479 ,  0.0199993        75,0.0200909 ,   0.0201311        76,0.0301478 ,   0.0201596        77,0.040162 ,    0.0201569        78,0.0501655 ,   0.0201507        79,0.0601664 ,   0.0201465       

Page 98: Getting Started With ABAQUS

 80,0.0701666 ,   0.0201443        81,0.0801666 ,   0.0201189        82,0.0800105 ,   0.0301555        83,0.0799231 ,   0.0401642        84,0.0792047 ,   0.0501634        85,0.0798683 ,   0.0601666        86,0.0798618 ,   0.0701667        87,0.0798831 ,   0.0801667        88,0.069845 ,    0.0800097        89,0.0601382 ,   0.0808345        90,0.0506204 ,   0.0815274        91,0.0410646 ,   0.0817862        92,0.0317326 ,   0.0820925        93,0.022659 ,    0.0830882        94,0.0141192 ,   0.0837189        95,0.0154997 ,   0.075066         96,0.0161073 ,   0.0668381        97,0.0172161 ,   0.0585046        98,0.0184092 ,   0.0496626        99,0.0192782 ,   0.0401657       100,0.0197972 ,   0.0300608       101,0.030197 ,    0.0303886       102,0.0403787 ,   0.0304388       103,0.0503986 ,   0.0299076       104,0.0604724 ,   0.0298293       105,0.0705017 ,   0.0303151       106,0.0236526 ,   0.0744256       107,0.0250679 ,   0.0655438       108,0.0264482 ,   0.0573525       109,0.0278873 ,   0.0491529       110,0.0291762 ,   0.0404657       111,0.0325028 ,   0.0734996       112,0.0338676 ,   0.0655433       113,0.0356554 ,   0.0577415       114,0.0374627 ,   0.0494021       115,0.0389564 ,   0.0403291       116,0.0417333 ,   0.0730185       117,0.0433002 ,   0.0649617       118,0.0449965 ,   0.0567479       119,0.0476309 ,   0.0483452       120,0.0488952 ,   0.0396955       121,0.0511686 ,   0.0725486       122,0.0523448 ,   0.0641522       123,0.053426 ,    0.0563392       124,0.0580377 ,   0.0480735       125,0.059107 ,    0.0389287       126,0.0691865 ,   0.0401552       127,0.0684489 ,   0.0502223       128,0.0702447 ,   0.0601388       129,0.0702772 ,   0.0702667       130,0.0607197 ,   0.0724696       131,0.0613644 ,   0.0641471       132,0.0607822 ,   0.0573286       *****ELEMENT, TYPE=CPE4R , ELSET=EALL       1,       3,      41,      40,       1       2,       4,      42,      41,       3       3,       5,      43,      42,       4       4,       6,      44,      43,       5       5,       7,      45,      44,       6

Page 99: Getting Started With ABAQUS

       6,       8,      46,      45,       7       7,       9,      47,      46,       8       8,      10,      48,      47,       9       9,      11,      49,      48,      10      10,      13,      49,      11,       2      11,      14,      50,      49,      13      12,      15,      51,      50,      14      13,      16,      52,      51,      15      14,      17,      53,      52,      16      15,      18,      54,      53,      17      16,      19,      55,      54,      18      17,      20,      56,      55,      19      18,      21,      57,      56,      20      19,      23,      57,      21,      12      20,      24,      58,      57,      23      21,      25,      59,      58,      24      22,      26,      60,      59,      25      23,      27,      61,      60,      26      24,      28,      62,      61,      27      25,      29,      63,      62,      28      26,      30,      64,      63,      29      27,      22,      65,      64,      30      28,      32,      66,      65,      22      29,      31,      67,      66,      32      30,      33,      68,      67,      31      31,      34,      69,      68,      33      32,      35,      70,      69,      34      33,      36,      71,      70,      35      34,      37,      72,      71,      36      35,      38,      73,      72,      37      36,      39,      74,      73,      38      37,      41,      74,      39,      40      38,      42,      75,      74,      41      39,      43,      76,      75,      42      40,      44,      77,      76,      43      41,      45,      78,      77,      44      42,      46,      79,      78,      45      43,      47,      80,      79,      46      44,      48,      81,      80,      47      45,      50,      81,      48,      49      46,      51,      82,      81,      50      47,      52,      83,      82,      51      48,      53,      84,      83,      52      49,      54,      85,      84,      53      50,      55,      86,      85,      54      51,      56,      87,      86,      55      52,      58,      87,      56,      57      53,      59,      88,      87,      58      54,      60,      89,      88,      59      55,      61,      90,      89,      60      56,      62,      91,      90,      61      57,      63,      92,      91,      62      58,      64,      93,      92,      63      59,      65,      94,      93,      64      60,      67,      94,      65,      66      61,      68,      95,      94,      67      62,      69,      96,      95,      68      63,      70,      97,      96,      69      64,      71,      98,      97,      70      65,      72,      99,      98,      71      66,      73,     100,      99,      72

Page 100: Getting Started With ABAQUS

      67,      75,     100,      73,      74      68,      76,     101,     100,      75      69,      77,     102,     101,      76      70,      78,     103,     102,      77      71,      79,     104,     103,      78      72,      80,     105,     104,      79      73,      82,     105,      80,      81      74,      95,     106,      93,      94      75,      96,     107,     106,      95      76,      97,     108,     107,      96      77,      98,     109,     108,      97      78,      99,     110,     109,      98      79,     101,     110,      99,     100      80,     106,     111,      92,      93      81,     107,     112,     111,     106      82,     108,     113,     112,     107      83,     109,     114,     113,     108      84,     110,     115,     114,     109      85,     102,     115,     110,     101      86,     111,     116,      91,      92      87,     112,     117,     116,     111      88,     113,     118,     117,     112      89,     114,     119,     118,     113      90,     115,     120,     119,     114      91,     103,     120,     115,     102      92,     116,     121,      90,      91      93,     117,     122,     121,     116      94,     118,     123,     122,     117      95,     119,     124,     123,     118      96,     120,     125,     124,     119      97,     104,     125,     120,     103      98,      83,     126,     105,      82      99,      84,     127,     126,      83     100,      85,     128,     127,      84     101,      86,     129,     128,      85     102,      88,     129,      86,      87     103,     121,     130,      89,      90     104,     122,     131,     130,     121     105,     123,     132,     131,     122     106,     124,     127,     132,     123     107,     104,     105,     126,     125     108,     130,     129,      88,      89     109,     131,     128,     129,     130     110,     132,     127,     128,     131     111,     124,     125,     126,     127**** BOT***NSET,NSET=NBOT       1,       3,       4,       5,       6,       7,       8,       9,      10,      11,**** RHS

Page 101: Getting Started With ABAQUS

***NSET,NSET=NRHS       2,       2,      12,      13,      14,      15,      16,      17,      18,      19,      20,      21,*SOLID SECTION,ELSET=EALL,MATERIAL=RUBBER.10,*MATERIAL,NAME=RUBBER** hyperelastic constants in Pa*HYPERELASTIC,POLYNOMIAL,N=13.2E6,.8E6** density is 1500 kg/m^3*DENSITY1500.,**** RIGID ELEMENT USED TO COMPRESS THE BLOCK***NODE, NSET=NRIGID20001,-.097071,-.00292920002,.102929,.19797120003,-.02,.12*NSET,NSET=NREF20003,*ELEMENT,TYPE=R2D2,ELSET=ERIGID20001,20002,20001*AMPLITUDE,NAME=CRUSH,DEFINITION=SMOOTH STEP0.,0.,.1,1.*BOUNDARYNBOT,2NRHS,1NREF,6***SURFACE,NAME=RIGIDERIGID,SPOS*SURFACE,NAME=SOLIDEALL,*RIGID BODY,ELSET=ERIGID,REFNODE=20003***ELSET,ELSET=QA_TEST_ALLELEMSEALL,***NSET, NSET=QA_TEST_ALLNODESQA_TEST_ALLNODES, NBOT, NRHS, NRIGIDNREF, ***STEPCompress the rubber block*DYNAMIC,EXPLICIT,0.1*CONTACT PAIR,INTERACTION=INTERSOLID,RIGID*SURFACE INTERACTION,NAME=INTER

Page 102: Getting Started With ABAQUS

** displace a total distance of .012 in both directions*BOUNDARY,TYPE=DISPLACEMENT,AMPLITUDE=CRUSHNREF,1,1,.009071NREF,2,2,-.009071***OUTPUT, FIELD, NUMBER INTERVAL=20, VARIABLE=PRESELECT*OUTPUT, HISTORY, FREQUENCY=1*ENERGY OUTPUTALLAE, ALLKE, ALLSE, ALLVD,ALLFD, ALLWK, ETOTAL************************************ OUTPUT FOR HKS QA PURPOSES***********************************OUTPUT, FIELD, NUMBER INTERVAL=1, TIMEMARKS=YES*NODE OUTPUT, NSET=QA_TEST_ALLNODESU,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIMEINT=0.1***FILE OUTPUT,NUMBER INTERVAL=1*NODE FILEU,*END STEPhourglass_rounded_fine.inp   *HEADINGHourglassing exampleFine rounded meshSI units (kg, m, s, N)***NODE, NSET=QA_TEST_ALLNODES       1,5.78316e-10 ,    5.78316e-10           2,0.1 ,            0.0                   3,0.00476191 ,     -8.74009e-09          4,0.00952381 ,     -8.88178e-18          5,0.0142857 ,      0.0                   6,0.0190476 ,      1.77636e-17           7,0.0238095 ,      0.0                   8,0.0285714 ,      0.0                   9,0.0333333 ,      -1.77636e-17         10,0.0380952 ,      8.88178e-18          11,0.0428571 ,      0.0                  12,0.047619 ,       -8.88178e-18         13,0.052381 ,       -8.88178e-18         14,0.0571429 ,      -8.88178e-18         15,0.0619048 ,      0.0                  16,0.0666667 ,      8.88178e-18          17,0.0714286 ,      0.0                  18,0.0761905 ,      0.0                  19,0.0809524 ,      -8.88178e-18         20,0.0857143 ,      8.88178e-18          21,0.0904762 ,      -8.88178e-18         22,0.0952381 ,      8.88178e-18          23,0.1 ,            0.1                  24,0.1 ,            0.005                25,0.1 ,            0.01                 26,0.1 ,            0.015                27,0.1 ,            0.02                 28,0.1 ,            0.025                29,0.1 ,            0.03                 30,0.1 ,            0.035                31,0.1 ,            0.04                 32,0.1 ,            0.045          

Page 103: Getting Started With ABAQUS

      33,0.1 ,            0.05                 34,0.1 ,            0.055                35,0.1 ,            0.06                 36,0.1 ,            0.065                37,0.1 ,            0.07                 38,0.1 ,            0.075                39,0.1 ,            0.08                 40,0.1 ,            0.085                41,0.1 ,            0.09                 42,0.1 ,            0.095                43,0.01 ,           0.1                  44,0.095 ,          0.1                  45,0.09 ,           0.1                  46,0.085 ,          0.1                  47,0.08 ,           0.1                  48,0.075 ,          0.1                  49,0.07 ,           0.1                  50,0.065 ,          0.1                  51,0.06 ,           0.1                  52,0.055 ,          0.1                  53,0.05 ,           0.1                  54,0.045 ,          0.1                  55,0.04 ,           0.1                  56,0.035 ,          0.1                  57,0.03 ,           0.1                  58,0.025 ,          0.1                  59,0.02 ,           0.1                  60,0.015 ,          0.1                  61,0.0 ,            0.09                 62,0.005 ,          0.0986602            63,0.00133975 ,     0.095                64,-8.88178e-18 ,   0.085                65,0.0 ,            0.08                 66,-1.77636e-17 ,   0.075                67,1.77636e-17 ,    0.07                 68,-8.88178e-18 ,   0.065                69,1.77636e-17 ,    0.06                 70,0.0 ,            0.055                71,0.0 ,            0.05                 72,-8.88178e-18 ,   0.045                73,-8.88178e-18 ,   0.04                 74,0.0 ,            0.035                75,8.88178e-18 ,    0.03                 76,8.88178e-18 ,    0.025                77,0.0 ,            0.02                 78,-8.88178e-18 ,   0.015                79,0.0 ,            0.00999998           80,8.88178e-18 ,    0.00499998           81,0.00476256 ,     0.00491069           82,0.00952401 ,     0.00484735           83,0.0142858 ,      0.00481              84,0.0190476 ,      0.00478884           85,0.0238095 ,      0.00477698           86,0.0285714 ,      0.00477033           87,0.0333333 ,      0.00476662           88,0.0380952 ,      0.00476454           89,0.0428571 ,      0.00476338           90,0.047619 ,       0.00476273           91,0.052381 ,       0.00476237           92,0.0571429 ,      0.00476216           93,0.0619048 ,      0.00476205     

Page 104: Getting Started With ABAQUS

      94,0.0666667 ,      0.00476199           95,0.0714286 ,      0.00476195           96,0.0761905 ,      0.00476193           97,0.0809524 ,      0.00476191           98,0.0857143 ,      0.00476191           99,0.0904762 ,      0.00476191          100,0.0952384 ,      0.00481482          101,0.095 ,          0.095               102,0.09 ,           0.095               103,0.085 ,          0.095               104,0.08 ,           0.095               105,0.075 ,          0.095               106,0.07 ,           0.095               107,0.065 ,          0.095               108,0.06 ,           0.095               109,0.055 ,          0.095               110,0.05 ,           0.095               111,0.045 ,          0.095               112,0.04 ,           0.095               113,0.035 ,          0.095               114,0.03 ,           0.095               115,0.025 ,          0.095               116,0.0202439 ,      0.095               117,0.0154874 ,      0.095               118,0.0111804 ,      0.0951625           119,0.00736927 ,     0.094562            120,0.00395472 ,     0.0927692           121,0.00358206 ,     0.0885104           122,0.00399329 ,     0.0837514           123,0.00446495 ,     0.0790828           124,0.00485982 ,     0.0744614           125,0.00486418 ,     0.0697215           126,0.00476997 ,     0.0649983           127,0.0048656 ,      0.0599996           128,0.0049239 ,      0.0549999           129,0.00495728 ,     0.05                130,0.00497607 ,     0.045               131,0.00498661 ,     0.04                132,0.00499251 ,     0.035               133,0.00499581 ,     0.03                134,0.00499766 ,     0.025               135,0.00499869 ,     0.02                136,0.00499927 ,     0.015               137,0.00494708 ,     0.00999964          138,0.0950956 ,      0.00995332          139,0.0950312 ,      0.0149882           140,0.0950093 ,      0.019997            141,0.0950026 ,      0.0249993           142,0.0950007 ,      0.0299998           143,0.0950002 ,      0.035               144,0.095 ,          0.04                145,0.095 ,          0.045               146,0.095 ,          0.05                147,0.095 ,          0.055               148,0.095 ,          0.06                149,0.095 ,          0.065               150,0.095 ,          0.07                151,0.095 ,          0.075               152,0.095 ,          0.08                153,0.095 ,          0.085               154,0.095 ,          0.09           

Page 105: Getting Started With ABAQUS

     155,0.00969311 ,     0.00981222          156,0.0144388 ,      0.00968934          157,0.0191861 ,      0.00962749          158,0.0239355 ,      0.00959954          159,0.0286871 ,      0.00958807          160,0.0334406 ,      0.00958417          161,0.038196 ,       0.00958357          162,0.0429528 ,      0.0095843           163,0.0477108 ,      0.00958545          164,0.0524697 ,      0.00958663          165,0.0572293 ,      0.00958769          166,0.0619894 ,      0.00958857          167,0.06675 ,        0.00958929          168,0.071511 ,       0.00958985          169,0.0762721 ,      0.00959029          170,0.0810334 ,      0.00959062          171,0.0857949 ,      0.00959088          172,0.0905497 ,      0.00964399          173,0.09 ,           0.09                174,0.085 ,          0.09                175,0.08 ,           0.09                176,0.075 ,          0.09                177,0.07 ,           0.09                178,0.065 ,          0.09                179,0.06 ,           0.09                180,0.055 ,          0.09                181,0.05 ,           0.0897364           182,0.0450128 ,      0.0904875           183,0.04 ,           0.09                184,0.035 ,          0.09                185,0.03 ,           0.09                186,0.025 ,          0.09                187,0.0201463 ,      0.090056            188,0.0156477 ,      0.0901038           189,0.0114117 ,      0.0905262           190,0.00749454 ,     0.0898208           191,0.0902107 ,      0.0148139           192,0.0900408 ,      0.0199138           193,0.0899907 ,      0.0249623           194,0.0899851 ,      0.0299841           195,0.0899898 ,      0.0349934           196,0.0899944 ,      0.0399973           197,0.0899973 ,      0.0449989           198,0.0899988 ,      0.0499996           199,0.0899995 ,      0.0549998           200,0.0899998 ,      0.0599999           201,0.0899999 ,      0.065               202,0.09 ,           0.07                203,0.09 ,           0.075               204,0.09 ,           0.08                205,0.09 ,           0.085               206,0.00784526 ,     0.0851443           207,0.00853498 ,     0.080095            208,0.00967079 ,     0.0750524           209,0.00973984 ,     0.0700113           210,0.00978195 ,     0.0650577           211,0.00985999 ,     0.0600674           212,0.00992457 ,     0.0550568           213,0.00996406 ,     0.0500415           214,0.00998455 ,     0.0450281           215,0.00999408 ,     0.0400182      

Page 106: Getting Started With ABAQUS

     216,0.00999813 ,     0.0350114           217,0.00999968 ,     0.030007            218,0.0100002 ,      0.0250042           219,0.0100003 ,      0.0200025           220,0.00997261 ,     0.0149884           221,0.0147512 ,      0.0147034           222,0.019503 ,       0.0145233           223,0.0242525 ,      0.0144475           224,0.0290008 ,      0.0144221           225,0.0337491 ,      0.014416            226,0.0384983 ,      0.0144166           227,0.0432485 ,      0.0144193           228,0.0480006 ,      0.0146643           229,0.0527528 ,      0.0144258           230,0.0575067 ,      0.0144288           231,0.0622617 ,      0.0144315           232,0.0670176 ,      0.0144338           233,0.0717744 ,      0.0144358           234,0.076532 ,       0.0144375           235,0.0812902 ,      0.014439            236,0.085741 ,       0.0144407           237,0.085 ,          0.085               238,0.08 ,           0.085               239,0.075 ,          0.085               240,0.07 ,           0.085               241,0.065 ,          0.085               242,0.06 ,           0.085               243,0.055 ,          0.085               244,0.0497093 ,      0.0841437           245,0.0450058 ,      0.085899            246,0.0400137 ,      0.0853578           247,0.0350001 ,      0.0852705           248,0.03 ,           0.085               249,0.0252767 ,      0.0850155           250,0.0207309 ,      0.0852459           251,0.0161891 ,      0.0852459           252,0.0117988 ,      0.0858309           253,0.0126945 ,      0.0809067           254,0.0140849 ,      0.075896            255,0.0148683 ,      0.0706397           256,0.0149574 ,      0.0654483           257,0.0149849 ,      0.0603158           258,0.0150056 ,      0.0552272           259,0.0150204 ,      0.0501605           260,0.015026 ,       0.0451102           261,0.0150246 ,      0.0400736           262,0.01502 ,        0.0350481           263,0.0150148 ,      0.0300309           264,0.0150103 ,      0.0250196           265,0.0149875 ,      0.0200064           266,0.085504 ,       0.0196104           267,0.0853652 ,      0.024735            268,0.0853371 ,      0.0298033           269,0.0852776 ,      0.0348925           270,0.0849545 ,      0.0399478           271,0.0849735 ,      0.0449707           272,0.0849854 ,      0.0499835           273,0.084992 ,       0.0549907           274,0.0849957 ,      0.0599948           275,0.0849976 ,      0.064997            276,0.0849987 ,      0.0699983      

Page 107: Getting Started With ABAQUS

     277,0.0849993 ,      0.0749991           278,0.0849995 ,      0.0799995           279,0.0198316 ,      0.0196089           280,0.0246018 ,      0.0193683           281,0.0293587 ,      0.0192786           282,0.0341133 ,      0.0192557           283,0.0388232 ,      0.0195078           284,0.0435806 ,      0.0195896           285,0.048402 ,       0.0201023           286,0.0531241 ,      0.0192628           287,0.0578769 ,      0.0192661           288,0.06263 ,        0.0192693           289,0.0673835 ,      0.0192723           290,0.0721376 ,      0.0192751           291,0.0765606 ,      0.0192767           292,0.0810093 ,      0.0192394           293,0.0799997 ,      0.0799999           294,0.0749999 ,      0.08                295,0.0699999 ,      0.08                296,0.0646637 ,      0.0800006           297,0.0593474 ,      0.079986            298,0.0537918 ,      0.0798593           299,0.0483624 ,      0.0785067           300,0.0444397 ,      0.0818527           301,0.0401636 ,      0.0810108           302,0.0353663 ,      0.0805349           303,0.0305006 ,      0.0803992           304,0.0257917 ,      0.0803748           305,0.0212672 ,      0.0804467           306,0.0170234 ,      0.0805618           307,0.018767 ,       0.0756879           308,0.0196936 ,      0.0709885           309,0.0200256 ,      0.0658202           310,0.0201145 ,      0.0606433           311,0.0201281 ,      0.0554937           312,0.0201216 ,      0.0503724           313,0.0201075 ,      0.0452747           314,0.0200893 ,      0.0401981           315,0.0200699 ,      0.0351399           316,0.0200521 ,      0.0300972           317,0.0200298 ,      0.025063            318,0.0807222 ,      0.0243303           319,0.0806742 ,      0.0294858           320,0.0805401 ,      0.0347306           321,0.0798441 ,      0.0397629           322,0.0798919 ,      0.0448468           323,0.0799312 ,      0.0499016           324,0.0799574 ,      0.054937            325,0.0799738 ,      0.0599597           326,0.0799837 ,      0.0649743           327,0.0799898 ,      0.0699836           328,0.0799927 ,      0.0749896           329,0.024923 ,       0.0245338           330,0.0295902 ,      0.0245417           331,0.0343522 ,      0.0245466           332,0.0391312 ,      0.0246084           333,0.0439817 ,      0.0247635           334,0.0489837 ,      0.0255213           335,0.0535794 ,      0.0237035           336,0.0583711 ,      0.024126            337,0.0630566 ,      0.0241092      

Page 108: Getting Started With ABAQUS

     338,0.0675354 ,      0.0243842           339,0.0720923 ,      0.0241132           340,0.0764514 ,      0.0240275           341,0.0231647 ,      0.075773            342,0.0244391 ,      0.0710298           343,0.025058 ,       0.0662511           344,0.0252451 ,      0.0610671           345,0.0252871 ,      0.0558784           346,0.0252752 ,      0.0506961           347,0.0252422 ,      0.0455317           348,0.0252006 ,      0.0403993           349,0.0251587 ,      0.0352949           350,0.0251078 ,      0.0299049           351,0.0278267 ,      0.0757026           352,0.0292771 ,      0.0711284           353,0.0298018 ,      0.0665854           354,0.0302456 ,      0.061445            355,0.0304024 ,      0.0562607           356,0.0304301 ,      0.0510698           357,0.0304052 ,      0.0458803           358,0.0303559 ,      0.0406974           359,0.0303824 ,      0.035272            360,0.0301692 ,      0.0298353           361,0.0327424 ,      0.0758878           362,0.0340745 ,      0.0712924           363,0.034687 ,       0.0667319           364,0.0351511 ,      0.0618474           365,0.035471 ,       0.0566767           366,0.0355743 ,      0.0514845           367,0.0355787 ,      0.0462867           368,0.0355385 ,      0.0410886           369,0.0355759 ,      0.03552             370,0.0352385 ,      0.029942            371,0.0377128 ,      0.0760459           372,0.0389279 ,      0.0715307           373,0.0395415 ,      0.0669765           374,0.0399766 ,      0.0621835           375,0.0404684 ,      0.0570852           376,0.0406805 ,      0.0519031           377,0.0407381 ,      0.0467066           378,0.0407215 ,      0.0415054           379,0.0407927 ,      0.0358567           380,0.0403158 ,      0.0301612           381,0.0429949 ,      0.0770777           382,0.0438735 ,      0.0724468           383,0.044453 ,       0.0678221           384,0.0450048 ,      0.0628627           385,0.0455152 ,      0.0577175           386,0.0458113 ,      0.0525224           387,0.0459334 ,      0.0473068           388,0.0459511 ,      0.0420846           389,0.0460155 ,      0.0363563           390,0.0453922 ,      0.0305318           391,0.0491573 ,      0.0735438           392,0.0496202 ,      0.0685562           393,0.049974 ,       0.0633561           394,0.0505053 ,      0.0582801           395,0.050887 ,       0.0531059           396,0.0510886 ,      0.0479006           397,0.0511606 ,      0.0426802           398,0.051237 ,       0.0370734      

Page 109: Getting Started With ABAQUS

     399,0.0504385 ,      0.0312928           400,0.0546041 ,      0.0748046           401,0.0547817 ,      0.0695641           402,0.0551609 ,      0.0643739           403,0.0556313 ,      0.0591955           404,0.0560376 ,      0.053992            405,0.056301 ,       0.0487611           406,0.0561574 ,      0.0435158           407,0.0564581 ,      0.0382622           408,0.0560631 ,      0.0330352           409,0.0543058 ,      0.0276458           410,0.058694 ,       0.028688            411,0.0633064 ,      0.0291063           412,0.0749954 ,      0.0749972           413,0.0699971 ,      0.0750003           414,0.0649982 ,      0.0750009           415,0.0599988 ,      0.0749833           416,0.0599357 ,      0.0699344           417,0.0601894 ,      0.0648894           418,0.0606345 ,      0.0598121           419,0.0607717 ,      0.0546921           420,0.0610156 ,      0.0495413           421,0.0611409 ,      0.0443579           422,0.0611731 ,      0.0391413           423,0.0614801 ,      0.0339643           424,0.0676202 ,      0.0295716           425,0.0719442 ,      0.0293197           426,0.076306 ,       0.029008            427,0.066424 ,       0.0348155           428,0.0712383 ,      0.0345775           429,0.0760571 ,      0.0342656           430,0.0749899 ,      0.0699945           431,0.0699917 ,      0.0700006           432,0.0649967 ,      0.0699991           433,0.074983 ,       0.0649904           434,0.0699849 ,      0.0650003           435,0.0649983 ,      0.064999            436,0.0749727 ,      0.0599843           437,0.0699751 ,      0.0599996           438,0.0653074 ,      0.0600472           439,0.0749561 ,      0.0549751           440,0.0702522 ,      0.0550192           441,0.0655331 ,      0.0550718           442,0.0749296 ,      0.0499607           443,0.0703401 ,      0.0500151           444,0.0657277 ,      0.0500776           445,0.0751652 ,      0.0448009           446,0.0703957 ,      0.0449914           447,0.0657962 ,      0.0450509           448,0.0751578 ,      0.0396081           449,0.0703148 ,      0.039945            450,0.0657913 ,      0.0400013      *****ELEMENT, TYPE=CPE4R , ELSET=EALL       1,       3,      81,      80,       1       2,       4,      82,      81,       3       3,       5,      83,      82,       4       4,       6,      84,      83,       5       5,       7,      85,      84,       6       6,       8,      86,      85,       7

Page 110: Getting Started With ABAQUS

       7,       9,      87,      86,       8       8,      10,      88,      87,       9       9,      11,      89,      88,      10      10,      12,      90,      89,      11      11,      13,      91,      90,      12      12,      14,      92,      91,      13      13,      15,      93,      92,      14      14,      16,      94,      93,      15      15,      17,      95,      94,      16      16,      18,      96,      95,      17      17,      19,      97,      96,      18      18,      20,      98,      97,      19      19,      21,      99,      98,      20      20,      22,     100,      99,      21      21,      24,     100,      22,       2      22,      44,     101,      42,      23      23,      45,     102,     101,      44      24,      46,     103,     102,      45      25,      47,     104,     103,      46      26,      48,     105,     104,      47      27,      49,     106,     105,      48      28,      50,     107,     106,      49      29,      51,     108,     107,      50      30,      52,     109,     108,      51      31,      53,     110,     109,      52      32,      54,     111,     110,      53      33,      55,     112,     111,      54      34,      56,     113,     112,      55      35,      57,     114,     113,      56      36,      58,     115,     114,      57      37,      59,     116,     115,      58      38,      60,     117,     116,      59      39,      43,     118,     117,      60      40,      62,     119,     118,      43      41,      63,     120,     119,      62      42,      61,     121,     120,      63      43,      64,     122,     121,      61      44,      65,     123,     122,      64      45,      66,     124,     123,      65      46,      67,     125,     124,      66      47,      68,     126,     125,      67      48,      69,     127,     126,      68      49,      70,     128,     127,      69      50,      71,     129,     128,      70      51,      72,     130,     129,      71      52,      73,     131,     130,      72      53,      74,     132,     131,      73      54,      75,     133,     132,      74      55,      76,     134,     133,      75      56,      77,     135,     134,      76      57,      78,     136,     135,      77      58,      79,     137,     136,      78      59,      81,     137,      79,      80      60,      25,     138,     100,      24      61,      26,     139,     138,      25      62,      27,     140,     139,      26      63,      28,     141,     140,      27      64,      29,     142,     141,      28      65,      30,     143,     142,      29      66,      31,     144,     143,      30      67,      32,     145,     144,      31

Page 111: Getting Started With ABAQUS

      68,      33,     146,     145,      32      69,      34,     147,     146,      33      70,      35,     148,     147,      34      71,      36,     149,     148,      35      72,      37,     150,     149,      36      73,      38,     151,     150,      37      74,      39,     152,     151,      38      75,      40,     153,     152,      39      76,      41,     154,     153,      40      77,     101,     154,      41,      42      78,      82,     155,     137,      81      79,      83,     156,     155,      82      80,      84,     157,     156,      83      81,      85,     158,     157,      84      82,      86,     159,     158,      85      83,      87,     160,     159,      86      84,      88,     161,     160,      87      85,      89,     162,     161,      88      86,      90,     163,     162,      89      87,      91,     164,     163,      90      88,      92,     165,     164,      91      89,      93,     166,     165,      92      90,      94,     167,     166,      93      91,      95,     168,     167,      94      92,      96,     169,     168,      95      93,      97,     170,     169,      96      94,      98,     171,     170,      97      95,      99,     172,     171,      98      96,     138,     172,      99,     100      97,     102,     173,     154,     101      98,     103,     174,     173,     102      99,     104,     175,     174,     103     100,     105,     176,     175,     104     101,     106,     177,     176,     105     102,     107,     178,     177,     106     103,     108,     179,     178,     107     104,     109,     180,     179,     108     105,     110,     181,     180,     109     106,     111,     182,     181,     110     107,     112,     183,     182,     111     108,     113,     184,     183,     112     109,     114,     185,     184,     113     110,     115,     186,     185,     114     111,     116,     187,     186,     115     112,     117,     188,     187,     116     113,     118,     189,     188,     117     114,     119,     190,     189,     118     115,     121,     190,     119,     120     116,     139,     191,     172,     138     117,     140,     192,     191,     139     118,     141,     193,     192,     140     119,     142,     194,     193,     141     120,     143,     195,     194,     142     121,     144,     196,     195,     143     122,     145,     197,     196,     144     123,     146,     198,     197,     145     124,     147,     199,     198,     146     125,     148,     200,     199,     147     126,     149,     201,     200,     148     127,     150,     202,     201,     149     128,     151,     203,     202,     150

Page 112: Getting Started With ABAQUS

     129,     152,     204,     203,     151     130,     153,     205,     204,     152     131,     173,     205,     153,     154     132,     122,     206,     190,     121     133,     123,     207,     206,     122     134,     124,     208,     207,     123     135,     125,     209,     208,     124     136,     126,     210,     209,     125     137,     127,     211,     210,     126     138,     128,     212,     211,     127     139,     129,     213,     212,     128     140,     130,     214,     213,     129     141,     131,     215,     214,     130     142,     132,     216,     215,     131     143,     133,     217,     216,     132     144,     134,     218,     217,     133     145,     135,     219,     218,     134     146,     136,     220,     219,     135     147,     155,     220,     136,     137     148,     156,     221,     220,     155     149,     157,     222,     221,     156     150,     158,     223,     222,     157     151,     159,     224,     223,     158     152,     160,     225,     224,     159     153,     161,     226,     225,     160     154,     162,     227,     226,     161     155,     163,     228,     227,     162     156,     164,     229,     228,     163     157,     165,     230,     229,     164     158,     166,     231,     230,     165     159,     167,     232,     231,     166     160,     168,     233,     232,     167     161,     169,     234,     233,     168     162,     170,     235,     234,     169     163,     171,     236,     235,     170     164,     191,     236,     171,     172     165,     174,     237,     205,     173     166,     175,     238,     237,     174     167,     176,     239,     238,     175     168,     177,     240,     239,     176     169,     178,     241,     240,     177     170,     179,     242,     241,     178     171,     180,     243,     242,     179     172,     181,     244,     243,     180     173,     182,     245,     244,     181     174,     183,     246,     245,     182     175,     184,     247,     246,     183     176,     185,     248,     247,     184     177,     186,     249,     248,     185     178,     187,     250,     249,     186     179,     188,     251,     250,     187     180,     189,     252,     251,     188     181,     206,     252,     189,     190     182,     207,     253,     252,     206     183,     208,     254,     253,     207     184,     209,     255,     254,     208     185,     210,     256,     255,     209     186,     211,     257,     256,     210     187,     212,     258,     257,     211     188,     213,     259,     258,     212     189,     214,     260,     259,     213

Page 113: Getting Started With ABAQUS

     190,     215,     261,     260,     214     191,     216,     262,     261,     215     192,     217,     263,     262,     216     193,     218,     264,     263,     217     194,     219,     265,     264,     218     195,     221,     265,     219,     220     196,     192,     266,     236,     191     197,     193,     267,     266,     192     198,     194,     268,     267,     193     199,     195,     269,     268,     194     200,     196,     270,     269,     195     201,     197,     271,     270,     196     202,     198,     272,     271,     197     203,     199,     273,     272,     198     204,     200,     274,     273,     199     205,     201,     275,     274,     200     206,     202,     276,     275,     201     207,     203,     277,     276,     202     208,     204,     278,     277,     203     209,     237,     278,     204,     205     210,     222,     279,     265,     221     211,     223,     280,     279,     222     212,     224,     281,     280,     223     213,     225,     282,     281,     224     214,     226,     283,     282,     225     215,     227,     284,     283,     226     216,     228,     285,     284,     227     217,     229,     286,     285,     228     218,     230,     287,     286,     229     219,     231,     288,     287,     230     220,     232,     289,     288,     231     221,     233,     290,     289,     232     222,     234,     291,     290,     233     223,     235,     292,     291,     234     224,     266,     292,     235,     236     225,     238,     293,     278,     237     226,     239,     294,     293,     238     227,     240,     295,     294,     239     228,     241,     296,     295,     240     229,     242,     297,     296,     241     230,     243,     298,     297,     242     231,     244,     299,     298,     243     232,     245,     300,     299,     244     233,     246,     301,     300,     245     234,     247,     302,     301,     246     235,     248,     303,     302,     247     236,     249,     304,     303,     248     237,     250,     305,     304,     249     238,     251,     306,     305,     250     239,     253,     306,     251,     252     240,     254,     307,     306,     253     241,     255,     308,     307,     254     242,     256,     309,     308,     255     243,     257,     310,     309,     256     244,     258,     311,     310,     257     245,     259,     312,     311,     258     246,     260,     313,     312,     259     247,     261,     314,     313,     260     248,     262,     315,     314,     261     249,     263,     316,     315,     262     250,     264,     317,     316,     263

Page 114: Getting Started With ABAQUS

     251,     279,     317,     264,     265     252,     267,     318,     292,     266     253,     268,     319,     318,     267     254,     269,     320,     319,     268     255,     270,     321,     320,     269     256,     271,     322,     321,     270     257,     272,     323,     322,     271     258,     273,     324,     323,     272     259,     274,     325,     324,     273     260,     275,     326,     325,     274     261,     276,     327,     326,     275     262,     277,     328,     327,     276     263,     293,     328,     277,     278     264,     280,     329,     317,     279     265,     281,     330,     329,     280     266,     282,     331,     330,     281     267,     283,     332,     331,     282     268,     284,     333,     332,     283     269,     285,     334,     333,     284     270,     286,     335,     334,     285     271,     287,     336,     335,     286     272,     288,     337,     336,     287     273,     289,     338,     337,     288     274,     290,     339,     338,     289     275,     291,     340,     339,     290     276,     318,     340,     291,     292     277,     307,     341,     305,     306     278,     308,     342,     341,     307     279,     309,     343,     342,     308     280,     310,     344,     343,     309     281,     311,     345,     344,     310     282,     312,     346,     345,     311     283,     313,     347,     346,     312     284,     314,     348,     347,     313     285,     315,     349,     348,     314     286,     316,     350,     349,     315     287,     329,     350,     316,     317     288,     341,     351,     304,     305     289,     342,     352,     351,     341     290,     343,     353,     352,     342     291,     344,     354,     353,     343     292,     345,     355,     354,     344     293,     346,     356,     355,     345     294,     347,     357,     356,     346     295,     348,     358,     357,     347     296,     349,     359,     358,     348     297,     350,     360,     359,     349     298,     330,     360,     350,     329     299,     351,     361,     303,     304     300,     352,     362,     361,     351     301,     353,     363,     362,     352     302,     354,     364,     363,     353     303,     355,     365,     364,     354     304,     356,     366,     365,     355     305,     357,     367,     366,     356     306,     358,     368,     367,     357     307,     359,     369,     368,     358     308,     360,     370,     369,     359     309,     331,     370,     360,     330     310,     361,     371,     302,     303     311,     362,     372,     371,     361

Page 115: Getting Started With ABAQUS

     312,     363,     373,     372,     362     313,     364,     374,     373,     363     314,     365,     375,     374,     364     315,     366,     376,     375,     365     316,     367,     377,     376,     366     317,     368,     378,     377,     367     318,     369,     379,     378,     368     319,     370,     380,     379,     369     320,     332,     380,     370,     331     321,     371,     381,     301,     302     322,     372,     382,     381,     371     323,     373,     383,     382,     372     324,     374,     384,     383,     373     325,     375,     385,     384,     374     326,     376,     386,     385,     375     327,     377,     387,     386,     376     328,     378,     388,     387,     377     329,     379,     389,     388,     378     330,     380,     390,     389,     379     331,     333,     390,     380,     332     332,     381,     299,     300,     301     333,     382,     391,     299,     381     334,     383,     392,     391,     382     335,     384,     393,     392,     383     336,     385,     394,     393,     384     337,     386,     395,     394,     385     338,     387,     396,     395,     386     339,     388,     397,     396,     387     340,     389,     398,     397,     388     341,     390,     399,     398,     389     342,     334,     399,     390,     333     343,     391,     400,     298,     299     344,     392,     401,     400,     391     345,     393,     402,     401,     392     346,     394,     403,     402,     393     347,     395,     404,     403,     394     348,     396,     405,     404,     395     349,     397,     406,     405,     396     350,     398,     407,     406,     397     351,     399,     408,     407,     398     352,     335,     409,     399,     334     353,     409,     410,     408,     399     354,     336,     410,     409,     335     355,     337,     411,     410,     336     356,     294,     412,     328,     293     357,     295,     413,     412,     294     358,     296,     414,     413,     295     359,     297,     415,     414,     296     360,     400,     415,     297,     298     361,     401,     416,     415,     400     362,     402,     417,     416,     401     363,     403,     418,     417,     402     364,     404,     419,     418,     403     365,     405,     420,     419,     404     366,     406,     421,     420,     405     367,     407,     422,     421,     406     368,     408,     423,     422,     407     369,     410,     411,     423,     408     370,     338,     424,     411,     337     371,     339,     425,     424,     338     372,     340,     426,     425,     339

Page 116: Getting Started With ABAQUS

     373,     319,     426,     340,     318     374,     424,     427,     423,     411     375,     425,     428,     427,     424     376,     426,     429,     428,     425     377,     320,     429,     426,     319     378,     412,     430,     327,     328     379,     413,     431,     430,     412     380,     414,     432,     431,     413     381,     416,     432,     414,     415     382,     430,     433,     326,     327     383,     431,     434,     433,     430     384,     432,     435,     434,     431     385,     417,     435,     432,     416     386,     433,     436,     325,     326     387,     434,     437,     436,     433     388,     435,     438,     437,     434     389,     418,     438,     435,     417     390,     436,     439,     324,     325     391,     437,     440,     439,     436     392,     438,     441,     440,     437     393,     419,     441,     438,     418     394,     439,     442,     323,     324     395,     440,     443,     442,     439     396,     441,     444,     443,     440     397,     420,     444,     441,     419     398,     442,     445,     322,     323     399,     443,     446,     445,     442     400,     444,     447,     446,     443     401,     421,     447,     444,     420     402,     445,     448,     321,     322     403,     446,     449,     448,     445     404,     447,     450,     449,     446     405,     422,     450,     447,     421     406,     448,     429,     320,     321     407,     449,     428,     429,     448     408,     450,     427,     428,     449     409,     450,     422,     423,     427**** BOT***NSET,NSET=NBOT       1,       3,       4,       5,       6,       7,       8,       9,      10,      11,      12,      13,      14,      15,      16,      17,      18,      19,      20,      21,

Page 117: Getting Started With ABAQUS

      22,**** RHS***NSET,NSET=NRHS       2,       2,      23,      24,      25,      26,      27,      28,      29,      30,      31,      32,      33,      34,      35,      36,      37,      38,      39,      40,      41,      42,*SOLID SECTION,ELSET=EALL,MATERIAL=RUBBER.10,*MATERIAL,NAME=RUBBER** hyperelastic constants in Pa*HYPERELASTIC,POLYNOMIAL,N=13.2E6,.8E6** density is 1500 kg/m^3*DENSITY1500.,**** RIGID ELEMENT USED TO COMPRESS THE BLOCK***NODE, NSET=NRIGID20001,-.09683,-.0031720002,.10317,.1968320003,-.02,.12*NSET,NSET=NREF20003,*ELEMENT,TYPE=R2D2,ELSET=ERIGID20001,20002,20001*AMPLITUDE,NAME=CRUSH,DEFINITION=SMOOTH STEP0.,0.,.1,1.*BOUNDARYNBOT,2NRHS,1NREF,6***SURFACE,NAME=RIGIDERIGID,SPOS*SURFACE,NAME=SOLIDEALL,*RIGID BODY,ELSET=ERIGID,REFNODE=20003***ELSET,ELSET=QA_TEST_ALLELEMS

Page 118: Getting Started With ABAQUS

EALL,***NSET, NSET=QA_TEST_ALLNODESQA_TEST_ALLNODES, NBOT, NRHS, NRIGIDNREF, ***STEPCompress the rubber block*DYNAMIC,EXPLICIT,0.1*CONTACT PAIR,INTERACTION=INTERSOLID,RIGID*SURFACE INTERACTION,NAME=INTER** displace a total distance of .012 in both directions*BOUNDARY,TYPE=DISPLACEMENT,AMPLITUDE=CRUSHNREF,1,1,.00883NREF,2,2,-.00883***OUTPUT, FIELD, NUMBER INTERVAL=20, VARIABLE=PRESELECT*OUTPUT, HISTORY, FREQUENCY=1*ENERGY OUTPUTALLAE, ALLKE, ALLSE, ALLVD,ALLFD, ALLWK, ETOTAL************************************ OUTPUT FOR HKS QA PURPOSES***********************************OUTPUT, FIELD, NUMBER INTERVAL=1, TIMEMARKS=YES*NODE OUTPUT, NSET=QA_TEST_ALLNODESU,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIMEINT=0.1***FILE OUTPUT,NUMBER INTERVAL=1*NODE FILEU,*END STEPA.5  Blast loading on a stiffened plateblast_base.inp   *HEADINGBlast load on a flat plate with stiffeners   S4R elements (20x20 mesh)     Normal stiffeners (20x2)     SI units (kg, m, s, N)      **** Define corners and edges of plate ***NODE, NSET=CORNERS     1,0.0, 0.0,0.0  21,0.0, 2.0, 0.0801, 0.0, 0.0, 2.0      821, 0.0, 2.0, 2.0      *NGEN,NSET=EDGE11,21,1  *NGEN,NSET=EDGE2801,821,1       *NFILL,NSET=NALLEDGE1,EDGE2,20,40       *NGEN,NSET=EDGE31,801,40*NGEN,NSET=EDGE421,821,40       *NSET,NSET=EDGE

Page 119: Getting Started With ABAQUS

EDGE1,EDGE2,EDGE3,EDGE4**** Define a node set for output***NSET, NSET=NOUT411  ,    **** Define stiffeners***NODE, NSET=STIFFN      4201,0.1, 0.0, 0.5       4221,0.1, 2.0, 0.5      4401,0.1, 0.0, 1.0      4421,0.1, 2.0, 1.0      4601,0.1, 0.0, 1.5      4621,0.1, 2.0, 1.5      **Generate inner edges of stiffeners    *NGEN,NSET=ST1EDGE1     4201,4221,1     *NGEN,NSET=ST2EDGE1     4401,4421,1     *NGEN,NSET=ST3EDGE1     4601,4621,1     ** Define node sets on plate for outer edge of stiffeners       *NSET, NSET=ST1EDGE2, GENERATE  201,221,1       *NSET, NSET=ST2EDGE2, GENERATE  401,421,1       *NSET, NSET=ST3EDGE2, GENERATE  601,621,1       *NFILL  ST1EDGE2,ST1EDGE1,2,2000*NFILL  ST2EDGE2,ST2EDGE1,2,2000*NFILL  ST3EDGE2,ST3EDGE1,2,2000**      ** Define master element type for plate (with associated nodes) ** and generate shell elements  *ELEMENT,TYPE=S4R,ELSET=PLATE       1,1,2,42,41     *ELGEN,ELSET=PLATE      1,20,1,1,20,40,20       ** Define master element type for stiffeners and generate       *ELEMENT,TYPE=S4R,ELSET=STIFF11001, 201,2201,2202,202 *ELGEN,ELSET=STIFF1     1001,20,1,1,2,2000,20   *ELEMENT,TYPE=S4R,ELSET=STIFF22001, 401,2401,2402,402 *ELGEN,ELSET=STIFF2     2001,20,1,1,2,2000,20   *ELEMENT,TYPE=S4R,ELSET=STIFF33001, 601,2601,2602,602 *ELGEN,ELSET=STIFF3     3001,20,1,1,2,2000,20   ** Define elset for el history output   ** Elements on central stiffener*ELSET, ELSET=STIFFMAX  2009, 2010, 2029, 2030   **      

Page 120: Getting Started With ABAQUS

*SHELL SECTION,MATERIAL=STEEL,ELSET=PLATE,OFFSET=SPOS      0.025   , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF1     0.0125  , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF2     0.0125, *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF3     0.0125, ***MATERIAL,NAME=STEEL*ELASTIC210.0E9,.3      *PLASTIC300.0E6, 0.000350.0E6, 0.025375.0E6, 0.100394.0E6, 0.200400.0E6, 0.350*DENSITY7800.0,  ***BOUNDARY       EDGE, ENCASTRE ** Specify time variation for blast load*AMPLITUDE, NAME=BLAST  0.0, 0.0, 1.0E-03, 7.0E5, 10E-03, 7.0E05, 20E-03, 0.0, 50E-03, 0.0    *STEP    Apply blast loading    ** Explicit analysis with a time duration of 50 ms*DYNAMIC, EXPLICIT       , 50E-03       ** Apply distributed load (surface pressure) to the element set PLATE   *DLOAD, AMPLITUDE=BLAST PLATE, P, 1.0  *MONITOR, NODE=411, DOF=1       *OUTPUT, FIELD, NUMBER INTERVAL=25*ELEMENT OUTPUTS,PE*NODE OUTPUTU*OUTPUT, HISTORY, TIME INTERVAL=1.0E-4 *ELEMENT OUTPUT, ELSET=STIFFMAX     PEEQ, MISES, ERV,*NODE OUTPUT, NSET=NOUTU,V     *ENERGY OUTPUTALLKE, ALLSE, ALLWK, ALLPD, ALLIE, ALLVD, ALLAE, ETOTAL ***NSET,NSET=QA_TEST370,371,372,410,411,412,450,451,452,*OUTPUT, FIELD, NUMBER INTERVAL=5, TIMEMARKS=YES*NODE OUTPUT,NSET=QA_TESTU*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=10E-03*END STEPblast_damp.inp   *HEADINGBlast load on a flat plate with stiffeners   S4R elements (20x20 mesh)     

Page 121: Getting Started With ABAQUS

Normal stiffeners (20x2)     SI units (kg, m, s, N)   Includes dampingLonger analysis time (150ms)**** Define corners and edges of plate       ***NODE, NSET=CORNERS     1,0.0, 0.0,0.0  21,0.0, 2.0, 0.0801, 0.0, 0.0, 2.0      821, 0.0, 2.0, 2.0      *NGEN,NSET=EDGE11,21,1  *NGEN,NSET=EDGE2801,821,1       *NFILL,NSET=NALLEDGE1,EDGE2,20,40       *NGEN,NSET=EDGE31,801,40*NGEN,NSET=EDGE421,821,40  *NSET,NSET=EDGEEDGE1,EDGE2,EDGE3,EDGE4**  ** Define a node set for output***NSET, NSET=NOUT411  ,    **** Define stiffeners***NODE, NSET=STIFFN      4201,0.1, 0.0, 0.5       4221,0.1, 2.0, 0.5      4401,0.1, 0.0, 1.0      4421,0.1, 2.0, 1.0      4601,0.1, 0.0, 1.5      4621,0.1, 2.0, 1.5      **Generate inner edges of stiffeners    *NGEN,NSET=ST1EDGE1     4201,4221,1     *NGEN,NSET=ST2EDGE1     4401,4421,1     *NGEN,NSET=ST3EDGE1     4601,4621,1     ** Define node sets on plate for outer edge of stiffeners       *NSET, NSET=ST1EDGE2, GENERATE  201,221,1       *NSET, NSET=ST2EDGE2, GENERATE  401,421,1       *NSET, NSET=ST3EDGE2, GENERATE  601,621,1       *NFILL  ST1EDGE2,ST1EDGE1,2,2000*NFILL  ST2EDGE2,ST2EDGE1,2,2000*NFILL  ST3EDGE2,ST3EDGE1,2,2000**      ** Define master element type for plate (with associated nodes) 

Page 122: Getting Started With ABAQUS

** and generate shell elements  *ELEMENT,TYPE=S4R,ELSET=PLATE1,1,2,42,41     *ELGEN,ELSET=PLATE      1,20,1,1,20,40,20       ** Define master element type for stiffeners and generate       *ELEMENT,TYPE=S4R,ELSET=STIFF11001, 201,2201,2202,202 *ELGEN,ELSET=STIFF1     1001,20,1,1,2,2000,20   *ELEMENT,TYPE=S4R,ELSET=STIFF2     2001, 401,2401,2402,402 *ELGEN,ELSET=STIFF2     2001,20,1,1,2,2000,20   *ELEMENT,TYPE=S4R,ELSET=STIFF3       3001, 601,2601,2602,602 *ELGEN,ELSET=STIFF3     3001,20,1,1,2,2000,20   ** Define elset for el history output   ** Elements on central stiffener*ELSET, ELSET=STIFFMAX  2009, 2010, 2029, 2030   **      *SHELL SECTION,MATERIAL=STEEL,ELSET=PLATE,OFFSET=SPOS      0.025   , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF1     0.0125  , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF2     0.0125  , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF3     0.0125  , ***MATERIAL,NAME=STEEL*ELASTIC210.0E9,.3      *PLASTIC300.0E6, 0.000350.0E6, 0.025375.0E6, 0.100394.0E6, 0.200400.0E6, 0.350*DENSITY7800.0, *DAMPING, ALPHA=50.0, BETA=0.0***BOUNDARY       EDGE, ENCASTRE ** Specify time variation for blast load*AMPLITUDE, NAME=BLAST  0.0, 0.0, 1.0E-03, 7.0E5, 10E-03, 7.0E05, 20E-03, 0.0, 50E-03, 0.0    *STEP    Apply blast loading    ** Explicit analysis with a time duration of 150 ms*DYNAMIC, EXPLICIT       ,150E-03       ** Apply distributed load (surface pressure) to the element set PLATE   *DLOAD, AMPLITUDE=BLAST PLATE, P, 1.0  *MONITOR, NODE=411, DOF=1       *OUTPUT, FIELD, NUMBER INTERVAL=25*ELEMENT OUTPUT

Page 123: Getting Started With ABAQUS

S,PE*NODE OUTPUTU*OUTPUT, HISTORY, TIME INTERVAL=1.0E-4 *ELEMENT OUTPUT, ELSET=STIFFMAX     PEEQ, MISES, ERV,*NODE OUTPUT, NSET=NOUTU,V   *ENERGY OUTPUTALLKE, ALLSE, ALLWK, ALLPD, ALLIE, ALLVD, ALLAE, ETOTAL ***NSET,NSET=QA_TEST370,371,372,410,411,412,450,451,452,*OUTPUT, FIELD, NUMBER INTERVAL=5, TIMEMARKS=YES*NODE OUTPUT,NSET=QA_TESTU*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=30E-03*END STEPblast_long.inp   *HEADINGBlast load on a flat plate with stiffeners   S4R elements (20x20 mesh)     Normal stiffeners (20x2)     SI units (kg, m, s, N)     Longer analysis time to compare to blast_damp**** Define corners and edges of plate***NODE, NSET=CORNERS     1,0.0, 0.0,0.0  21,0.0, 2.0, 0.0801, 0.0, 0.0, 2.0      821, 0.0, 2.0, 2.0      *NGEN,NSET=EDGE11,21,1  *NGEN,NSET=EDGE2801,821,1       *NFILL,NSET=NALLEDGE1,EDGE2,20,40       *NGEN,NSET=EDGE31,801,40*NGEN,NSET=EDGE421,821,40*NSET,NSET=EDGEEDGE1,EDGE2,EDGE3,EDGE4       **** Define a node set for output***NSET, NSET=NOUT411  ,    **** Define stiffeners***NODE, NSET=STIFFN      4201,0.1, 0.0, 0.5       4221,0.1, 2.0, 0.5      4401,0.1, 0.0, 1.0      4421,0.1, 2.0, 1.0      4601,0.1, 0.0, 1.5      

Page 124: Getting Started With ABAQUS

4621,0.1, 2.0, 1.5      **Generate inner edges of stiffeners    *NGEN,NSET=ST1EDGE1     4201,4221,1     *NGEN,NSET=ST2EDGE1     4401,4421,1     *NGEN,NSET=ST3EDGE1     4601,4621,1     ** Define node sets on plate for outer edge of stiffeners       *NSET, NSET=ST1EDGE2, GENERATE  201,221,1       *NSET, NSET=ST2EDGE2, GENERATE  401,421,1       *NSET, NSET=ST3EDGE2, GENERATE  601,621,1       *NFILL  ST1EDGE2,ST1EDGE1,2,2000*NFILL  ST2EDGE2,ST2EDGE1,2,2000*NFILL  ST3EDGE2,ST3EDGE1,2,2000**      ** Define master element type for plate (with associated nodes) ** and generate shell elements  *ELEMENT,TYPE=S4R,ELSET=PLATE       1,1,2,42,41     *ELGEN,ELSET=PLATE      1,20,1,1,20,40,20       ** Define master element type for stiffeners and generate       *ELEMENT,TYPE=S4R,ELSET=STIFF1      1001, 201,2201,2202,202 *ELGEN,ELSET=STIFF1     1001,20,1,1,2,2000,20   *ELEMENT,TYPE=S4R,ELSET=STIFF2       2001, 401,2401,2402,402 *ELGEN,ELSET=STIFF2     2001,20,1,1,2,2000,20   *ELEMENT,TYPE=S4R,ELSET=STIFF3       3001, 601,2601,2602,602 *ELGEN,ELSET=STIFF3     3001,20,1,1,2,2000,20   ** Define elset for el history output   ** Elements on central stiffener*ELSET, ELSET=STIFFMAX  2009, 2010, 2029, 2030   **      *SHELL SECTION,MATERIAL=STEEL,ELSET=PLATE,OFFSET=SPOS0.025   , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF1     0.0125  , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF2     0.0125  , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF3     0.0125  , ***MATERIAL,NAME=STEEL*ELASTIC210.0E9,.3      *PLASTIC300.0E6, 0.000350.0E6, 0.025

Page 125: Getting Started With ABAQUS

375.0E6, 0.100394.0E6, 0.200400.0E6, 0.350*DENSITY7800.0  , ***BOUNDARY       EDGE, ENCASTRE ** Specify time variation for blast load*AMPLITUDE, NAME=BLAST  0.0, 0.0, 1.0E-03, 7.0E5, 10E-03, 7.0E05, 20E-03, 0.0, 50E-03, 0.0    *STEP    Apply blast loading    ** Explicit analysis with a time duration of 150 ms*DYNAMIC, EXPLICIT       ,150E-03       ** Apply distributed load (surface pressure) to the element set PLATE   *DLOAD, AMPLITUDE=BLAST PLATE, P, 1.0  *MONITOR, NODE=411, DOF=1       *OUTPUT, FIELD, NUMBER INTERVAL=25*ELEMENT OUTPUTS,PE*NODE OUTPUTU*OUTPUT, HISTORY, TIME INTERVAL=1.0E-4 *ELEMENT OUTPUT, ELSET=STIFFMAX     PEEQ, MISES, ERV, *NODE OUTPUT, NSET=NOUTU,V  *ENERGY OUTPUTALLKE, ALLSE, ALLWK, ALLPD, ALLIE, ALLVD, ALLAE, ETOTAL ***NSET,NSET=QA_TEST370,371,372,410,411,412,450,451,452,*OUTPUT, FIELD, NUMBER INTERVAL=5, TIMEMARKS=YES*NODE OUTPUT,NSET=QA_TESTU*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=30E-03*END STEPblast_refined.inp   *HEADINGBlast load on a flat plate with stiffeners   S4R elements (20x20 mesh)     Refined stiffeners (20x4)     SI units (kg, m, s, N)      **** Define corners and edges of plate       ***NODE, NSET=CORNERS     1,0.0, 0.0,0.0  21,0.0, 2.0, 0.0801, 0.0, 0.0, 2.0      821, 0.0, 2.0, 2.0      *NGEN,NSET=EDGE11,21,1  *NGEN,NSET=EDGE2801,821,1       *NFILL, NSET=NALL  

Page 126: Getting Started With ABAQUS

EDGE1,EDGE2,20,40       *NGEN,NSET=EDGE31,801,40*NGEN,NSET=EDGE421,821,40 *NSET,NSET=EDGEEDGE1,EDGE2,EDGE3,EDGE4**     ** Define a node set for output***NSET, NSET=NOUT411  ,    **** define stiffeners***NODE, NSET=STIFFN      4201,0.1, 0.0, 0.5       4221,0.1, 2.0, 0.5      4401,0.1, 0.0, 1.0      4421,0.1, 2.0, 1.0      4601,0.1, 0.0, 1.5      4621,0.1, 2.0, 1.5      **Generate inner edges of stiffeners    *NGEN,NSET=ST1EDGE1     4201,4221,1     *NGEN,NSET=ST2EDGE1     4401,4421,1     *NGEN,NSET=ST3EDGE1     4601,4621,1     ** Define node sets on plate for outer edge of stiffeners       *NSET, NSET=ST1EDGE2, GENERATE  201,221,1       *NSET, NSET=ST2EDGE2, GENERATE  401,421,1       *NSET, NSET=ST3EDGE2, GENERATE  601,621,1       *NFILL  ST1EDGE2,ST1EDGE1,4,1000*NFILL  ST2EDGE2,ST2EDGE1,4,1000*NFILL  ST3EDGE2,ST3EDGE1,4,1000**      ** Define master element type for plate (with associated nodes) ** and generate shell elements  *ELEMENT,TYPE=S4R,ELSET=PLATE     1,1,2,42,41     *ELGEN,ELSET=PLATE      1,20,1,1,20,40,20       ** Define master element type for stiffeners and generate       *ELEMENT,TYPE=S4R,ELSET=STIFF1       1001, 201,1201,1202,202 *ELGEN,ELSET=STIFF1     1001,20,1,1,4,1000,20   *ELEMENT,TYPE=S4R,ELSET=STIFF2       2001, 401,1401,1402,402 *ELGEN,ELSET=STIFF2     2001,20,1,1,4,1000,20   *ELEMENT,TYPE=S4R,ELSET=STIFF3       3001, 601,1601,1602,602 *ELGEN,ELSET=STIFF3     

Page 127: Getting Started With ABAQUS

3001,20,1,1,4,1000,20   ** Define elset for el history output   ** Elements on central stiffener*ELSET, ELSET=STIFFMAX  2009, 2010, 2029,2030,2050,2051,2070,2071***SHELL SECTION,MATERIAL=STEEL,ELSET=PLATE,OFFSET=SPOS0.025   , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF1     0.0125  , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF2     0.0125  , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF3     0.0125  , **      *MATERIAL,NAME=STEEL*ELASTIC210.0E9,.3      *PLASTIC300.0E6, 0.000350.0E6, 0.025375.0E6, 0.100394.0E6, 0.200400.0E6, 0.350*DENSITY7800.0,  ***BOUNDARY       EDGE, ENCASTRE ** Specify time variation for blast load*AMPLITUDE, NAME=BLAST  0.0, 0.0, 1.0E-03, 7.0E5, 10E-03, 7.0E05, 20E-03, 0.0, 50E-03, 0.0    *STEP    Apply blast loading    ** Explicit analysis with a time duration of 50 ms*DYNAMIC, EXPLICIT       , 50E-03       ** Apply distributed load (surface pressure) to the element set PLATE   *DLOAD, AMPLITUDE=BLAST PLATE, P, 1.0  *MONITOR, NODE=411, DOF=1       *OUTPUT, FIELD, NUMBER INTERVAL=25*ELEMENT OUTPUTS,PE*NODE OUTPUTU*OUTPUT, HISTORY, TIME INTERVAL=1.0E-4 *ELEMENT OUTPUT, ELSET=STIFFMAX     PEEQ, MISES, ERV,*NODE OUTPUT, NSET=NOUTU,V *ENERGY OUTPUT ALLKE, ALLSE, ALLWK, ALLPD, ALLIE, ALLVD, ALLAE, ETOTAL ***NSET,NSET=QA_TEST370,371,372,410,411,412,450,451,452,*OUTPUT, FIELD, NUMBER INTERVAL=5, TIMEMARKS=YES*NODE OUTPUT,NSET=QA_TESTU

Page 128: Getting Started With ABAQUS

*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=10E-03*END STEPblast_rate.inp   *HEADINGBlast load on a flat plate with stiffeners   S4R elements (20x20 mesh)     Normal stiffeners (20x2)     SI units (kg, m, s, N)      Includes dampingIncludes rate-dependent plasticity**** Define corners and edges of plate       ***NODE, NSET=CORNERS     1,0.0, 0.0,0.0  21,0.0, 2.0, 0.0801, 0.0, 0.0, 2.0      821, 0.0, 2.0, 2.0      *NGEN,NSET=EDGE11,21,1  *NGEN,NSET=EDGE2801,821,1       *NFILL,NSET=NALLEDGE1,EDGE2,20,40       *NGEN,NSET=EDGE31,801,40*NGEN,NSET=EDGE421,821,40*NSET,NSET=EDGEEDGE1,EDGE2,EDGE3,EDGE4**     ** Define a node set for output***NSET, NSET=NOUT411  ,    **** Define stiffeners***NODE, NSET=STIFFN      4201,0.1, 0.0, 0.5       4221,0.1, 2.0, 0.5      4401,0.1, 0.0, 1.0      4421,0.1, 2.0, 1.0      4601,0.1, 0.0, 1.5      4621,0.1, 2.0, 1.5      **Generate inner edges of stiffeners    *NGEN,NSET=ST1EDGE1     4201,4221,1     *NGEN,NSET=ST2EDGE1     4401,4421,1     *NGEN,NSET=ST3EDGE1     4601,4621,1     ** Define node sets on plate for outer edge of stiffeners       *NSET, NSET=ST1EDGE2, GENERATE  201,221,1       *NSET, NSET=ST2EDGE2, GENERATE  401,421,1       *NSET, NSET=ST3EDGE2, GENERATE  601,621,1       *NFILL  ST1EDGE2,ST1EDGE1,2,2000

Page 129: Getting Started With ABAQUS

*NFILL  ST2EDGE2,ST2EDGE1,2,2000*NFILL  ST3EDGE2,ST3EDGE1,2,2000**      ** Define master element type for plate (with associated nodes) ** and generate shell elements  *ELEMENT,TYPE=S4R,ELSET=PLATE       1,1,2,42,41     *ELGEN,ELSET=PLATE      1,20,1,1,20,40,20       ** Define master element type for stiffeners and generate       *ELEMENT,TYPE=S4R,ELSET=STIFF1       1001, 201,2201,2202,202 *ELGEN,ELSET=STIFF1     1001,20,1,1,2,2000,20   *ELEMENT,TYPE=S4R,ELSET=STIFF2       2001, 401,2401,2402,402 *ELGEN,ELSET=STIFF2     2001,20,1,1,2,2000,20   *ELEMENT,TYPE=S4R,ELSET=STIFF3       3001, 601,2601,2602,602 *ELGEN,ELSET=STIFF3     3001,20,1,1,2,2000,20   ** Define elset for el history output   ** Elements on central stiffener*ELSET, ELSET=STIFFMAX  2009, 2010, 2029, 2030   **      *SHELL SECTION,MATERIAL=STEEL,ELSET=PLATE,OFFSET=SPOS 0.025   , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF1     0.0125  , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF2     0.0125  , *SHELL SECTION,MATERIAL=STEEL,ELSET=STIFF3     0.0125  , ***MATERIAL,NAME=STEEL*ELASTIC210.0E9,.3      *PLASTIC300.0E6, 0.000350.0E6, 0.025375.0E6, 0.100394.0E6, 0.200400.0E6, 0.350*RATE DEPENDENT40.0,5.0*DENSITY7800.0, *DAMPING, ALPHA=50.0, BETA=0.0***BOUNDARY       EDGE, ENCASTRE ** Specify time variation for blast load*AMPLITUDE, NAME=BLAST  0.0, 0.0, 1.0E-03, 7.0E5, 10E-03, 7.0E05, 20E-03, 0.0, 50E-03, 0.0    *STEP    Apply blast loading    ** Explicit analysis with a time duration of 50 ms

Page 130: Getting Started With ABAQUS

*DYNAMIC, EXPLICIT       , 50E-03       ** Apply distributed load (surface pressure) to the element set PLATE   *DLOAD, AMPLITUDE=BLAST PLATE, P, 1.0  *MONITOR, NODE=411, DOF=1       *OUTPUT, FIELD, NUMBER INTERVAL=25*ELEMENT OUTPUTS,PE*NODE OUTPUTU*OUTPUT, HISTORY, TIME INTERVAL=1.0E-4*ELEMENT OUTPUT, ELSET=STIFFMAX     PEEQ, MISES, ERV,*NODE OUTPUT, NSET=NOUTU,V   *ENERGY OUTPUT ALLKE, ALLSE, ALLWK, ALLPD, ALLIE, ALLVD, ALLAE, ETOTAL ***NSET,NSET=QA_TEST370,371,372,410,411,412,450,451,452,*OUTPUT, FIELD, NUMBER INTERVAL=5, TIMEMARKS=YES*NODE OUTPUT,NSET=QA_TESTU*OUTPUT, HISTORY, VARIABLE=PRESELECT, TIME INTERVAL=10E-03*END STEPA.6  Circuit board drop testcircuit.inp   *HEADINGCircuit board drop test1.0 meter dropSI units (kg, m, s, N)*SYSTEM0.,0.,0., .5,.707,.25-.5,.707,-.5*NODE1,     0.005, -0.010, 0.01211,    0.005, -0.010, 0.162501,   0.105, -0.010, 0.012511,   0.105, -0.010, 0.1621001,  0.,     0.,    0.1004,  0.,    -0.009, 0.1005,  0.,    -0.011, 0.1008,  0.,    -0.02,  0.1061,  0.,     0.,    0.0241064,  0.,    -0.009, 0.0241065,  0.,    -0.011, 0.0241068,  0.,    -0.02,  0.02416001, 0.110,  0.,    0.16004, 0.110, -0.009, 0.16005, 0.110, -0.011, 0.16008, 0.110, -0.02,  0.16061, 0.110,  0.,    0.02416064, 0.110, -0.009, 0.02416065, 0.110, -0.011, 0.02416068, 0.110, -0.02,  0.024*NGEN, NSET=BOARDA1,501,50*NGEN, NSET=BOARDB

Page 131: Getting Started With ABAQUS

11,511,50*NFILL,NSET=BOARDBOARDA, BOARDB, 10, 1***NGEN, NSET=PACKAA1001,1004,11005,1008,1*NGEN, NSET=PACKAB1061,1064,11065,1068,1*NFILL,NSET=PACKAPACKAA,PACKAB,6,10*NGEN, NSET=PACKBA16001,16008,1*NGEN, NSET=PACKBB16061,16068,1*NFILL,NSET=PACKBPACKBA,PACKBB,6,10*NFILL,NSET=PACKPACKA,PACKB,15,1000**** Reset coordinate system***SYSTEM*NODE50000, -0.10, -0.10, -0.000150001, -0.10,  0.10, -0.000150002,  0.15,  0.10, -0.000150003,  0.15, -0.10, -0.000199999,  0.,    0.,   -0.001**** Element definitions***ELEMENT,TYPE=S4R,ELSET=BOARD1,1,51,52,2*ELGEN,ELSET=BOARD1,10,50,1,10,1,10*ELEMENT,TYPE=C3D8R,ELSET=PACK500, 1001,1002,2002,2001, 1011,1012,2012,2011530, 1031,1032,2032,2031, 1041,1042,2042,2041534, 1035,1036,2036,2035, 1045,1046,2046,2045*ELGEN,ELSET=PACK500, 7,1,1, 3,10,10, 15,1000,100530, 3,1,1, 3,10,10, 15,1000,100534, 3,1,1, 3,10,10, 15,1000,100*ELEMENT,TYPE=MASS,ELSET=CHIPS6001,606002,3576003,403*ELEMENT,TYPE=R3D4,ELSET=FLOOR50000, 50000,50003,50002,50001**** Section properties***SOLID SECTION,ELSET=PACK,MATERIAL=FOAM*SHELL SECTION,ELSET=BOARD,MATERIAL=PCB,ORIENTATION=OR10.002,*ORIENTATION,NAME=OR1,SYSTEM=RECTANGULAR,DEFINITION=COORDINATES.5,.707,.25,-.5,.707,-.53,0*MASS,ELSET=CHIPS

Page 132: Getting Started With ABAQUS

0.005,*RIGID BODY, ELSET=FLOOR, REFNODE=99999*NSET,NSET=REF99999,**** Materials***MATERIAL,NAME=PCB*ELASTIC45.E9,0.3*DENSITY500.,*MATERIAL,NAME=FOAM*ELASTIC 3.E6,0.0*DENSITY 100.,*FOAM 1.0,0.02E6,0.22E6,*FOAM HARDENING0.20745E5,0.00.42916E5,0.20.75427E5,0.40.11738E6,0.60.16653E6,0.80.22000E6,1.00.24745E6,1.10.27494E6,1.20.30217E6,1.30.32890E6,1.40.35492E6,1.50.38006E6,1.60.40418E6,1.70.42720E6,1.80.44905E6,1.90.46969E6,2.00.50729E6,2.20.54008E6,2.40.56834E6,2.60.59247E6,2.80.61291E6,3.00.65083E6,3.50.67484E6,4.00.70810E6,6.00.71340E6,11.0**** Element Faces for Contact***ELSET,GENERATE,ELSET=LOWBOARD1,10,1**** Define output locations and variables***NSET,NSET=CHIPS60,357,403*ELSET,ELSET=BOTPART18,*ELSET,ELSET=PARTS18,57,81****

Page 133: Getting Started With ABAQUS

** Define contact surfaces***SURFACE, NAME=LOWBOARDLOWBOARD,*SURFACE, NAME=PACKPACK,*SURFACE, NAME=FLOORFLOOR,SPOS*****BOUNDARYREF,ENCASTRE***INITIAL CONDITIONS,TYPE=VELOCITYBOARD,3,-4.43PACK,3,-4.43*****************************STEP*DYNAMIC, EXPLICIT,0.02****** Define contact pairs***CONTACT PAIR,INTERACTION=FRIC,WEIGHT=0.5PACK,LOWBOARD*CONTACT PAIR,INTERACTION=FRICPACK,FLOOR**** Define surface interactions***SURFACE INTERACTION,NAME=FRIC*FRICTION0.3,*OUTPUT, FIELD, VARIABLE=PRESELECT, NUMBER INTERVAL=20*OUTPUT, HISTORY, TIME INTERVAL=0.1E-3*NODE OUTPUT, NSET=CHIPSU, V, A*ELEMENT OUTPUT, ELSET=BOTPART1,5LE, S, SP, LEP*ENERGY OUTPUTALLIE, ALLKE, ALLPD, ALLAE, ALLSE************************************ OUTPUT FOR HKS QA PURPOSES***********************************FILE OUTPUT,NUMBER INTERVAL=3,TIMEMARKS=YES*ENERGY FILE*NODE FILE,NSET=CHIPSU,*END STEPA.7  Crushing of a tubetube_buckle.inp   *HEADINGTube crush (x-direction) -- buckling analysisTube dimensions:  0.4m x 0.1m x 0.1mSI units (kg, m, s, N)*NODE, NSET=QA_TEST_ALLNODES33,  0.0 , 0.05, -0.05833, 0.0 , 0.05,  0.051633, 0.0,  -0.05, 0.05

Page 134: Getting Started With ABAQUS

2433, 0.0,  -0.05, -0.053233, 0.0, 0.05, -0.05***NODE, NSET=TOP1,   0.4, 0.05,  -0.05101, 0.4, 0.05, -0.0375201, 0.4, 0.05, -0.025301, 0.4, 0.05, -0.0125401, 0.4, 0.05,   0.0501, 0.4, 0.05,  0.0125 601, 0.4, 0.05,  0.025701, 0.4, 0.05,  0.0375801, 0.4, 0.05,  0.05**901, 0.4,  0.0375,  0.051001, 0.4, 0.025,  0.051101, 0.4, 0.0125,  0.051201, 0.4, 0.0,  0.051301, 0.4, -0.0125, 0.051401, 0.4, -0.025, 0.051501, 0.4, -0.0375, 0.051601, 0.4, -0.05, 0.05**1701, 0.4, -0.05,  0.0375 1801, 0.4, -0.05,  0.0251901, 0.4, -0.05,  0.01252001, 0.4, -0.05,  0.02101, 0.4, -0.05, -0.01252201, 0.4, -0.05, -0.0252301, 0.4, -0.05, -0.03752401, 0.4, -0.05, -0.05**     2501, 0.4, -0.0375,  -0.05 2601, 0.4, -0.025,  -0.052701, 0.4, -0.0125,  -0.052801, 0.4,  0.0,  -0.052901, 0.4,  0.0125,  -0.053001, 0.4,  0.025,  -0.053101, 0.4,  0.0375,  -0.053201, 0.4,  0.05,  -0.05***NGEN, NSET=BOT33, 833,    100833, 1633,  1001633, 2433, 1002433, 3233, 100***NFILL, NSET=ALLTOP, BOT, 32, 1**** SHELL ELEMENT DEFINITIONS***ELEMENT, TYPE=S4R, ELSET=YPOS1, 1, 2, 102, 101*ELGEN, ELSET=YPOS1, 32, 1, 1, 8, 100, 100***ELEMENT, TYPE=S4R, ELSET=ZPOS801, 801,802,902,901*ELGEN, ELSET=ZPOS801, 32, 1, 1, 8, 100, 100

Page 135: Getting Started With ABAQUS

***ELEMENT, TYPE=S4R, ELSET=YNEG1601, 1601, 1602, 1702, 1701*ELGEN, ELSET=YNEG1601, 32, 1, 1, 8, 100, 100***ELEMENT, TYPE=S4R, ELSET=ZNEG2401, 2401,2402,2502,2501*ELGEN, ELSET=ZNEG2401, 32, 1, 1, 7, 100, 100*ELEMENT, TYPE=S4R, ELSET=ZNEG3101, 3101, 3102, 2, 1*ELGEN, ELSET=ZNEG3101, 32, 1, 1***ELSET, ELSET=TUBEZPOS, ZNEG, YPOS, YNEG***SHELL SECTION,ELSET=TUBE,MATERIAL=STEEL0.001,3**** MATERIAL BEHAVIOR***MATERIAL,NAME=STEEL*ELASTIC207.E9,.3*PLASTIC1.587E8,0.01.631E8,0.0151.863E8,0.0331.932E8,0.0442.020E8,0.0622.070E8,1.500*DENSITY7800.,**** RIGID SURFACE ELEMENTS***NODE, NSET=QA_TEST_ALLNODES20000, 0.41,  0.0,  0.020001, 0.4, -0.1, 0.120002, 0.4,  0.1, 0.120003, 0.4,  0.1,-0.120004, 0.4, -0.1,-0.1**30000, -0.1,  0.0,  0.030001, 0.0, -0.1,  0.130002, 0.0,  0.1,  0.130003, 0.0,  0.1, -0.130004, 0.0, -0.1, -0.1*NSET,NSET=REFTOP20000,*NSET,NSET=REFBOT30000,***ELEMENT,TYPE=R3D4,ELSET=RIGTOP20001,20001,20002,20003,20004***RIGID BODY,ELSET=RIGTOP,REFNODE=20000***ELEMENT, TYPE=R3D4,ELSET=RIGBOT

Page 136: Getting Started With ABAQUS

30001,30001,30004,30003,30002***RIGID BODY,ELSET=RIGBOT,REFNODE=30000**** MASS FOR RIGID BODIES***ELEMENT,TYPE=MASS,ELSET=MASS35001,30000***MASS,ELSET=MASS500.,**** MISC NSETS AND ELSETS***NSET, NSET=PRINTOP, REFTOP, BOT, REFBOT**** BOUNDARY CONDITIONS***BOUNDARYREFTOP, 1,6REFBOT, 2,6**** RIGID SURFACES***SURFACE, NAME=TOPSURIGTOP, SPOS*SURFACE, NAME=BOTSURIGBOT, SPOS**** IMPACT CONTACT***SURFACE, TYPE=NODE, NAME=TOPTOP,*CONTACT PAIR, ADJUST=.01, INTERACTION=TUBETOP, TOPSU***SURFACE INTERACTION, NAME=TUBE**** BOTTOM CONTACT ***SURFACE, TYPE=NODE, NAME=BOTBOT,** the bottom end of the tube is fixed to the bottom rigid plate*TIE, NAME=FIXEDBOTTOM, POSITION TOLERANCE=0.01, ADJUST=YES,NO ROTATIONBOT, BOTSU****** HISTORY DEFINITION***NSET, NSET=QA_TEST_ALLNODESQA_TEST_ALLNODES, TOP, BOT, ALLREFTOP, REFBOT, PRIN***STEPBuckling analysis of the tube*BUCKLE,EIGENSOLVER=SUBSPACE10,*CLOADREFBOT, 1, 500

Page 137: Getting Started With ABAQUS

*NODE FILEU,*NODE PRINT, FREQUENCY=0*EL PRINT, FREQUENCY=0*OUTPUT,FIELD,VARIABLE=PRESELECT,FREQUENCY=9999*OUTPUT,FIELD*NODE OUTPUTU,*OUTPUT,HISTORY*NODE OUTPUT, NSET=QA_TEST_ALLNODESU,*END STEPtube_crush.inp   *HEADINGTube crush (x-direction) -- crushing analysisTube dimensions:  0.4m x 0.1m x 0.1mSI units (kg, m, s, N)*NODE33,  0.0 , 0.05, -0.05833, 0.0 , 0.05,  0.051633, 0.0,  -0.05, 0.052433, 0.0,  -0.05, -0.053233, 0.0, 0.05, -0.05***NODE, NSET=TOP1,   0.4, 0.05,  -0.05101, 0.4, 0.05, -0.0375201, 0.4, 0.05, -0.025301, 0.4, 0.05, -0.0125401, 0.4, 0.05,   0.0501, 0.4, 0.05,  0.0125 601, 0.4, 0.05,  0.025701, 0.4, 0.05,  0.0375801, 0.4, 0.05,  0.05**901, 0.4,  0.0375,  0.051001, 0.4, 0.025,  0.051101, 0.4, 0.0125,  0.051201, 0.4, 0.0,  0.051301, 0.4, -0.0125, 0.051401, 0.4, -0.025, 0.051501, 0.4, -0.0375, 0.051601, 0.4, -0.05, 0.05**1701, 0.4, -0.05,  0.0375 1801, 0.4, -0.05,  0.0251901, 0.4, -0.05,  0.01252001, 0.4, -0.05,  0.02101, 0.4, -0.05, -0.01252201, 0.4, -0.05, -0.0252301, 0.4, -0.05, -0.03752401, 0.4, -0.05, -0.05**     2501, 0.4, -0.0375,  -0.05 2601, 0.4, -0.025,  -0.052701, 0.4, -0.0125,  -0.052801, 0.4,  0.0,  -0.052901, 0.4,  0.0125,  -0.053001, 0.4,  0.025,  -0.053101, 0.4,  0.0375,  -0.053201, 0.4,  0.05,  -0.05

Page 138: Getting Started With ABAQUS

***NGEN, NSET=BOT33, 833,    100833, 1633,  1001633, 2433, 1002433, 3233, 100***NFILL, NSET=ALLTOP, BOT, 32, 1**** SHELL ELEMENT DEFINITIONS***ELEMENT, TYPE=S4R, ELSET=YPOS1, 1, 2, 102, 101*ELGEN, ELSET=YPOS1, 32, 1, 1, 8, 100, 100***ELEMENT, TYPE=S4R, ELSET=ZPOS801, 801,802,902,901*ELGEN, ELSET=ZPOS801, 32, 1, 1, 8, 100, 100***ELEMENT, TYPE=S4R, ELSET=YNEG1601, 1601, 1602, 1702, 1701*ELGEN, ELSET=YNEG1601, 32, 1, 1, 8, 100, 100***ELEMENT, TYPE=S4R, ELSET=ZNEG2401, 2401,2402,2502,2501*ELGEN, ELSET=ZNEG2401, 32, 1, 1, 7, 100, 100*ELEMENT, TYPE=S4R, ELSET=ZNEG3101, 3101, 3102, 2, 1*ELGEN, ELSET=ZNEG3101, 32, 1, 1***ELSET, ELSET=TUBEZPOS, ZNEG, YPOS, YNEG***SHELL SECTION,ELSET=TUBE,MATERIAL=STEEL0.001,3**** MATERIAL BEHAVIOR***MATERIAL,NAME=STEEL*ELASTIC207.E9,.3*PLASTIC1.587E8,0.01.631E8,0.0151.863E8,0.0331.932E8,0.0442.020E8,0.0622.070E8,1.500*DENSITY7800.,**** RIGID BODY ELEMENTS***NODE20000, 0.41,  0.0,  0.0

Page 139: Getting Started With ABAQUS

20001, 0.4, -0.1, 0.120002, 0.4,  0.1, 0.120003, 0.4,  0.1,-0.120004, 0.4, -0.1,-0.1**30000, -0.01,  0.0,  0.030001, 0.0, -0.1,  0.130002, 0.0,  0.1,  0.130003, 0.0,  0.1, -0.130004, 0.0, -0.1, -0.1*NSET,NSET=REFTOP20000,*NSET,NSET=REFBOT30000,***ELEMENT,TYPE=R3D4,ELSET=RIGTOP20001,20001,20002,20003,20004***RIGID BODY,ELSET=RIGTOP,REFNODE=20000***ELEMENT, TYPE=R3D4,ELSET=RIGBOT30001,30001,30004,30003,30002***RIGID BODY,ELSET=RIGBOT,TIE NSET=BOT,REFNODE=30000**** MASS FOR RIGID BODIES***ELEMENT,TYPE=MASS,ELSET=MASS35001,30000***MASS,ELSET=MASS500.,**** MISC NSETS AND ELSETS***NSET, NSET=PRINTOP, REFTOP, BOT, REFBOT***INITIAL CONDITIONS,TYPE=VELOCITY** 1 mph = 0.44701 m/s** 20 mph = 8.9408 m/sREFBOT,1,8.9408ALL,1,8.9408**** BOUNDARY CONDITIONS***BOUNDARYREFTOP, 1,6REFBOT, 2,6**** IMPERFECTIONS BASED ON BUCKLING MODES***IMPERFECTION, FILE=tube_buckle, STEP=11, 2.0E-52, 0.8E-53, 0.4E-54, 0.18E-55, 0.16E-56, 0.10E-57, 0.10E-58, 0.08E-5

Page 140: Getting Started With ABAQUS

9, 0.02E-510, 0.02E-5*****SURFACE, NAME=TOPSURIGTOP, SPOS*SURFACE, NAME=TUBETUBE,**** HISTORY DEFINITON***STEPImpact of square tube with free decelerationInitial velocity=8.9408m/s (20mph)*DYNAMIC, EXPLICIT,0.03**** SELF CONTACT***CONTACT PAIR, INTERACTION=SELFTUBE,*SURFACE INTERACTION, NAME=SELF*FRICTION0.1,**** IMPACT CONTACT**   ** faces of the rail (both inside and out) near the impact wall** may contact the wall*CONTACT PAIR, INTERACTION=IMPACTTUBE, TOPSU*SURFACE INTERACTION, NAME=IMPACT*****OUTPUT, HISTORY, TIME INTERVAL=0.00008*ENERGY OUTPUT ALLWK, ALLKE, ETOTAL, ALLPD, ALLIE, ALLVD, ALLAE, ALLSE*NODE OUTPUT, NSET=PRINU, V, A, RF1, RF2, RF3*MONITOR, NODE=30000, DOF=1*OUTPUT, FIELD, VARIABLE=PRESELECT, NUMBER INTERVAL=20************************************ OUTPUT FOR HKS QA PURPOSES***********************************FILE OUTPUT, NUMBER INTERVAL=1*ENERGY FILE*NODE FILEU,*END STEPtube_crush_noimper.inp   *HEADINGTube crush (x-direction) -- crushing analysisTube dimensions:  0.4m x 0.1m x 0.1mSI units (kg, m, s, N)*NODE33,  0.0 , 0.05, -0.05833, 0.0 , 0.05,  0.051633, 0.0,  -0.05, 0.052433, 0.0,  -0.05, -0.053233, 0.0, 0.05, -0.05**

Page 141: Getting Started With ABAQUS

*NODE, NSET=TOP1,   0.4, 0.05,  -0.05101, 0.4, 0.05, -0.0375201, 0.4, 0.05, -0.025301, 0.4, 0.05, -0.0125401, 0.4, 0.05,   0.0501, 0.4, 0.05,  0.0125 601, 0.4, 0.05,  0.025701, 0.4, 0.05,  0.0375801, 0.4, 0.05,  0.05**901, 0.4,  0.0375,  0.051001, 0.4, 0.025,  0.051101, 0.4, 0.0125,  0.051201, 0.4, 0.0,  0.051301, 0.4, -0.0125, 0.051401, 0.4, -0.025, 0.051501, 0.4, -0.0375, 0.051601, 0.4, -0.05, 0.05**1701, 0.4, -0.05,  0.0375 1801, 0.4, -0.05,  0.0251901, 0.4, -0.05,  0.01252001, 0.4, -0.05,  0.02101, 0.4, -0.05, -0.01252201, 0.4, -0.05, -0.0252301, 0.4, -0.05, -0.03752401, 0.4, -0.05, -0.05**     2501, 0.4, -0.0375,  -0.05 2601, 0.4, -0.025,  -0.052701, 0.4, -0.0125,  -0.052801, 0.4,  0.0,  -0.052901, 0.4,  0.0125,  -0.053001, 0.4,  0.025,  -0.053101, 0.4,  0.0375,  -0.053201, 0.4,  0.05,  -0.05***NGEN, NSET=BOT33, 833,    100833, 1633,  1001633, 2433, 1002433, 3233, 100***NFILL, NSET=ALLTOP, BOT, 32, 1**** SHELL ELEMENT DEFINITIONS***ELEMENT, TYPE=S4R, ELSET=YPOS1, 1, 2, 102, 101*ELGEN, ELSET=YPOS1, 32, 1, 1, 8, 100, 100***ELEMENT, TYPE=S4R, ELSET=ZPOS801, 801,802,902,901*ELGEN, ELSET=ZPOS801, 32, 1, 1, 8, 100, 100***ELEMENT, TYPE=S4R, ELSET=YNEG1601, 1601, 1602, 1702, 1701

Page 142: Getting Started With ABAQUS

*ELGEN, ELSET=YNEG1601, 32, 1, 1, 8, 100, 100***ELEMENT, TYPE=S4R, ELSET=ZNEG2401, 2401,2402,2502,2501*ELGEN, ELSET=ZNEG2401, 32, 1, 1, 7, 100, 100*ELEMENT, TYPE=S4R, ELSET=ZNEG3101, 3101, 3102, 2, 1*ELGEN, ELSET=ZNEG3101, 32, 1, 1***ELSET, ELSET=TUBEZPOS, ZNEG, YPOS, YNEG***SHELL SECTION,ELSET=TUBE,MATERIAL=STEEL0.001,3**** MATERIAL BEHAVIOR***MATERIAL,NAME=STEEL*ELASTIC207.E9,.3*PLASTIC1.587E8,0.01.631E8,0.0151.863E8,0.0331.932E8,0.0442.020E8,0.0622.070E8,1.500*DENSITY7800.,**** RIGID BODY ELEMENTS***NODE20000, 0.41,  0.0,  0.020001, 0.4, -0.1, 0.120002, 0.4,  0.1, 0.120003, 0.4,  0.1,-0.120004, 0.4, -0.1,-0.1**30000, -0.01,  0.0,  0.030001, 0.0, -0.1,  0.130002, 0.0,  0.1,  0.130003, 0.0,  0.1, -0.130004, 0.0, -0.1, -0.1*NSET,NSET=REFTOP20000,*NSET,NSET=REFBOT30000,***ELEMENT,TYPE=R3D4,ELSET=RIGTOP20001,20001,20002,20003,20004***RIGID BODY,ELSET=RIGTOP,REFNODE=20000***ELEMENT, TYPE=R3D4,ELSET=RIGBOT30001,30001,30004,30003,30002***RIGID BODY,ELSET=RIGBOT,TIE NSET=BOT,REFNODE=30000

Page 143: Getting Started With ABAQUS

**** MASS FOR RIGID BODIES***ELEMENT,TYPE=MASS,ELSET=MASS35001,30000***MASS,ELSET=MASS500.,**** MISC NSETS AND ELSETS***NSET, NSET=PRINTOP, REFTOP, BOT, REFBOT***INITIAL CONDITIONS,TYPE=VELOCITY** 1 mph = 0.44701 m/s** 20 mph = 8.9408 m/sREFBOT,1,8.9408ALL,1,8.9408**** BOUNDARY CONDITIONS***BOUNDARYREFTOP, 1,6REFBOT, 2,6*****SURFACE, NAME=TOPSURIGTOP, SPOS*SURFACE, NAME=TUBETUBE,**** HISTORY DEFINITON***STEPImpact of square tube with free decelerationInitial velocity=8.9408m/s (20mph)*DYNAMIC, EXPLICIT,0.03**** SELF CONTACT***CONTACT PAIR, INTERACTION=SELFTUBE,*SURFACE INTERACTION, NAME=SELF*FRICTION0.1,**** IMPACT CONTACT**   ** faces of the rail (both inside and out) near the impact wall may** contact the wall*CONTACT PAIR, INTERACTION=IMPACTTUBE, TOPSU*SURFACE INTERACTION, NAME=IMPACT*****OUTPUT, HISTORY, TIME INTERVAL=0.00008*ENERGY OUTPUTALLWK, ALLKE, ETOTAL, ALLPD, ALLIE, ALLVD, ALLAE, ALLSE*NODE OUTPUT, NSET=PRIN

Page 144: Getting Started With ABAQUS

U, V, A, RF1, RF2, RF3*MONITOR, NODE=30000, DOF=1*OUTPUT, FIELD, VARIABLE=PRESELECT, NUMBER INTERVAL=20************************************ OUTPUT FOR HKS QA PURPOSES***********************************FILE OUTPUT, NUMBER INTERVAL=1*ENERGY FILE*NODE FILEU,*END STEPA.8  Deep drawing of a can bottomdraw_freq_std.inp   *HEADINGDeep drawing of a can bottom -- frequency analysisABAQUS/StandardSI units (kg, m, s, N)**** BLANK***NODE,NSET=BLANK501,.000,.000601,.045,.000*NGEN,NSET=BLANK501,601,1*NSET,NSET=BSYM501,*NSET,NSET=BEND601,*ELEMENT,TYPE=SAX1,ELSET=BLANK501,501,503*ELGEN,ELSET=BLANK501,50,2,2*SHELL SECTION,ELSET=BLANK,MATERIAL=STEEL,SECTION INTEGRATION=GAUSS.0005,5*MATERIAL,NAME=STEEL*ELASTIC210.0E9, 0.3*DENSITY7800.,*BOUNDARYBSYM,1BSYM,6BEND,2*STEP*FREQUENCY1,*RESTART,WRITE*EL PRINT,FREQ=0*NODE PRINT,FREQ=0*NODE FILE,FREQ=999U,*OUTPUT, FIELD*NODE OUTPUT, NSET=BLANKU,*END STEPdraw_stage1_attempt1.inp   *HEADINGDeep drawing of a can bottom -- stage 1, attempt 1SI units (kg, m, s, N)

Page 145: Getting Started With ABAQUS

***NODE,NSET=REFP11001,0.,0.024*NODE,NSET=REFD11101,0.050,-0.012**** BLANK***NODE,NSET=BLANK501,.000,.000601,.045,.000*NGEN,NSET=BLANK501,601,1*ELEMENT,TYPE=SAX1,ELSET=BLANK501,501,503*ELGEN,ELSET=BLANK501,50,2,2*SHELL SECTION,ELSET=BLANK,MATERIAL=STEEL,SECTION INTEGRATION=GAUSS.0005,5*NSET,NSET=BSYM501,*NSET,NSET=NHIST521,601**** PUNCH1 -- PUNCH FOR FORMING STAGE 1 (Analytical Rigid Surface)***SURFACE, NAME=PUNCH1, TYPE=SEGMENTSSTART,0.032,0.03025LINE,0.032,0.00625CIRCL,0.026,0.00025,0.026,0.00625LINE,0.,0.00025*RIGID BODY, REF NODE=1001, ANALYTICAL SURFACE=PUNCH1**** DIE1 -- DIE FOR FORMING STAGE 1 (Analytical Rigid Surface)***SURFACE, NAME=DIE1, TYPE=SEGMENTSSTART,0.0326,-0.02825LINE,0.0326,-0.00425CIRCL,0.0366,-0.00025,0.0366,-0.00425LINE,0.050,-0.00025*RIGID BODY, REF NODE=1101, ANALYTICAL SURFACE=DIE1**** SURFACE  DEFINITIONS***SURFACE, NAME=BLANK_TOPBLANK,SPOS*SURFACE, NAME=BLANK_BOTBLANK,SNEG**** BLANK MATERIAL***MATERIAL,NAME=STEEL*ELASTIC210.0E9,0.3*DENSITY7800.,*PLASTIC  0.912E8, 0.0  0.131E9, 0.159E-02  0.171E9, 0.649E-02

Page 146: Getting Started With ABAQUS

  0.211E9, 0.177E-01  0.251E9, 0.395E-01  0.291E9, 0.776E-01  0.331E9, 0.139  0.391E9, 0.295**** AMPLITUDE DEFINITIONS***AMPLITUDE,NAME=FORM10.,0.,.033,1.**** INITIAL FIXED BOUNDARY CONDITIONS***BOUNDARYREFP1,1REFP1,6REFD1,1,6BSYM,1BSYM,6**** STEP 1 -- FIRST FORMING STAGE*****ELSET,ELSET=QA_TEST_ALLELEMSBLANK,***NSET, NSET=QA_TEST_ALLNODESREFP1, REFD1, BLANK, BLANKBSYM, NHIST***STEP*DYNAMIC,EXPLICIT,.033**** Contact Pair Definition***CONTACT PAIR,INTERACTION=INTERPUNCH1,BLANK_TOPDIE1,BLANK_BOT*SURFACE INTERACTION,NAME=INTER*FRICTION.1,*BOUNDARY,TYPE=DISPLACEMENT,AMPLITUDE=FORM1REFP1,2,2,-.015*RESTART,WRITE,NUMBER INTERVAL=10*OUTPUT, HISTORY, TIME INTERVAL=1.E-5 *NODE OUTPUT, NSET=NHIST U,V*ENERGY OUTPUTALLKE, ALLIE, ALLWK, ALLVD, ALLAE, ALLPD, ETOTAL*OUTPUT, FIELD, NUMBER=4*ELEMENT OUTPUT, ELSET=BLANKSTH, SF, S*NODE OUTPUTU,RF **** Output for HKS QA purposes***FILE OUTPUT,NUMBER INTERVAL=1*ENERGY FILE*NODE FILE

Page 147: Getting Started With ABAQUS

U,RF*EL FILES,*OUTPUT, FIELD, NUMBER INTERVAL=1*NODE OUTPUT, NSET=QA_TEST_ALLNODESU,RF*ELEMENT OUTPUT, ELSET=QA_TEST_ALLELEMSS,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIMEINT=0.033***OUTPUT,HISTORY,VARIABLE=PRESELECT*END STEPdraw_spring1_std.inp   *HEADINGDeep drawing of a can bottom -- first springbackABAQUS/Standard springback followingdraw_stage1_attempt3_sqrt10.inpSI units (kg, m, s, N)*IMPORT,STEP=1,INTERVAL=10,STATE=YES,UPDATE=NOBLANK,*IMPORT ELSETBLANK,*IMPORT NSETBSYM,NHIST,BLANK*BOUNDARYBSYM,1BSYM,6*RESTART,WRITE,FREQ=999*STEP,NLGEOM*STATIC.1,1.*BOUNDARY,FIXEDBSYM,2,2*OUTPUT, FIELD, FREQUENCY=10 *ELEMENT OUTPUT, ELSET=BLANKSTH, SF, S*NODE OUTPUTU, **** Output for HKS QA purposes***NODE FILE,FREQ=999U,*EL FILE,FREQ=999S,*END STEPdraw_stage1_attempt2.inp   *HEADINGDeep drawing of a can bottom -- stage 1, attempt 2SI units (kg, m, s, N)***NODE,NSET=REFP11001,0.,0.024*NODE,NSET=REFD11101,0.050,-0.012**** BLANK***NODE,NSET=BLANK501,.000,.000601,.045,.000*NGEN,NSET=BLANK

Page 148: Getting Started With ABAQUS

501,601,1*ELEMENT,TYPE=SAX1,ELSET=BLANK501,501,503*ELGEN,ELSET=BLANK501,50,2,2*SHELL SECTION,ELSET=BLANK,MATERIAL=STEEL,SECTION INTEGRATION=GAUSS.0005,5*NSET,NSET=BSYM501,*NSET,NSET=NHIST521,601**** PUNCH1 -- PUNCH FOR FORMING STAGE 1 (Analytical Rigid Surface)***SURFACE, NAME=PUNCH1, TYPE=SEGMENTSSTART,0.032,0.03025LINE,0.032,0.00625CIRCL,0.026,0.00025,0.026,0.00625LINE,0.,0.00025*RIGID BODY, REF NODE=1001, ANALYTICAL SURFACE=PUNCH1**** DIE1 -- DIE FOR FORMING STAGE 1 (Analytical Rigid Surface)***SURFACE, NAME=DIE1, TYPE=SEGMENTSSTART,0.0326,-0.02825LINE,0.0326,-0.00425CIRCL,0.0366,-0.00025,0.0366,-0.00425LINE,0.050,-0.00025*RIGID BODY, REF NODE=1101, ANALYTICAL SURFACE=DIE1**** SURFACE  DEFINITIONS***SURFACE, NAME=BLANK_TOPBLANK,SPOS*SURFACE, NAME=BLANK_BOTBLANK,SNEG**** BLANK MATERIAL***MATERIAL,NAME=STEEL*ELASTIC210.0E9,0.3*DENSITY7800.,*PLASTIC  0.912E8, 0.0  0.131E9, 0.159E-02  0.171E9, 0.649E-02  0.211E9, 0.177E-01  0.251E9, 0.395E-01  0.291E9, 0.776E-01  0.331E9, 0.139  0.391E9, 0.295**** AMPLITUDE DEFINITIONS***AMPLITUDE,NAME=FORM1, DEFINITION=SMOOTH STEP0.,0.,.033,1.**** INITIAL FIXED BOUNDARY CONDITIONS**

Page 149: Getting Started With ABAQUS

*BOUNDARYREFP1,1REFP1,6REFD1,1,6BSYM,1BSYM,6**** STEP 1 -- FIRST FORMING STAGE*****ELSET,ELSET=QA_TEST_ALLELEMSBLANK,***NSET, NSET=QA_TEST_ALLNODESREFP1, REFD1, BLANK, BLANKBSYM, NHIST***STEP*DYNAMIC,EXPLICIT,.033**** Contact Pair Definition***CONTACT PAIR,INTERACTION=INTERPUNCH1,BLANK_TOPDIE1,BLANK_BOT*SURFACE INTERACTION,NAME=INTER*FRICTION.1,*BOUNDARY,TYPE=DISPLACEMENT,AMPLITUDE=FORM1REFP1,2,2,-.015*RESTART,WRITE,NUMBER INTERVAL=10*OUTPUT, HISTORY, TIME INTERVAL=1.E-5 *NODE OUTPUT, NSET=NHIST U,V*ENERGY OUTPUTALLKE, ALLIE, ALLWK, ALLVD, ALLAE, ALLPD, ETOTAL*OUTPUT, FIELD, NUMBER=4*ELEMENT OUTPUT, ELSET=BLANKSTH, SF, S*NODE OUTPUTU,RF **** Output for HKS QA purposes***FILE OUTPUT,NUMBER INTERVAL=1*ENERGY FILE*NODE FILEU,RF*EL FILES,*OUTPUT, FIELD, NUMBER INTERVAL=1*NODE OUTPUT, NSET=QA_TEST_ALLNODESU,RF*ELEMENT OUTPUT, ELSET=QA_TEST_ALLELEMSS,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIMEINT=0.033***OUTPUT,HISTORY,VARIABLE=PRESELECT*END STEPdraw_stage1_attempt3.inp   *HEADING

Page 150: Getting Started With ABAQUS

Deep drawing of a can bottom -- stage 1, attempt 3SI units (kg, m, s, N)***NODE,NSET=REFP11001,0.,0.024*NODE,NSET=REFD11101,0.050,-0.012**** BLANK***NODE,NSET=BLANK501,.000,.000601,.045,.000*NGEN,NSET=BLANK501,601,1*ELEMENT,TYPE=SAX1,ELSET=BLANK501,501,503*ELGEN,ELSET=BLANK501,50,2,2*SHELL SECTION,ELSET=BLANK,MATERIAL=STEEL,SECTION INTEGRATION=GAUSS.0005,5*NSET,NSET=BSYM501,*NSET,NSET=NHIST521,601**** PUNCH1 -- PUNCH FOR FORMING STAGE 1 (Analytical Rigid Surface)***SURFACE, NAME=PUNCH1, TYPE=SEGMENTSSTART,0.032,0.03025LINE,0.032,0.00625CIRCL,0.026,0.00025,0.026,0.00625LINE,0.,0.00025*RIGID BODY, REF NODE=1001, ANALYTICAL SURFACE=PUNCH1**** DIE1 -- DIE FOR FORMING STAGE 1 (Analytical Rigid Surface)***SURFACE, NAME=DIE1, TYPE=SEGMENTSSTART,0.0326,-0.02825LINE,0.0326,-0.00425CIRCL,0.0366,-0.00025,0.0366,-0.00425LINE,0.050,-0.00025*RIGID BODY, REF NODE=1101, ANALYTICAL SURFACE=DIE1**** SURFACE  DEFINITIONS***SURFACE, NAME=BLANK_TOPBLANK,SPOS*SURFACE, NAME=BLANK_BOTBLANK,SNEG**** BLANK MATERIAL***MATERIAL,NAME=STEEL*ELASTIC210.0E9,0.3*DENSITY7800.,*DAMPING,BETA=1.E-7*PLASTIC  0.912E8, 0.0

Page 151: Getting Started With ABAQUS

  0.131E9, 0.159E-02  0.171E9, 0.649E-02  0.211E9, 0.177E-01  0.251E9, 0.395E-01  0.291E9, 0.776E-01  0.331E9, 0.139  0.391E9, 0.295**** AMPLITUDE DEFINITIONS***AMPLITUDE,NAME=FORM1, DEFINITION=SMOOTH STEP0.,0.,.033,1.**** INITIAL FIXED BOUNDARY CONDITIONS***BOUNDARYREFP1,1REFP1,6REFD1,1,6BSYM,1BSYM,6**** STEP 1 -- FIRST FORMING STAGE***STEP*DYNAMIC,EXPLICIT,.033**** Contact Pair Definition***CONTACT PAIR,INTERACTION=INTERPUNCH1,BLANK_TOPDIE1,BLANK_BOT*SURFACE INTERACTION,NAME=INTER*FRICTION.1,*BOUNDARY,TYPE=DISPLACEMENT,AMPLITUDE=FORM1REFP1,2,2,-.015*RESTART,WRITE,NUMBER INTERVAL=10*OUTPUT, HISTORY, TIME INTERVAL=1.E-5 *NODE OUTPUT, NSET=NHIST U,V*ENERGY OUTPUTALLKE, ALLIE, ALLWK, ALLVD, ALLAE, ALLPD, ETOTAL*OUTPUT, FIELD, NUMBER=4*ELEMENT OUTPUT, ELSET=BLANKSTH, SF, S*NODE OUTPUTU,RF **** Output for HKS QA purposes***FILE OUTPUT,NUMBER INTERVAL=1*ENERGY FILE*NODE FILEU,RF*EL FILES,*END STEPdraw_stage1_attempt3_sqrt10.inp   *HEADING

Page 152: Getting Started With ABAQUS

Deep drawing of a can bottom -- stage 1, attempt 3Mass scaling factor = 10 (speedup of sqrt10)SI units (kg, m, s, N)***NODE,NSET=REFP11001,0.,0.024*NODE,NSET=REFD11101,0.050,-0.012**** BLANK***NODE,NSET=BLANK501,.000,.000601,.045,.000*NGEN,NSET=BLANK501,601,1*ELEMENT,TYPE=SAX1,ELSET=BLANK501,501,503*ELGEN,ELSET=BLANK501,50,2,2*SHELL SECTION,ELSET=BLANK,MATERIAL=STEEL,SECTION INTEGRATION=GAUSS.0005,5*NSET,NSET=BSYM501,*NSET,NSET=NHIST521,601**** PUNCH1 -- PUNCH FOR FORMING STAGE 1 (Analytical Rigid Surface)***SURFACE, NAME=PUNCH1, TYPE=SEGMENTSSTART,0.032,0.03025LINE,0.032,0.00625CIRCL,0.026,0.00025,0.026,0.00625LINE,0.,0.00025*RIGID BODY, REF NODE=1001, ANALYTICAL SURFACE=PUNCH1**** DIE1 -- DIE FOR FORMING STAGE 1 (Analytical Rigid Surface)***SURFACE, NAME=DIE1, TYPE=SEGMENTSSTART,0.0326,-0.02825LINE,0.0326,-0.00425CIRCL,0.0366,-0.00025,0.0366,-0.00425LINE,0.050,-0.00025*RIGID BODY, REF NODE=1101, ANALYTICAL SURFACE=DIE1**** SURFACE  DEFINITIONS***SURFACE, NAME=BLANK_TOPBLANK,SPOS*SURFACE, NAME=BLANK_BOTBLANK,SNEG**** BLANK MATERIAL***MATERIAL,NAME=STEEL*ELASTIC210.0E9,0.3*DENSITY7800.,*DAMPING,BETA=1.E-7*PLASTIC

Page 153: Getting Started With ABAQUS

  0.912E8, 0.0  0.131E9, 0.159E-02  0.171E9, 0.649E-02  0.211E9, 0.177E-01  0.251E9, 0.395E-01  0.291E9, 0.776E-01  0.331E9, 0.139  0.391E9, 0.295**** AMPLITUDE DEFINITIONS***AMPLITUDE,NAME=FORM1, DEFINITION=SMOOTH STEP0.,0.,.033,1.**** INITIAL FIXED BOUNDARY CONDITIONS***BOUNDARYREFP1,1REFP1,6REFD1,1,6BSYM,1BSYM,6**** STEP 1 -- FIRST FORMING STAGE*****ELSET,ELSET=QA_TEST_ALLELEMSBLANK,***NSET, NSET=QA_TEST_ALLNODESREFP1, REFD1, BLANK, BLANKBSYM, NHIST***STEP*DYNAMIC,EXPLICIT,.033*FIXED MASS SCALING, FACTOR=10**** Contact Pair Definition***CONTACT PAIR,INTERACTION=INTERPUNCH1,BLANK_TOPDIE1,BLANK_BOT*SURFACE INTERACTION,NAME=INTER*FRICTION.1,*BOUNDARY,TYPE=DISPLACEMENT,AMPLITUDE=FORM1REFP1,2,2,-.015*RESTART,WRITE,NUMBER INTERVAL=10*OUTPUT, HISTORY, TIME INTERVAL=1.E-5 *NODE OUTPUT, NSET=NHIST U,V*ENERGY OUTPUTALLKE, ALLIE, ALLWK, ALLVD, ALLAE, ALLPD, ETOTAL*OUTPUT, FIELD, NUMBER=4*ELEMENT OUTPUT, ELSET=BLANKSTH, SF, S*NODE OUTPUTU,RF **** Output for HKS QA purposes

Page 154: Getting Started With ABAQUS

***FILE OUTPUT,NUMBER INTERVAL=1*ENERGY FILE*NODE FILEU,RF*EL FILES,*OUTPUT, FIELD, NUMBER INTERVAL=1*NODE OUTPUT, NSET=QA_TEST_ALLNODESU,RF*ELEMENT OUTPUT, ELSET=QA_TEST_ALLELEMSS,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIMEINT=0.033***OUTPUT,HISTORY,VARIABLE=PRESELECT*END STEPdraw_stage1_attempt3_10.inp   *HEADINGDeep drawing of a can bottom -- stage 1, attempt 3Mass scaling factor = 100 (speedup of 10)SI units (kg, m, s, N)***NODE,NSET=REFP11001,0.,0.024*NODE,NSET=REFD11101,0.050,-0.012**** BLANK***NODE,NSET=BLANK501,.000,.000601,.045,.000*NGEN,NSET=BLANK501,601,1*ELEMENT,TYPE=SAX1,ELSET=BLANK501,501,503*ELGEN,ELSET=BLANK501,50,2,2*SHELL SECTION,ELSET=BLANK,MATERIAL=STEEL,SECTION INTEGRATION=GAUSS.0005,5*NSET,NSET=BSYM501,*NSET,NSET=NHIST521,601**** PUNCH1 -- PUNCH FOR FORMING STAGE 1 (Analytical Rigid Surface)***SURFACE, NAME=PUNCH1, TYPE=SEGMENTSSTART,0.032,0.03025LINE,0.032,0.00625CIRCL,0.026,0.00025,0.026,0.00625LINE,0.,0.00025*RIGID BODY, REF NODE=1001, ANALYTICAL SURFACE=PUNCH1**** DIE1 -- DIE FOR FORMING STAGE 1 (Analytical Rigid Surface)***SURFACE, NAME=DIE1, TYPE=SEGMENTSSTART,0.0326,-0.02825LINE,0.0326,-0.00425CIRCL,0.0366,-0.00025,0.0366,-0.00425LINE,0.050,-0.00025*RIGID BODY, REF NODE=1101, ANALYTICAL SURFACE=DIE1

Page 155: Getting Started With ABAQUS

**** SURFACE  DEFINITIONS***SURFACE, NAME=BLANK_TOPBLANK,SPOS*SURFACE, NAME=BLANK_BOTBLANK,SNEG**** BLANK MATERIAL***MATERIAL,NAME=STEEL*ELASTIC210.0E9,0.3*DENSITY7800.,*DAMPING,BETA=1.E-7*PLASTIC  0.912E8, 0.0  0.131E9, 0.159E-02  0.171E9, 0.649E-02  0.211E9, 0.177E-01  0.251E9, 0.395E-01  0.291E9, 0.776E-01  0.331E9, 0.139  0.391E9, 0.295**** AMPLITUDE DEFINITIONS***AMPLITUDE,NAME=FORM1, DEFINITION=SMOOTH STEP0.,0.,.033,1.**** INITIAL FIXED BOUNDARY CONDITIONS***BOUNDARYREFP1,1REFP1,6REFD1,1,6BSYM,1BSYM,6**** STEP 1 -- FIRST FORMING STAGE*****ELSET,ELSET=QA_TEST_ALLELEMSBLANK,***NSET, NSET=QA_TEST_ALLNODESREFP1, REFD1, BLANK, BLANKBSYM, NHIST***STEP*DYNAMIC,EXPLICIT,.033*FIXED MASS SCALING, FACTOR=100**** Contact Pair Definition***CONTACT PAIR,INTERACTION=INTERPUNCH1,BLANK_TOPDIE1,BLANK_BOT*SURFACE INTERACTION,NAME=INTER

Page 156: Getting Started With ABAQUS

*FRICTION.1,*BOUNDARY,TYPE=DISPLACEMENT,AMPLITUDE=FORM1REFP1,2,2,-.015*RESTART,WRITE,NUMBER INTERVAL=10*OUTPUT, HISTORY, TIME INTERVAL=1.E-5 *NODE OUTPUT, NSET=NHIST U,V*ENERGY OUTPUTALLKE, ALLIE, ALLWK, ALLVD, ALLAE, ALLPD, ETOTAL*OUTPUT, FIELD, NUMBER=4*ELEMENT OUTPUT, ELSET=BLANKSTH, SF, S*NODE OUTPUTU,RF **** Output for HKS QA purposes***FILE OUTPUT,NUMBER INTERVAL=1*ENERGY FILE*NODE FILEU,RF*EL FILES,*OUTPUT, FIELD, NUMBER INTERVAL=1*NODE OUTPUT, NSET=QA_TEST_ALLNODESU,RF*ELEMENT OUTPUT, ELSET=QA_TEST_ALLELEMSS,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIMEINT=0.033***OUTPUT,HISTORY,VARIABLE=PRESELECT*END STEPdraw_stage1_attempt3_30.inp   *HEADINGDeep drawing of a can bottom -- stage 1, attempt 3Mass scaling factor = 900 (speedup of 30)SI units (kg, m, s, N)***NODE,NSET=REFP11001,0.,0.024*NODE,NSET=REFD11101,0.050,-0.012**** BLANK***NODE,NSET=BLANK501,.000,.000601,.045,.000*NGEN,NSET=BLANK501,601,1*ELEMENT,TYPE=SAX1,ELSET=BLANK501,501,503*ELGEN,ELSET=BLANK501,50,2,2*SHELL SECTION,ELSET=BLANK,MATERIAL=STEEL,SECTION INTEGRATION=GAUSS.0005,5*NSET,NSET=BSYM501,*NSET,NSET=NHIST521,601**

Page 157: Getting Started With ABAQUS

** PUNCH1 -- PUNCH FOR FORMING STAGE 1 (Analytical Rigid Surface)***SURFACE, NAME=PUNCH1, TYPE=SEGMENTSSTART,0.032,0.03025LINE,0.032,0.00625CIRCL,0.026,0.00025,0.026,0.00625LINE,0.,0.00025*RIGID BODY, REF NODE=1001, ANALYTICAL SURFACE=PUNCH1**** DIE1 -- DIE FOR FORMING STAGE 1 (Analytical Rigid Surface)***SURFACE, NAME=DIE1, TYPE=SEGMENTSSTART,0.0326,-0.02825LINE,0.0326,-0.00425CIRCL,0.0366,-0.00025,0.0366,-0.00425LINE,0.050,-0.00025*RIGID BODY, REF NODE=1101, ANALYTICAL SURFACE=DIE1**** SURFACE  DEFINITIONS***SURFACE, NAME=BLANK_TOPBLANK,SPOS*SURFACE, NAME=BLANK_BOTBLANK,SNEG**** BLANK MATERIAL***MATERIAL,NAME=STEEL*ELASTIC210.0E9,0.3*DENSITY7800.,*DAMPING,BETA=1.E-7*PLASTIC  0.912E8, 0.0  0.131E9, 0.159E-02  0.171E9, 0.649E-02  0.211E9, 0.177E-01  0.251E9, 0.395E-01  0.291E9, 0.776E-01  0.331E9, 0.139  0.391E9, 0.295**** AMPLITUDE DEFINITIONS***AMPLITUDE,NAME=FORM1, DEFINITION=SMOOTH STEP0.,0.,.033,1.**** INITIAL FIXED BOUNDARY CONDITIONS***BOUNDARYREFP1,1REFP1,6REFD1,1,6BSYM,1BSYM,6**** STEP 1 -- FIRST FORMING STAGE*****ELSET,ELSET=QA_TEST_ALLELEMS

Page 158: Getting Started With ABAQUS

BLANK,***NSET, NSET=QA_TEST_ALLNODESREFP1, REFD1, BLANK, BLANKBSYM, NHIST***STEP*DYNAMIC,EXPLICIT,.033*FIXED MASS SCALING, FACTOR=900**** Contact Pair Definition***CONTACT PAIR,INTERACTION=INTERPUNCH1,BLANK_TOPDIE1,BLANK_BOT*SURFACE INTERACTION,NAME=INTER*FRICTION.1,*BOUNDARY,TYPE=DISPLACEMENT,AMPLITUDE=FORM1REFP1,2,2,-.015*RESTART,WRITE,NUMBER INTERVAL=10*OUTPUT, HISTORY, TIME INTERVAL=1.E-5 *NODE OUTPUT, NSET=NHIST U,V*ENERGY OUTPUTALLKE, ALLIE, ALLWK, ALLVD, ALLAE, ALLPD, ETOTAL*OUTPUT, FIELD, NUMBER=4*ELEMENT OUTPUT, ELSET=BLANKSTH, SF, S*NODE OUTPUTU,RF **** Output for HKS QA purposes***FILE OUTPUT,NUMBER INTERVAL=1*ENERGY FILE*NODE FILEU,RF*EL FILES,*OUTPUT, FIELD, NUMBER INTERVAL=1*NODE OUTPUT, NSET=QA_TEST_ALLNODESU,RF*ELEMENT OUTPUT, ELSET=QA_TEST_ALLELEMSS,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIMEINT=0.033***OUTPUT,HISTORY,VARIABLE=PRESELECT*END STEPdraw_stage2.inp   *HEADINGDeep drawing of a can bottom -- stage 2ABAQUS/Explicit forming stage 2 following draw_spring1_std.inpSI units (kg, m, s, N)*IMPORT,STATE=YES,UPDATE=NOBLANK,*IMPORT NSETBSYM,NHIST,BLANK**** PUNCH2 -- PUNCH FOR FORMING STAGE 2**

Page 159: Getting Started With ABAQUS

*NODE,NSET=PUNCH2201,.023875,.030202,.023875,.002232,.025875,.000262,.031875,.006263,.031875,.030298,.025875,.002299,.025875,.0061201,.023875,.030*NGEN,NSET=PUNCH2,LINE=C202,232,1,298232,262,1,299*ELEMENT,TYPE=RAX2,ELSET=PUNCH2201,201,202*ELGEN,ELSET=PUNCH2201,62,1,1*RIGID BODY,ELSET=PUNCH2,REF NODE=1201*NSET,NSET=REFP21201,**** DIE2 -- DIE FOR FORMING STAGE 2***NODE,NSET=DIE2301,.026,-.010302,.026, .000332,.0325, .0065333,.050, .0065399,.026, .00651301,.026,-.0101302,.026,-.030*NGEN,NSET=DIE2,LINE=C302,332,1,399*ELEMENT,TYPE=RAX2,ELSET=DIE2301,301,302*ELGEN,ELSET=DIE2301,32,1,1*RIGID BODY,ELSET=DIE2,REF NODE=1301*NSET,NSET=REFD21301,**** DOMER -- DOMER DIE FOR FORMING STAGE 2***NODE,NSET=DOMER401, .000,   .008431, .022,   .000432, .022,  -.010499, .000,  -.026251401,.000,   .008*NGEN,NSET=DOMER,LINE=C401,431,1,499*ELEMENT,TYPE=RAX2,ELSET=DOMER401,401,402*ELGEN,ELSET=DOMER401,31,1,1*RIGID BODY,ELSET=DOMER,REF NODE=1401*NSET,NSET=REFDOMER1401,**** Surface Definitions***SURFACE, NAME=BLANK_TOP

Page 160: Getting Started With ABAQUS

BLANK,SPOS*SURFACE, NAME=BLANK_BOTBLANK,SNEG*SURFACE, NAME=PUNCH2PUNCH2,SNEG*SURFACE, NAME=DIE2DIE2,SPOS*SURFACE, NAME=DOMERDOMER,SPOS**** SPRING AND DASHPOT FOR FORMING STAGE 2***ELEMENT,TYPE=SPRINGA,ELSET=SPRING1301,1301,1302*NSET,NSET=SPEND1302,*SPRING,ELSET=SPRING6.3E6,*ELEMENT,TYPE=DASHPOTA,ELSET=DASHPOT2301,1301,1302*DASHPOT,ELSET=DASHPOT1.E4,*NSET,NSET=REFREFP2,REFD2,REFDOMER,SPEND**** MASS FOR SPRING IN FORMING STAGE 2***ELEMENT,TYPE=MASS,ELSET=MASS1302,1301*MASS,ELSET=MASS10.,**** AMPLITUDE DEFINITIONS***AMPLITUDE,NAME=RIGID,DEFINITION=SMOOTH STEP0.,0.,1.E-6,1.*AMPLITUDE,NAME=FORM2,DEFINITION=SMOOTH STEP0.,0.,.033,1.**** STEP 4 -- POSITION RIGID BODIES FOR SECOND PUNCHING STAGE***STEP*DYNAMIC,EXPLICIT,1.E-6*RESTART,WRITE,NUM=1*BOUNDARY,TYPE=VELOCITYREFDOMER,1,1,0.REFDOMER,6,6,0.REFD2,1,1,0.REFD2,6,6,0.SPEND,1,1,0.SPEND,3,3,0.REFP2,1,1,0.REFP2,6,6,0.*BOUNDARY,AMPLITUDE=RIGIDREFDOMER,2,2,-.02355REFD2,2,2,-.0153SPEND,2,2,-.0153REFP2,2,2,-.01465*BOUNDARYBLANK, ENCASTRE

Page 161: Getting Started With ABAQUS

*DIAGNOSTICS,CONTACT INITIAL OVERCLOSURE=DETAIL,DEFORMATION SPEED=DETAIL*OUTPUT, HISTORY, TIME INTERVAL=1.E-5 *NODE OUTPUT, NSET=NHIST U,V*NODE OUTPUT, NSET=REFU, RF*ENERGY OUTPUTALLKE, ALLIE, ALLWK, ALLVD, ALLAE, ALLPD, ETOTAL*OUTPUT, FIELD, NUMBER=4*ELEMENT OUTPUT, ELSET=BLANKSTH, SF, S*NODE OUTPUTU,*END STEP**** STEP 5 -- ANNEAL***STEP*ANNEAL*END STEP**** STEP 6 -- SECOND PUNCHING STAGE***STEP*DYNAMIC,EXPLICIT,.033*FIXED MASS SCALING, FACTOR=10, ELSET=BLANK*DIAGNOSTICS,CONTACT INITIAL OVERCLOSURE=DETAIL,DEFORMATION SPEED=DETAIL*CONTACT PAIR,INTERACTION=INTERPUNCH2,BLANK_TOPDIE2,BLANK_BOTDOMER,BLANK_BOT*SURFACE INTERACTION,NAME=INTER*FRICTION.1,*BOUNDARY,TYPE=DISPLACEMENT,AMPLITUDE=FORM2,OP=NEWREFP2,2,2,-0.010*BOUNDARY,TYPE=VELOCITY,OP=NEWREFP2,1,1,0.REFP2,6,6,0.REFD2,1,1,0.REFD2,6,6,0.SPEND,1,3,0.REFDOMER,1,6,0.BSYM,1,1,0.BSYM,6,6,0.*MONITOR,NODE=1301,DOF=2*RESTART,WRITE,NUMBER INTERVAL=10**** Output for HKS QA purposes***FILE OUTPUT,NUMBER INTERVAL=1*ENERGY FILE*NODE FILEU,RF*EL FILES,*END STEP

draw_spring2_std.inp   *HEADING

Page 162: Getting Started With ABAQUS

Deep drawing of a can bottom -- second springbackABAQUS/Standard springback following draw_stage2.inpSI units (kg, m, s, N)*IMPORT, STATE=YES, UPDATE=NOBLANK,*IMPORT ELSETBLANK,*IMPORT NSETBSYM,*BOUNDARYBSYM,1BSYM,6*RESTART,WRITE,FREQ=999*STEP,NLGEOM*STATIC.1,1.*BOUNDARY,FIXEDBSYM,2,2*OUTPUT, FIELD, FREQUENCY=10 *ELEMENT OUTPUT, ELSET=BLANKSTH, SF, S*NODE OUTPUTU, **** Output for HKS QA purposes***NODE FILE,FREQ=999U,*EL FILE,FREQ=999S,*END STEP 


12 (12.2.1.3.0) Getting Started Oracle Data …Getting Started with Oracle® Data Integrator Getting Started 12c (12.2.1.3.0) E96509-02 March 2019 Oracle Data Integrator Getting Started

12 (12.2.1.3.0) Getting Started Oracle Data …Getting Started with Oracle® Data Integrator Getting Started 12c (12.2.1.3.0) E96509-02 March 2019 Oracle Data Integrator Getting Started

WaveSurfer 3000 Oscilloscope Getting Started Guidecdn.teledynelecroy.com/.../wavesurfer-3000-getting-started-guide.pdf · WaveSurfer 3000 Getting Started Guide ... However, clients

WaveSurfer 3000 Oscilloscope Getting Started Guidecdn.teledynelecroy.com/.../wavesurfer-3000-getting-started-guide.pdf · WaveSurfer 3000 Getting Started Guide ... However, clients

Getting Started - cisco.com · Getting Started Thischapterdescribestheinterfacesthatyouusetoconfigure,administer,andmaintainCiscoFinesseand describeshowtoaccessthem. • UserAccounts,

Getting Started - cisco.com · Getting Started Thischapterdescribestheinterfacesthatyouusetoconfigure,administer,andmaintainCiscoFinesseand describeshowtoaccessthem. • UserAccounts,

Getting Started V6 - University of Wisconsin–Madison · DATASTREAM GETTING STARTED GUIDE DATASTREAM GETTING STARTED GUIDE DATASTREAM GETTING STARTED GUIDE DATASTREAM GETTING STARTED

Getting Started V6 - University of Wisconsin–Madison · DATASTREAM GETTING STARTED GUIDE DATASTREAM GETTING STARTED GUIDE DATASTREAM GETTING STARTED GUIDE DATASTREAM GETTING STARTED

LTspice IV Getting Started GuideLTspice IV Getting Started Guide

LTspice IV Getting Started GuideLTspice IV Getting Started Guide

Getting Started V5 - Thomson Reuters · DATASTREAM GETTING STARTED GUIDE DATASTREAM GETTING STARTED GUIDE DATASTREAM GETTING STARTED GUIDE DATASTREAM GETTING STARTED GUIDE DATASTREAM

Getting Started V5 - Thomson Reuters · DATASTREAM GETTING STARTED GUIDE DATASTREAM GETTING STARTED GUIDE DATASTREAM GETTING STARTED GUIDE DATASTREAM GETTING STARTED GUIDE DATASTREAM

Skaffold - storage.googleapis.com · [getting-started getting-started] Hello world! [getting-started getting-started] Hello world! [getting-started getting-started] Hello world! 5.

Skaffold - storage.googleapis.com · [getting-started getting-started] Hello world! [getting-started getting-started] Hello world! [getting-started getting-started] Hello world! 5.

Getting Started Guide - Engravers Network · DCS_Direct_Jet_1024UVMVP_Getting_Started_Guide_1.2_030314 Getting Started Guide

Getting Started Guide - Engravers Network · DCS_Direct_Jet_1024UVMVP_Getting_Started_Guide_1.2_030314 Getting Started Guide

Getting Started With Abaqus

Getting Started With Abaqus

ShMC Getting Started - Samway - Products Getting Started... · ShMC Getting Started Rev 1.0 ShMC Getting Started Revision History: Rev 1.0 01.10.2013 First Draft Table of Contents

ShMC Getting Started - Samway - Products Getting Started... · ShMC Getting Started Rev 1.0 ShMC Getting Started Revision History: Rev 1.0 01.10.2013 First Draft Table of Contents

GETTING STARTED · GETTING STARTED Always check the Owner’s Manual for more operating information and safety features Getting Started Getting Started Quick Tips 2004 Mazda MPV page

GETTING STARTED · GETTING STARTED Always check the Owner’s Manual for more operating information and safety features Getting Started Getting Started Quick Tips 2004 Mazda MPV page

ASEE Introduction to Abaqus Workshopasee.engin.umich.edu/.../02/Abaqus-Presentation-Slides-from-Worksh… · ASEE Introduction to Abaqus Workshop What to do to get started Open Abaqus

ASEE Introduction to Abaqus Workshopasee.engin.umich.edu/.../02/Abaqus-Presentation-Slides-from-Worksh… · ASEE Introduction to Abaqus Workshop What to do to get started Open Abaqus

WinCC flexible Getting Started Básico - Grup DAP · WinCC flexible Getting Started Básico Getting Started, Edición 04/2006, 6ZB5370-1CL04-0BA2 Bienvenido al «Getting Started –

WinCC flexible Getting Started Básico - Grup DAP · WinCC flexible Getting Started Básico Getting Started, Edición 04/2006, 6ZB5370-1CL04-0BA2 Bienvenido al «Getting Started –

Getting Started with Abaqus: Interactive Edition - iMechanica

Getting Started with Abaqus: Interactive Edition - iMechanica

Getting Started with RAD Studio 2009 Getting Started with Delphi ...

Getting Started with RAD Studio 2009 Getting Started with Delphi ...

Getting started Deployment Getting started.

Getting started Deployment Getting started.

Getting Started Guide - NetSupportresources.netsupportsoftware.com/...Notify-Getting-Started-Guide.pdf · Getting Started Guide. 2 CONTENTS . ... or 'Windows networking', ... from

Getting Started Guide - NetSupportresources.netsupportsoftware.com/...Notify-Getting-Started-Guide.pdf · Getting Started Guide. 2 CONTENTS . ... or 'Windows networking', ... from

LTspice IV Getting Started GuideLTspice IV Getting Started ...

LTspice IV Getting Started GuideLTspice IV Getting Started ...

MendeleyMendeley Manual - Getting Started Manual - Getting Started

MendeleyMendeley Manual - Getting Started Manual - Getting Started

Getting Started 4 latest - University of York · 2019-12-20 · Introduction ADVANCE GETTING STARTED GUIDE ADVANCE GETTING STARTED GUIDE ADVANCE GETTING STARTED GUIDE ADVANCE GETTING

Getting Started 4 latest - University of York · 2019-12-20 · Introduction ADVANCE GETTING STARTED GUIDE ADVANCE GETTING STARTED GUIDE ADVANCE GETTING STARTED GUIDE ADVANCE GETTING