Arbitrary lagragian eulerian method

ADAPTIVITY TECHNIQUES

12. Adaptivity Techniques

Adaptivity techniques: overview 12.1

ALE adaptive meshing 12.2

Adaptive remeshing 12.3

Analysis continuation after mesh replacement 12.4

ADAPTIVITY TECHNIQUES: OVERVIEW

12.1 Adaptivity techniques: overview

!Adaptivity techniques," Section 12.1.1

12.11


12.1.1 ADAPTIVITY TECHNIQUES

Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE

References

!ALE adaptive meshing: overview," Section 12.2.1 !Adaptive remeshing: overview," Section 12.3.1 !Mesh-to-mesh solution mapping," Section 12.4.1 *ADAPTIVE MESH !Understanding adaptive remeshing," Section 17.13 of the Abaqus/CAE User#s Manual

Overview

The nite element discretization that results from suboptimal meshing of models can limit your abilityto obtain adequate analysis results at a reasonable CPU cost. This section provides an overview of theadaptivity techniques available in Abaqus that help you optimize a mesh and, therefore, obtain qualitysolutions while controlling the cost of your analysis. The term !adaptivity" re ects the adaptive, orsolution-dependent, processes that Abaqus uses to adapt your mesh to meet your analysis goals.

Selecting an adaptivity technique

Three adaptivity techniques are available in Abaqus: Arbitrary Lagrangian-Eulerian (ALE) adaptivemeshing; varying topology adaptive remeshing (this functionality is not applicable to V6); and mesh-to-mesh solution mapping, to enable rezoning analysis. Table 12.1.1$1 shows that the adaptivity techniquescan be classi ed according to

their applicability to achieving particular goals, eitheraccuracy or control of mesh distortion; their impact on mesh de nitions, either through smoothing a single mesh or through generating

multiple dissimilar meshes; and

when adaptivity occurs with respect to analysis steps.

12.1.11


Table 12.1.11 The characteristics of the adaptivity techniques.

Accuracy Distortioncontrol

Singlemesh

Multiplemeshes

Adaptivity occurs

ALE adaptivemeshing

Throughout a step

Adaptive remeshing(not applicable to V6)

Separately fromanalysis steps

Mesh-to-meshsolution mapping

Between analysissteps

ALE adaptive meshing

Arbitrary Lagrangian-Eulerian (ALE) adaptive meshing provides control of mesh distortion. ALEadaptive meshing uses a single mesh de nition that is gradually smoothed within analysis steps.ALE adaptive meshing is available for limited applicationsin Abaqus/Standard and is more generallyapplicable in Abaqus/Explicit. The term ALE implies a broadrange of analysis approaches, frompurely Lagrangian analysis, in which the node motion corresponds to material motion, to purelyEulerian analysis, in which the nodes remain xed in space and material ! ows" through the elements.Typically ALE analyses use an approach between these two extremes. The ALE feature is distinctfrom the Eulerian analysis capability in Abaqus/Explicit,which is described in !Eulerian analysis,"Section 14.1.1.

You can use adaptive meshing to control element distortion in cases where large deformation or lossof material occurs. Figure 12.1.1$1 illustrates a case where adaptive meshing limits mesh distortion in abulk forming simulation.

12.1.12


rigid die

axis

of s

ymm

etry

rigid die

symmetry plane

sym

met

ry a

xis

withoutALE adaptive

meshing

withALE adaptivemeshing

Figure 12.1.11 Use of ALE adaptive meshing to control element distortion.

Unlike other adaptivity techniques, adaptive meshing operates on your original mesh de nition andis, therefore, useful only when a single mesh can be effective for the duration of a simulation. The meshis adapted through smoothing of the mesh nodes. This smoothing is typically applied frequently withinanalysis steps. ALE adaptive meshing requires only one analysis job. See !ALE adaptive meshing:overview," Section 12.2.1, for details.

Adaptive remeshing (varying topology adaptivity)

Adaptive remeshing is typically used for accuracy control,although it can also be used for distortioncontrol in some situations. The adaptive remeshing processinvolves the iterative generation of multipledissimilar meshes to determine a single, optimized mesh that is used throughout an analysis. Adaptiveremeshing is available only for Abaqus/Standard analyses submitted from Abaqus/CAE. The goal ofadaptive remeshing is to obtain a solution that satis es mesh discretization error indicator targets thatyou set, while minimizing the number of elements and, hence,the cost of your analysis. You can use

12.1.13


adaptive remeshing to obtain a mesh that provides a balance between solution cost and desired accuracy.Figure 12.1.1$2 illustrates a case where adaptive remeshing improves the quality of the stress resultaround a llet with targeted mesh re nement.

Figure 12.1.12 Use of adaptive remeshing to improve the quality of a stress result.

Adaptive remeshing involves an iterative process to determine a single, optimized mesh that is usedthrough an analysis. The iterative process and the remeshing are controlled in Abaqus/CAE. Eachsuccessive analysis job covers the same simulation historytime period but uses a different mesh. Oncethe adaptive remeshing process is complete, a single mesh and a single analysis job represent your entireanalysis history. See !Adaptive remeshing: overview," Section 12.3.1, and !Understanding adaptiveremeshing," Section 17.13 of the Abaqus/CAE User#s Manual.

Mesh-to-mesh solution mapping

Mesh-to-mesh solution mapping is available only in Abaqus/Standard. You can use this technique tocontrol element distortion in cases where large deformation occurs by replacing the mesh and continuingthe analysis. Figure 12.1.1$3 illustrates a case where solution mapping is used in conjunction with a newmesh to overcome dif culties associated with element distortion.

12.1.14


Figure 12.1.13 Use of mesh-to-mesh solution mappingas a component of a rezoning technique.

Mesh replacement, or rezoning, involves the creation of multiple Abaqus jobs, each of which representsthe con guration of the model in distinct, sequential periods of thesimulation history. You use meshreplacement when a single mesh cannot be effective for the duration of a simulation. Each meshsubsequent to the initial con guration re ects a solution-dependent deformed con guration of themodel. Therefore, analyses that use mesh replacement are sequentially dependent, and Abaqus usesmesh-to-mesh solution mapping to propagate solution variables from one analysis to the next. Incontrast to adaptive remeshing, each mesh replacement job represents a component of the overallanalysis history%no single mesh and no single analysis job represent your entire analysis. See!Mesh-to-mesh solution mapping," Section 12.4.1, for details.

12.1.15

ALE ADAPTIVE MESHING

12.2 ALE adaptive meshing

!ALE adaptive meshing: overview," Section 12.2.1 !De ning ALE adaptive mesh domains in Abaqus/Explicit," Section 12.2.2 !ALE adaptive meshing and remapping in Abaqus/Explicit," Section 12.2.3 !Modeling techniques for Eulerian adaptive mesh domains inAbaqus/Explicit," Section 12.2.4 !Output and diagnostics for ALE adaptive meshing in Abaqus/Explicit," Section 12.2.5 !De ning ALE adaptive mesh domains in Abaqus/Standard," Section 12.2.6 !ALE adaptive meshing and remapping in Abaqus/Standard," Section 12.2.7

12.21

ALE ADAPTIVE MESHING: OVERVIEW

12.2.1 ALE ADAPTIVE MESHING: OVERVIEW

The adaptive meshing technique in Abaqus combines the features of pure Lagrangian analysis and pureEulerian analysis. This type of adaptive meshing is often referred to as Arbitrary Lagrangian-Eulerian (ALE)analysis. The Abaqus documentation often refers to !ALE adaptive meshing" simply as !adaptive meshing."

ALE adaptive meshing is a tool that makes it possible to maintain a high-quality mesh throughout ananalysis, even when large deformation or loss of material occurs, by allowing the mesh to move independentlyof the material. ALE adaptive meshing does not alter the topology (elements and connectivity) of the mesh,which implies some limitations on the ability of this methodto maintain a high-quality mesh upon extremedeformation. Refer to !Adaptivity techniques," Section 12.1.1, for a comparison between ALE adaptivemeshing and other Abaqus adaptivity methods.

ALE adaptive meshing is distinct from the pure Eulerian analysis capability in Abaqus/Explicit. Thepure Eulerian capability supports multiple materials and voids within a single element, which allows effectivehandling of analyses involving extreme deformation (such as uid ow). In contrast, ALE elements are always100& full of a single material; while this formulation limits the deformation of material in the model to thedeformation of the elements, it allows more precise de nitions of material boundaries and more complexcontact interactions. For more information on pure Eulerian analysis, see !Eulerian analysis," Section 14.1.1.

Although the adaptive meshing techniques and the user interface are similar in Abaqus/Explicitand Abaqus/Standard, the use-cases and the level of functionality are different. Adaptive meshing inAbaqus/Explicit is intended to model large-deformation problems. It does not attempt to minimizediscretization errors in small-deformation analyses. Adaptive meshing in Abaqus/Standard is intended foruse in acoustic domains and for modeling the effects of ablation, or wear, of material. A comparison betweenthe adaptive remeshing functionality in Abaqus/Explicit and Abaqus/Standard is provided in this section.

Features of ALE adaptive meshing

ALE adaptive meshing:

can often maintain a high-quality mesh under severe material deformation by allowing the mesh tomove independently of the underlying material; and

maintains a topologically similar mesh throughout the analysis (i.e., elements are not created ordestroyed).

In Abaqus/Explicit ALE adaptive meshing:

can be used to analyze Lagrangian problems (in which no material leaves the mesh) and Eulerianproblems (in which material ows through the mesh);

can be used as a continuous adaptive meshing tool for transient analysis problems undergoing largedeformations (such as dynamic impact, penetration, and forging problems);

can be used as a solution technique to model steady-state processes (such as extrusion or rolling); can be used as a tool to analyze the transient phase in a steady-state process; and

12.2.11


can be used in explicit dynamics (including adiabatic thermal analysis) and fully coupled thermal-stress procedures.

In Abaqus/Standard ALE adaptive meshing:

can be used to solve Lagrangian problems (in which no material leaves the mesh) and to modeleffects of ablation, or wear (in which material is eroded at the boundary);

can be used to update the acoustic mesh when structural preloading causes signi cant geometricchanges in the acoustic domain; and

can be used in geometrically nonlinear static, steady-state transport, coupled pore uid ow andstress, and coupled temperature-displacement procedures.

Activating ALE adaptive meshing

Adaptive meshing can be applied to an entire model or to individual parts of a model. A Lagrangianadaptive mesh domain will be created, so that the domain as a whole will follow the material originallyinside it, which is the proper physical interpretation for most structural analyses. Additional options areprovided for controlling the mesh. In Abaqus/Explicit analyses you can de ne Eulerian boundaries toallow material to ow into or out of the domain modeled.

The subsequent sections of !ALE adaptive meshing," Section12.2, describe the various optionsthat can be used with adaptive meshing. Although these options give you the ability to exercise detailedcontrol over adaptive meshing, they are not necessary for many Lagrangian problems.

To take full advantage of all the adaptive mesh features in Abaqus, it is important to understandthe concepts of adaptive mesh domains, boundary regions, boundary edges, geometric features,and mesh constraints. These concepts are explained in !De ning ALE adaptive mesh domains inAbaqus/Explicit," Section 12.2.2, and !De ning ALE adaptive mesh domains in Abaqus/Standard,"Section 12.2.6. Instructions for applying boundary conditions, loads, and surfaces to adaptive meshboundaries are also provided in those sections.

!ALE adaptive meshing and remapping in Abaqus/Explicit," Section 12.2.3, and !ALE adaptivemeshing and remapping in Abaqus/Standard," Section 12.2.7, outline the methods used to movethe mesh and to remap solution variables to the new mesh. These sections also present optionsfor controlling these algorithms. Although the default methods have been chosen to work well fora wide variety of problems, you may wish to override the defaults to balance the robustness andef ciency of adaptive meshing or to extend the use of adaptive meshing to relatively dif cult orunusual applications.

Various output and diagnostics are available for verifyingthe formation of adaptive mesh domainsand for interpreting the results of an analysis. These options are explained in !Output anddiagnostics for ALE adaptive meshing in Abaqus/Explicit,"Section 12.2.5.

!Modeling techniques for Eulerian adaptive mesh domains inAbaqus/Explicit," Section 12.2.4,gives advice, in the form of examples and modeling hints, on setting up and interpreting Eulerianproblems in Abaqus/Explicit using adaptive meshing.

12.2.12


Input File Usage: *ADAPTIVE MESH, ELSET=elset_name

Abaqus/CAE Usage: Step module:Other : ALE Adaptive Mesh Domain : Edit : toggle onUsethe ALE adaptive mesh domain below , and clickEdit to select the region

Uses for ALE adaptive meshing

Adaptive meshing is of great value in a variety of problems. Abaqus/Explicit and Abaqus/Standard eachemploy adaptive meshing in ways that provide the greatest value within the particular solver.

Uses in Abaqus/ExplicitIn problems where large deformation is anticipated the improved mesh quality resulting from adaptivemeshing can prevent the analysis from terminating as a result of severe mesh distortion. In thesesituations you can use adaptive meshing to obtain faster, more accurate, and more robust solutions thanwith pure Lagrangian analyses.

Adaptive meshing is particularly effective for simulations of metal forming processes such asforging, extrusion, and rolling because these types of problems usually involve large amounts ofnonrecoverable deformation. Because the nal shape of the product can be drastically different fromthe original shape, a mesh that is optimal for the original product geometry can become unsuitablein later stages of the process when large material deformation leads to severe element distortion andentanglement. Element aspect ratios can also degrade in zones with high strain concentrations. Both ofthese factors can lead to a loss of accuracy, a reduction in the size of the stable time increment, or eventermination of the problem.

Uses in Abaqus/StandardYou can use adaptive meshing to enable acoustic domain meshes to follow the large deformations of thebounding structure. In other applications you can use adaptive meshing and adaptive mesh constraintsto model arbitrarily large amounts of ablation of material away from the domain.

Adaptive meshing of acoustic regions greatly extends the utility of acoustic analysis procedures.Abaqus can be used to model the response of a coupled structural-acoustic system subjected to structuralpreloads. By default, the structural-acoustic calculations are based on the original con guration ofthe acoustic domain. This approximation is adequate as longas the boundary between the uid andstructure does not experience large deformation during application of the preload. However, when thegeometry of the acoustic domain changes signi cantly as a result of structural loading, the originalacoustic con guration must be updated. An example is the interior cavity of a tire subjected to in ation,rim mounting, and footprint pressure loads.

The acoustic elements in Abaqus do not have mechanical behavior and, therefore, cannot model thedeformation of the uid when the structure undergoes large deformation. Abaqus/Standard solves theproblem of computing the current con guration of the acoustic domain by periodically creating a newacoustic mesh that uses the same topology as the original mesh but with the nodal locations adjusted sothat the deformation of the structural-acoustic boundary does not lead to severe distortion of the acousticelements.

The geometric changes associated with the new acoustic meshare then taken into account in asubsequent coupled structural-acoustic analysis. However, it is assumed that the material properties ofthe uid, such as the density, do not change as a result of mesh smoothing.

12.2.13


Adaptive meshing can also model effects of ablation, or wear, by enabling you to de ne boundarymesh motions independent of the underlying material motion. An example is the wearing of a tire duringits life, an effect that can signi cantly affect the performance of the structure.

Comparison of ALE adaptive meshing in Abaqus/Explicit and A baqus/Standard

Adaptive meshing in Abaqus/Explicit is generally more robust and provides more features for controllingthe mesh than does adaptive meshing in Abaqus/Standard.

ALE adaptive meshing in Abaqus/Explicit

Adaptive meshing in Abaqus/Explicit is designed to handle alarge variety of problem classes, andemploys a variety of smoothing methods, with controls that you can use to tailor the adaptivity tospeci c problems. The Abaqus/Explicit implementation allows youto do the following:

to create entirely Eulerian models; to improve the quality of the mesh initially, before deformation begins; and to de ne tracer particles, which enable tracking and output of material-based results quantities.

ALE adaptive meshing in Abaqus/Standard

Adaptive meshing in Abaqus/Standard uses a single smoothing algorithm that works well for structuralacoustic analyses and the modeling of ablation processes. The Abaqus/Standard implementation ofadaptive meshing has the following limitations:

Initial mesh sweeps cannot be used to improve the quality of the initial mesh de nition. The method is not intended to be used in general classes of large-deformation problems, such as

bulk forming.

Diagnostics capabilities are currently limited.

Illustrative examples

To illustrate the value of adaptive meshing, simple examples of transient and steady-state formingapplications follow. For simplicity, two-dimensional cases are shown. In each case Abaqus/Explicit isused in the simulation.

Axisymmetric forging

In this example a well-lubricated rigid die of sinusoidal shape moves down to deform a blank ofrectangular cross-section (see Figure 12.2.1$1). The indentation depth is 80& of the original blankthickness. Material extrudes upward and outward (radially) as the blank is indented. The die is modeledwith an analytical rigid surface, and the blank is modeled with axisymmetric continuum elements in aregular mesh con guration. The blank is assumed to have elastic-plastic material properties.

A pure Lagrangian analysis of this problem does not run to completion because of excessivedistortion in several elements, as shown in Figure 12.2.1$2. The contact surface cannot be treatedcorrectly because of the gross distortion of the elements atthe troughs of the sinusoidal rigid surface.

12.2.14


rigid die

axis

of s

ymm

etry

plane of symmetry

Figure 12.2.11 A blank and a sinusoidal die.

Figure 12.2.12 Eventually, the purely Lagrangian analysis willterminate because of excessive element distortion.

Adaptive meshing allows the problem to run to completion. A Lagrangian adaptive mesh domainis created for the entire blank. Abaqus/Explicit automatically chooses suitable defaults for adaptivemeshing; hence, the adaptive mesh approach requires only two additional input lines:

* HEADING...

* ELSET, ELSET=BLANK**************************** STEP

12.2.15


* DYNAMIC, EXPLICIT...

* ADAPTIVE MESH, ELSET=BLANK...

* END STEP

Figure 12.2.1$3 and Figure 12.2.1$4 show the deformed mesh at various stages of the forminganalysis. Because the mesh re nement is maintained on the areas of the slave surface that contact the dietroughs as the material ows radially, contact conditions are resolved correctly throughout the analysis.

Figure 12.2.13 Deformed con guration at an intermediate stage of the analysis.

Figure 12.2.14 Deformed con guration upon completion of the analysis.

12.2.16


Steady-state rolling example

This example shows how adaptive meshing can be used in a steady-state simulation to allow the ow ofmaterial through Eulerian boundaries on the problem domain. A steel plate is passed through a symmetricroll stand to reduce its height by 50&. This simulation is rununtil it reaches steady-state conditions.

Figure 12.2.1$5 and Figure 12.2.1$6 show the initial and nal (steady-state) con gurations in apurely Lagrangian model of this problem.

rigid roller

plane of symmetry

Figure 12.2.15 The initial con guration of the roller and theundeformed blank in the pure Lagrangian model.

Figure 12.2.16 The nal steady-state con guration in the pure Lagrangian model.

Figure 12.2.1$7 shows this problem modeled using an Eulerian adaptive mesh domain, wherematerial ows through the mesh. Only the region near the roller is modeled. The exact location of thefree surface does not need to be known to set up the problem: itis created in a likely location, and the nal steady-state position is found as part of the solution. Although not shown, a focused mesh can be

12.2.17


100

INFLOW OUTFLOW

free surface

Figure 12.2.17 The initial Eulerian adaptive mesh domain.

used to capture steep strain gradients directly beneath theroller. The Eulerian domain reaches the samesteady-state solution as obtained with the Lagrangian approach.

The Eulerian adaptive mesh domain is created by de ning an in ow and an out ow boundary onthe adaptive mesh domain. Adaptive mesh constraints are applied normal to these boundaries so thatmaterial will ow through the mesh (see !De ning ALE adaptive mesh domains in Abaqus/Explicit,"Section 12.2.2). Frictional contact between the roller andthe blank pulls material through the adaptivemesh domain.

The problem is set up by making the following modi cations to the input le for the pure Lagrangiananalysis:

* HEADING...

* ELSET, ELSET=BILLET...

* ELSET, ELSET=INFLOW...

* ELSET, ELSET=OUTFLOW...

* NSET, NSET=INFLOW...

* NSET, NSET=OUTFLOW...

* SURFACE, NAME=INFLOW, REGION TYPE=EULERIANINFLOW, S1

* SURFACE, NAME=OUTFLOW, REGION TYPE=EULERIANOUTFLOW, S2

**************************** STEP* DYNAMIC, EXPLICITData line to specify the time period of the step

...* ADAPTIVE MESH, ELSET=BILLET, CONTROLS=ADAPT

12.2.18


* ADAPTIVE MESH CONTROLS, NAME=ADAPT* ADAPTIVE MESH CONSTRAINT, TYPE=DISPLACEMENT

INFLOW, 1, 1, 0.0100, 2, 2, 0.0OUTFLOW, 1, 1, 0.0...

* END STEP

Adaptive mesh controls were not required to solve this problem; they were included for illustrativepurposes (see !ALE adaptive meshing and remapping in Abaqus/Explicit," Section 12.2.3, for details).

12.2.19

ALE ADAPTIVE MESH DOMAINS IN Abaqus/Explicit

12.2.2 DEFINING ALE ADAPTIVE MESH DOMAINS IN Abaqus/Explic it

Products: Abaqus/Explicit Abaqus/CAE

References

!ALE adaptive meshing: overview," Section 12.2.1 !ALE adaptive meshing and remapping in Abaqus/Explicit," Section 12.2.3 *ADAPTIVE MESH !Understanding ALE adaptive meshing," Section 14.6 of the Abaqus/CAE User#s Manual

Overview

Arbitrary Lagrangian-Eulerian (ALE) adaptive mesh domains:

de ne the portions of a nite element model where mesh movement is independent of materialdeformation;

can be used to analyze Lagrangian or Eulerian problems; can contain only rst-order, reduced-integration, solid elements (4-node quadrilaterals, 3-node

triangles, 8-node hexahedra, 6-node wedges, and 4-node tetrahedra);

can be used in planar, axisymmetric, and three-dimensionalgeometries; have boundary regions where loads, boundary conditions, and surfaces can be de ned; and are active only for geometrically nonlinear steps.

Defining an ALE adaptive mesh domain

ALE adaptive meshing is performed in adaptive mesh domains,which can be either Lagrangianor Eulerian. Within either type of adaptive mesh domain the mesh will move independently of thematerial. Lagrangian adaptive mesh domains are usually used to analyze transient problems withlarge deformations. On the boundary of a Lagrangian domain the mesh will follow the material inthe direction normal to the boundary, so that the mesh coversthe same material domain at all times.Eulerian adaptive mesh domains are usually used to analyze steady-state processes involving material ow. On certain user-de ned boundaries of an Eulerian domain, material can ow into or out of themesh. By default, the mesh is not xed spatially on these boundaries; mesh constraints must beappliedto prevent the mesh from moving with the material, as described in !Mesh constraints," presented laterin this section. There can never be any !empty" elements; allelements in the domain must be lledcompletely with material at all times.

You must specify the region of the original mesh that will be subject to adaptive meshing.

Input File Usage: *ADAPTIVE MESH, ELSET=name

Multiple adaptive mesh domains can be de ned in a step by reusing the*ADAPTIVE MESH option (for example, to prevent material from owing

12.2.21


from one domain to another or to apply adaptive meshing to unconnecteddomains). The element sets used to create adaptive mesh domains cannotoverlap.

Abaqus/CAE Usage: Step module:Other : ALE Adaptive Mesh Domain : Edit : toggle onUsethe ALE adaptive mesh domain below , and clickEdit to select the region

Only one adaptive mesh domain can be de ned in Abaqus/CAE for anyparticular step.

Modifying an ALE adaptive mesh domain

By default, all adaptive mesh domains de ned in the previous analysis step remain unchanged inthe subsequent step. You de ne the adaptive mesh domains in effect for a given step relative to thepreexisting adaptive mesh domains. At each new step the existing adaptive mesh domains can bemodi ed and additional adaptive mesh domains can be speci ed (except in Abaqus/CAE, where onlyone adaptive mesh domain can be in effect for a given step).

Input File Usage: Use either of the following options to modify an existing adaptive mesh domainor to specify an additional adaptive mesh domain:

*ADAPTIVE MESH, ELSET=name*ADAPTIVE MESH, ELSET=name, OP=MOD

Abaqus/CAE Usage: Step module:Other : ALE Adaptive Mesh Domain : Edit

Removing an ALE adaptive mesh domain

If you choose to remove any adaptive mesh domain in a step, no adaptive mesh domains will bepropagated from the previous step. Therefore, all adaptivemesh domains that are in effect during thisstep must be respeci ed.

Input File Usage: Use the following option to remove all previously de ned adaptive meshdomains and to specify new adaptive mesh domains:

*ADAPTIVE MESH, ELSET=name, OP=NEW

If the OP=NEW parameter is used on any*ADAPTIVE MESH option withina step, it must be used on all*ADAPTIVE MESH options in the step.

Abaqus/CAE Usage: Step module:Other : ALE Adaptive Mesh Domain : Edit : toggleon No adaptive mesh domain for this step

Splitting ALE adaptive mesh domains

User-de ned adaptive mesh domains are examined by Abaqus/Explicit.The user-de ned domain willbe modeled using a single adaptive mesh if the domain:

consists of a single element type; consists of a single connected region; consists of a single material;

12.2.22


is subject to a uniform body force (including zero body force); and has identical section controls.

The user-de ned domain will be split into multiple adaptive mesh domains, separated by boundaryregions, if the domain:

consists of multiple element types; spans part instances; consists of multiple regions (including regions that are connected by less than a single element face,

only by contact conditions, or only by connectors such as MPCs);

consists of multiple materials; is subject to multiple body force de nitions; or is subject to multiple section control de nitions.

In this documentation the term !adaptive mesh domain" refers to a single domain after splitting byAbaqus/Explicit. On the rare occasion that a reference is made to an adaptive mesh domain prior tothe automatic splitting, it is referred to as a !user-de ned adaptive mesh domain." Since adaptive meshdomains are split across element types, degenerate elements should be used for mixed domains thatinclude both triangles and quadrilaterals (or tetrahedronand bricks). For example, when de ning amixed plane strain domain with quadrilateral and triangular elements, the CPE4R element type shouldbe used to de ne both quadrilaterals and degenerated quadrilaterals. Using the CPE3 element will resultin split domains, which is generally not desirable.

ALE adaptive mesh boundary regions

Each ALE adaptive mesh domain has a boundary, which can consist of one or more regions. (Regions,in this context, are surfaces in three-dimensional models or lines in two-dimensional or axisymmetricmodels.) A boundary region can be either Lagrangian, sliding, or Eulerian. Some boundary regions arecreated automatically by Abaqus/Explicit; others can be created by de ning boundary conditions, loads,and surfaces. Adaptive mesh boundary regions are separatedby edges in three dimensions and by cornersin two dimensions. Both edges and corners are referred to as !boundary region edges" throughout thisdocumentation.

Boundary region edges

Two types of boundary region edges can exist: Lagrangian andsliding. Lagrangian edges are alwaysassociated with a material line. Material can never ow past a Lagrangian edge, and nodes can moveonly along a Lagrangian edge (like beads on a string). Sliding edges are associated only with the mesh.Material can ow past a sliding edge (that is, sliding edges are free to slide over the underlying material).

Lagrangian edges can be viewed with Abaqus/CAE; see !Outputand diagnostics for ALE adaptivemeshing in Abaqus/Explicit," Section 12.2.5.

12.2.23


Lagrangian boundary regions

Lagrangian boundary regions are the most common boundary regions in structural nite element analysis;therefore, with the exception of contact surfaces, they arealways the default in Abaqus/Explicit. ALagrangian boundary region has the most constraints of all the boundary region types. The mesh isconstrained to move with the material in the direction normal to the surface of the boundary region andin the directions perpendicular to the boundary region edges.

Lagrangian boundary regions have Lagrangian edges: the edges follow the material. On the interiorof a Lagrangian boundary region, the mesh can move independently of the material in the surface of theboundary region. Thus, a Lagrangian boundary region can be thought of as a !mesh patch" that followsthe material. Nodes are free to move within and along the edges of the patch but cannot leave the patch.

Lagrangian corners

A Lagrangian corner is formed where two Lagrangian edges meet. The node at a Lagrangian corner isconstrained to move with the material in all directions; it is nonadaptive.

Sliding boundary regions

A sliding boundary region is the same as a Lagrangian boundary region except that it has a sliding edge.Sliding boundary regions are created by default when you de ne a surface on the boundary of an adaptivemesh domain (see !Surfaces: overview," Section 2.3.1).

The mesh is constrained to move with the material in the direction normal to the boundary region,but it is completely unconstrained in the directions tangential to the boundary region. Thus, a slidingboundary region can be thought of as a !mesh patch" that movesindependently of the underlying material.

Sliding boundary regions can be created by de ning a surface, boundary condition, or loadon the boundary of an adaptive mesh domain (as explained later in this section). Since the meshis totally unconstrained in the directions tangential to a sliding boundary region, the location of anapplied boundary condition or load may not be physically meaningful as the mesh moves over thematerial. Therefore, to retain the spatial meaning of an applied boundary condition or load, spatialmesh constraints (described in !Mesh constraints," presented later in this section) are usually appliedtangential to sliding boundary regions.

Eulerian boundary regions

Eulerian boundary regions can be de ned on the exterior of a model where it makes physical sense toletmaterial ow across the boundary (for example, at the inlet and outlet of a steady-state extrusion or rollingproblem). This ow across the boundary distinguishes Eulerian boundary regions from Lagrangian orsliding boundary regions.

Eulerian boundary regions have sliding edges and must lie completely on an exterior surface of amodel. It makes no physical sense to allow material ow to originate on an interior surface. You mustexplicitly de ne Eulerian boundary regions since, by default, Abaqus/Explicit assumes that no material ows into or out of an adaptive mesh domain.

Eulerian boundary regions are created by de ning a surface, a boundary condition, or a load on theboundary of an adaptive mesh domain. On Eulerian boundary regions the mesh motion usually should

12.2.24


be constrained in the direction normal to the material motion; therefore, the surface mesh should be xedin space using spatial mesh constraints (described in !Meshconstraints," presented later in this section).Applying these constraints normal to an Eulerian boundary region allows material to ow into or outof the mesh, as in a uid ow problem, while allowing adaptive meshing to occur on the surface of theboundary region to maximize mesh quality.

The material owing into an Eulerian boundary region is assumed to have thesame properties asthe material that is inside the adaptive mesh domain.

Techniques for modeling Eulerian domains are presented in !Modeling techniques for Eulerianadaptive mesh domains in Abaqus/Explicit," Section 12.2.4.

Creation of boundary regions

Abaqus/Explicit will create adaptive mesh boundary regions automatically on

the exterior of a model, the boundary between different adaptive mesh domains, or the boundary between an adaptive mesh domain and a nonadaptive domain.

By default, a boundary region on the exterior of a model will be Lagrangian, so that the boundary regionfollows the material, and loads, boundary conditions, etc.will retain their Lagrangian interpretation. Aboundary region between different adaptive mesh domains isalways Lagrangian: no material can owthrough such a boundary region. An additional constraint isapplied when the model contains multipleparallel domains (see !Parallel execution in Abaqus/Explicit," Section 3.5.3). In this case the boundaryregion is nonadaptive: no material can ow through the boundary region, and the nodes on this boundaryare constrained to move exactly with the underlying material in all directions. A boundary region betweenan adaptive mesh domain and a nonadaptive domain is always nonadaptive. The only exception to thisoccurs if an Eulerian boundary region is de ned on the boundary between an adaptive mesh domainand a nonadaptive domain that comprises displacement-based in nite elements. In this case the nodeson the boundary behave as in Eulerian boundary regions (see the description under !Eulerian boundaryregions," presented earlier in this section), and the mesh motion at the boundary nodes can be constrainedusing spatial mesh constraints.

The boundary between two different materials can never ! ow" through the mesh; such a physicalboundary is always associated with a Lagrangian boundary region or a nonadaptive mesh boundary.

Figure 12.2.2$1 shows some boundary regions that will be created automatically byAbaqus/Explicit. In the model shown in this gure Abaqus/Explicit splits the user-de nedadaptive mesh domain into two adaptive mesh domains becausethe original domain is composed oftwo different materials.

In addition to the boundary regions created automatically by Abaqus/Explicit, Lagrangian, sliding,and Eulerian boundary regions can be created by the de nition of surfaces, boundary conditions, andloads, as described later in this section.

Geometric features

Many models include distinct geometric kinks that take the form of geometric edges or corners. It isusually not desirable to perform adaptive meshing across such geometric features unless they atten.

12.2.25


nonadaptivedomain

adaptive meshdomain

adaptive meshdomain

material 1

material 2

user-defined adaptive mesh domain: right half of box

nonadaptive boundary region

Lagrangian boundary region

Figure 12.2.21 Automatic splitting of mesh domains and creation of boundary regions.

Once a geometric feature does atten, it is usually best if the feature is deactivated so that adaptivemeshing will occur across it. This is especially true when adaptive mesh domains are subject to largedeformation.

The adaptive meshing algorithm in Abaqus/Explicit will respect geometric features on Lagrangianand sliding boundaries. In three dimensions geometric features consist of edges and corners (seeFigure 12.2.2$2), while in two dimensions they consist of only corners. If a geometric edge coincideswith the edge of a Lagrangian boundary region, the presence of the geometric feature has no effect onthe treatment of the edge: material cannot ow perpendicular to a Lagrangian edge.

Geometric features are not detected or tracked on Eulerian boundary regions because they generallyare not physically meaningful.

Output options are available for viewing the formation of geometric edges and corners%see !Outputand diagnostics for ALE adaptive meshing in Abaqus/Explicit," Section 12.2.5.

Controlling the detection of geometric edges and corners

Geometric features are identi ed initially as edges on boundary regions where the angle between thenormals on adjacent element faces is greater than the initial geometric feature angle, (

). See Figure 12.2.2$3. The default value for the initial geometric feature angle is .

12.2.26


z

x

y

geometric corner

Lagrangian corner plusgeometric corner

geometric edge

Lagrangian edge

z-symmetry

y-symmetry

x-symmetry

crack front

Figure 12.2.22 Geometric features formed on a solid block with a crack.

n nn nq > qI

Initial mesh with a geometric feature: no mesh flow is permitted past the corner.

qq qT

The geometric featureis deactivated duringsimulation.

Figure 12.2.23 Detection and deactivation of geometric features.

You can change the value of the angle that will be used to recognize geometric features. Settingwill ensure that no geometric edges or corners are formed on the boundary of the adaptive

mesh domain.

Input File Usage: *ADAPTIVE MESH CONTROLS, NAME=name,INITIAL FEATURE ANGLE=

12.2.27


Abaqus/CAE Usage: Step module:Other : ALE Adaptive Mesh Controls : Create :Name: name, Initial feature angle:

Controlling the deactivation of geometric edges and corner s

Geometric features affect only Lagrangian and sliding boundary regions, where they act as temporaryLagrangian edges. During each mesh sweep in an adaptive meshincrement, nodes along a geometricedge are positioned by applying the basic smoothing methods (see ALE adaptive meshing andremapping in Abaqus/Explicit,! Section 12.2.3). The nodesare constrained to lie along the discretegeometric edge unless the angle forming the geometric edge becomes less than the transition geometricfeature angle, ( ). The default value for the transition feature angle is .If the angle across the geometric edge becomes less than, the boundary surface is considered to be attened suf ciently for the feature to be deactivated, and the mesh is allowed to slide freely over thematerial (unconstrained by the deactivated geometric edge). Geometric corners are allowed to attenin a similar fashion. This logic allows great exibility in mesh adaptation while preserving geometricfeatures in the model.

You can change the transition feature angle. Setting will ensure that no geometric edgesor corners are ever deactivated.

Input File Usage: *ADAPTIVE MESH CONTROLS, NAME=name,TRANSITION FEATURE ANGLE=

Abaqus/CAE Usage: Step module:Other : ALE Adaptive Mesh Controls : Create :Name: name, Transition feature angle:

Mesh constraints

In most adaptive mesh problems the motion of nodes in the meshis determined by the meshing algorithm,with constraints imposed by the domain boundary and the boundary region edges. However, there arecases when you must explicitly de ne the motion of the nodes. As explained earlier, Eulerian and slidingboundary regions generally require mesh constraints for the regions to be physically meaningful. Insome problems you may wish to keep certain nodes xed, to move nodes in a particular direction, or toforce certain nodes to move with the material. In other problems you may desire a node or particularset of nodes to follow the material motion. Adaptive mesh constraints allow full control over the meshmovement and act independently of any boundary conditions or loads applied to the underlying material.

Applying spatial mesh constraints

Use a spatial mesh constraint (the default) to prescribe spatial mesh motion that is independent of thematerial motion. You specify the nodes to which the constraint is applied, the directions of the prescribedmotion, and the amplitude of the prescribed motion. You can prescribe either a displacement or a velocityfor the spatial mesh motion.

Input File Usage: Use the following option to de ne the mesh constraints explicitly:

*ADAPTIVE MESH CONSTRAINT, CONSTRAINT TYPE=SPATIAL,TYPE=DISPLACEMENT or VELOCITY

12.2.28


Abaqus/CAE Usage: To de ne the mesh constraints explicitly:

Step module:Other : ALE Adaptive Mesh Constraint : Create : Typesfor selected step: Displacement/Rotation or Velocity/Angular velocity :select region:Motion: Independent of underlying material

Rules for applying spatial mesh constraints

Spatial mesh constraints can be applied without restriction to nodes on an Eulerian boundary region orin the interior of an adaptive mesh domain.

In both two and three dimensions nodes at Lagrangian and active geometric corners are fullyconstrained to move with the underlying material. No mesh constraints can be applied at such corners.

Adaptive mesh constraints must not con ict with other mesh constraints inherent to Lagrangianand sliding boundary regions; therefore, adaptive mesh constraints can be applied only tangentially toa Lagrangian or sliding boundary region. This restriction implies that adaptive mesh constraints canbe applied only in two directions in a three-dimensional boundary region, in one direction in a two-dimensional boundary region, or in one direction on a Lagrangian or active geometric edge. It maynot always be feasible to adhere to this rule, particularly if the boundary experiences nite rotation.Therefore, if the normal to a boundary region is not perpendicular to a prescribed mesh constraint at anode, it is always moved along the current surface of the boundary region so that the projection of themesh motion in the direction of the prescribed constraint iscorrect (see Figure 12.2.2"4).

If the normal to the boundary region approaches the direction of the applied mesh constraint, largemesh motions will be required to satisfy the constraint. By default, an analysis is terminated if the anglebetween the normal to the boundary region and the direction of the prescribed constraint becomes lessthan . This cutoff angle is referred to as the mesh constraint angle, and its default value is 60.

The mesh constraint angle, , is also used when adaptive mesh constraints are applied to nodesalong a Lagrangian or active geometric edge. Since independent mesh motion cannot be prescribedperpendicular to these edges, an analysis is terminated if the angle between the prescribed constraint andthe plane perpendicular to the edge falls below the speci ed mesh constraint angle.

You can change the value of the mesh constraint angle ( ). Setting isnot recommended because it may cause errors in determining the free surface geometry, especially forcurved surfaces.

Input File Usage: *ADAPTIVE MESH CONTROLS, MESH CONSTRAINT ANGLE=

Abaqus/CAE Usage: Step module:Other : ALE Adaptive Mesh Controls : Create :Mesh constraint angle:

Defining mesh constraints that vary with time

The prescribed magnitude of a nonzero mesh constraint can vary with time during a step according to anamplitude de nition (see Amplitude curves,! Section 33.1.2).

Input File Usage: Use both of the following options:

*AMPLITUDE, NAME=name*ADAPTIVE MESH CONSTRAINT, AMPLITUDE=name

12.2.29


1

2

3direction ofapplied constraint

Q

Q < Qc, analysis is terminated

t = t1n

y

4

5

t = t0

Q

n5

1

2

3

4boundaryregion

projection ofmesh motionin prescribed direction

x

movement of node 3without mesh constraint

motion of node 3 alongsurface to satisfy constraint

zero-displacement adaptive mesh constraint appliedat node 3 in direction 1

Figure 12.2.24 Enforcing a spatial mesh constraint.

Abaqus/CAE Usage: Step module:Other : ALE Adaptive Mesh Constraint : Create : Typesfor selected step: Displacement/Rotation or Velocity/Angularvelocity : select region:Motion: Independent of underlyingmaterial : Amplitude: amplitude

Applying spatial mesh constraints in local directions

Spatial mesh constraints are applied in local directions ifa local coordinate system is de ned at a node(see Transformed coordinate systems,! Section 2.1.5); otherwise, they are applied in global directions.

Applying Lagrangian mesh constraints

Lagrangian mesh constraints on a node are used to indicate that mesh smoothing should not be applied;i.e., the node must follow the material.

12.2.210


Input File Usage: *ADAPTIVE MESH CONSTRAINT,CONSTRAINT TYPE=LAGRANGIAN

Abaqus/CAE Usage: Step module:Other : ALE Adaptive Mesh Constraint : Create : Typesfor selected step: Displacement/Rotation or Velocity/Angular velocity :select region:Motion: Follow underlying material

Modifying ALE adaptive mesh constraints

By default, all adaptive mesh constraints de ned in the previous analysis step remain unchanged inthe subsequent step. You de ne the adaptive mesh constraints in effect for a given step relative to thepreexisting adaptive mesh constraints. At each new step theexisting adaptive mesh constraints can bemodi ed and additional adaptive mesh constraints can be speci ed.

Input File Usage: Use either of the following options to modify an existing adaptive meshconstraint or to specify an additional adaptive mesh constraint:

*ADAPTIVE MESH CONSTRAINT,*ADAPTIVE MESH CONSTRAINT, OP=MOD

Abaqus/CAE Usage: Step module:Other : ALE Adaptive Mesh Constraint : Manager :select the desired step and mesh constraint:Edit

Removing ALE adaptive mesh constraints

If you choose to remove any adaptive mesh constraint in a step, no adaptive mesh constraints will bepropagated from the previous step. Therefore, all adaptivemesh constraints that are in effect during thisstep must be respeci ed.

Input File Usage: Use the following option to remove all previously de ned adaptive meshconstraints and to specify new adaptive mesh constraints:

*ADAPTIVE MESH CONSTRAINT, OP=NEW

If the OP=NEW parameter is used on any*ADAPTIVE MESH CONSTRAINToption within a step, it must be used on all*ADAPTIVE MESHCONSTRAINT options in the step.

Abaqus/CAE Usage: Step module:Other : ALE Adaptive Mesh Constraint : Manager :select the desired step and mesh constraint:Deactivate

Initial conditions

There are no initial conditions speci c to adaptive meshing; initial conditions can be de ned in thesame way as in nonadaptive problems. If initial mesh sweeps are performed to smooth the mesh at thebeginning of a step (see ALE adaptive meshing and remappingin Abaqus/Explicit,! Section 12.2.3),all initial conditions (except temperatures and eld variables, which are discussed in Prede ned elds,!presented later in this section) are remapped to the new mesh. Initial temperatures are remapped duringadaptive meshing in an adiabatic analysis.

12.2.211


Initial conditions prescribed near an in ow Eulerian boundary region will affect the state of thematerial owing into the domain throughout the analysis. See Modeling techniques for Eulerianadaptive mesh domains in Abaqus/Explicit,! Section 12.2.4, for a discussion of the proper treatmentof in ow boundaries.

Defining surfaces on ALE adaptive mesh boundaries

When you de ne a surface on the boundary of an adaptive mesh domain (see Surfaces: overview,!Section 2.3.1), Abaqus creates a boundary region coinciding with the surface. By default, a slidingboundary region is created. You can choose to create a Lagrangian or Eulerian boundary region instead.

A surface de ned in the interior of an adaptive mesh domain will move independently of the material(unless constrained by mesh constraints).

Defining a sliding boundary region using a surface

By default, the boundary region created by a surface de nition will be sliding (the surface edge will slidefreely over the material).

Input File Usage: *SURFACE, REGION TYPE=SLIDING

Abaqus/CAE Usage: Boundary regions de ned using surfaces are not supported in Abaqus/CAE.

Defining a Lagrangian boundary region using a surface

To force the surface edge to follow the material, create a Lagrangian boundary region.

Input File Usage: *SURFACE, REGION TYPE=LAGRANGIAN


Defining an Eulerian boundary region using a surface

To decouple the surface from the material motion, create an Eulerian boundary region and apply spatialmesh constraints normal to the surface. If no mesh constraints are applied, the surface will behave likea sliding boundary region (no material will ow through the surface).

As an example, it is often assumed that there is no normal or shear stress in the material at the out owboundary of an Eulerian domain. This condition can be modeled by de ning an Eulerian boundaryregion using a surface and applying spatial mesh constraints perpendicular to the surface, as shown inFigure 12.2.2"5.

Input File Usage: *SURFACE, REGION TYPE=EULERIAN


Contact

Lagrangian and sliding boundary regions created using surfaces can be used in contact pairs; they havethe same meaning as surfaces de ned on nonadaptive regions. Since contact generally involves relativesliding between bodies, sliding boundary regions are typically appropriate for contact surfaces.

Surfaces de ned on Eulerian boundary regions cannot be used in contact pairs.

12.2.212


node set OUT

symmetry

free surface

Lagrangian boundaryregion (automatic)

Lagrangian boundaryregion (automatic)

flow

zero-displacement adaptive mesh constraintapplied to node set OUT in direction 1

Eulerian boundary region(defined using a surface)

Figure 12.2.25 Modeling the out ow boundary of an Eulerian adaptive mesh domain.

If the small-sliding formulation is used for a contact pair,all the nodes on both surfaces arenonadaptive (see De ning contact pairs in Abaqus/Explicit,! Section 35.5.1, and Contact formulationsfor contact pairs in Abaqus/Explicit,! Section 37.2.2). The nodes of an element-based surface ina no-separation contact pair are nonadaptive (see Contactpressure-overclosure relationships,!Section 36.1.2). All nodes in a general contact domain are nonadaptive (see De ning general contactinteractions in Abaqus/Explicit,! Section 35.4.1). Similarly, the nodes at which spot welds are de nedare nonadaptive (see Breakable bonds,! Section 36.1.9.)

Distributed loads

When a distributed pressure load is applied to the boundary of an adaptive mesh domain, Abaqus/Explicitcreates a boundary region that coincides with the area of theload application. The characteristics ofboundary regions created in this way are identical to those of boundary regions created by de ningsurfaces. If a pressure load is applied to a surface in the interior of an adaptive mesh domain, the nodeson the surface will move with the material in all directions (i.e., they will be nonadaptive).

Boundary regions created by different pressure loads may overlap. If pressure loads with thesame magnitude and amplitude de nition are applied to adjacent regions, the regions will be mergedinto a single boundary region to minimize the number of Lagrangian edges and corners formed (seeFigure 12.2.2"6).

If a nonuniform pressure is applied (for example, a pressurethat varies linearly over a surface) orif a pressure load is de ned in user subroutineVDLOAD, each element face or edge becomes a separateLagrangian boundary region. Since Lagrangian corners are formed where Lagrangian edges meet, all

12.2.213


LLL

L

S

If these distributed loadshave identical magnitudes and amplitude definitions, they will be combined into one Lagrangian boundary region.

Overlapping distributed loads result in three Lagrangian boundary regions.

L = Lagrangian boundary region created by pressure loadS = Sliding boundary region created by pressure load = Lagrangian corner

This node is adaptivebecause the slidingboundary region does not create a Lagrangian corner.

Figure 12.2.26 Applying distributed pressure loads to an adaptive mesh domain.

nodes will follow the material in every direction, and each region becomes nonadaptive. Likewise, if anonuniform body force is applied to an adaptive mesh domain,the domain is split into multiple domains,each with a uniform body force. If this splitting results in one-element domains, the region becomesnonadaptive.

Defining a Lagrangian boundary region with a pressure load

By default, the boundary region created to coincide with a pressure load will be Lagrangian. Pressureloads applied to Lagrangian regions are identical to pressure loads applied to nonadaptive regions, exceptthat the mesh can move inside the boundary region.

Input File Usage: *DLOAD, REGION TYPE=LAGRANGIAN

Abaqus/CAE Usage: Boundary regions de ned using pressure loads are not supported inAbaqus/CAE.

Defining a sliding boundary region with a pressure load

A pressure load can be applied to a sliding boundary region tosimulate a load that is xed in space whilematerial moves past it (see Figure 12.2.2"7). A sliding edgeis unconstrained in the direction tangentialto the boundary region; therefore, unless adaptive mesh constraints are applied, the area of the loadapplication will move according to the adaptive meshing algorithm, which is probably not physicallymeaningful.

To allow a pressure load to slide over the material, create a sliding boundary region.

Input File Usage: *DLOAD, REGION TYPE=SLIDING


12.2.214


flow

flow

flow

t = t1

t = t0

t = t1

P0

= sliding boundary region created by pressure load

= zero-displacement adaptive mesh constraints

applied to nodes 1 and 4 in direction 1

Lagrangianinterpretation

Spatial (sliding)interpretation1 4

Figure 12.2.27 Applying a sliding distributed pressure load to an adaptivemesh domain.

Defining an Eulerian boundary region with a pressure load

To decouple the area of pressure application from the material motion, create an Eulerian boundary regionand apply spatial mesh constraints normal to the surface. Ifno mesh constraints are applied, the meshwill behave like a sliding boundary region (no material will ow through the surface).

As an example, it is often assumed that a uniform ambient pressure exists at the out ow boundaryof an Eulerian domain. This condition can be modeled by de ning the pressure at an Eulerian boundaryregion using a distributed load and applying spatial mesh constraints perpendicular to the surface, asshown in Figure 12.2.2"8.

Input File Usage: *DLOAD, REGION TYPE=EULERIAN


Distributed surface fluxes and thermal conditions

In coupled thermal-stress analysis Abaqus/Explicit also creates boundary regions for distributed surface uxes, convective lm conditions, and radiation conditions. The rules governing boundary regions for

12.2.215


node set OUT

symmetry

free surface

flow

= Eulerian boundary region created by pressure load= zero-displacement adaptive mesh constraint applied to node set OUT in direction 1

y

x

Figure 12.2.28 Modeling an ambient pressure at the out owboundary of an Eulerian adaptive mesh domain.

these loads are identical to those discussed for distributed loads. The ability to specify the boundaryregion type is also the same.

Concentrated loads

When a concentrated load is applied to the boundary of an adaptive mesh domain, Abaqus/Explicitcreates a boundary region to coincide with the load. Every node to which a concentrated load is appliedwill be considered its own boundary region because it is not possible to identify a surface area associatedwith a concentrated load. However, you can control the behavior of each one-node region.

If concentrated loads are applied to nodes in the interior ofan adaptive mesh domain, those nodeswill move with the material in all directions (i.e., they will be nonadaptive).

Defining a Lagrangian boundary region with a concentrated l oad

By default, the boundary region created by a concentrated load will be Lagrangian. Each one-nodeLagrangian boundary region will follow the material in every direction (the nodes will be nonadaptive).

Input File Usage: *CLOAD, REGION TYPE=LAGRANGIAN

Abaqus/CAE Usage: Boundary regions de ned using concentrated loads are not supported inAbaqus/CAE.

Defining a sliding boundary region with a concentrated load

A concentrated load can be applied to a sliding boundary region to simulate a load that is xed in spacewhile material moves past it (see Figure 12.2.2"9). A sliding node is unconstrained in the direction

12.2.216


flow

flow

flow

zero-displacement adaptive meshconstraint applied to node N indirection 1

t = t0

t = t1

t = t1

F

F

F

N

N

N

Lagrangianinterpretation

Sliding interpretation

material slides past this node

y

x

Figure 12.2.29 Applying a concentrated sliding load to an adaptive mesh domain.

tangential to the boundary region; therefore, unless adaptive mesh constraints are applied, the point ofload application will move according to the adaptive meshing algorithm, which is probably not physicallymeaningful.

To allow the concentrated load to slide freely over the material, create a sliding boundary region.

Input File Usage: *CLOAD, REGION TYPE=SLIDING


Defining an Eulerian boundary region with a concentrated lo ad

To decouple the concentrated load from the material motion,create an Eulerian boundary region andapply spatial mesh constraints normal to the surface. If no mesh constraints are applied, each one-nodeboundary region will behave like a sliding boundary region.

Input File Usage: *CLOAD, REGION TYPE=EULERIAN

12.2.217



Concentrated fluxes and thermal conditions

In coupled thermal-stress analysis Abaqus/Explicit also creates boundary regions for concentrated heat uxes, lm conditions, and radiation conditions. The rules governing boundary regions for these loadsare identical to those discussed for concentrated loads. The ability to specify the boundary region typeis also the same.

Boundary conditions

Lagrangian, sliding, and Eulerian boundary regions can be created by applying kinematic constraints tothe boundary of an adaptive mesh domain. If kinematic boundary conditions are applied to nodes in theinterior of an adaptive mesh domain, those nodes will move with the material in all directions (i.e., theywill be nonadaptive), regardless of the speci ed boundary region type.

Defining a Lagrangian boundary region using a boundary cond ition

By default, the boundary region created by a kinematic boundary condition will be Lagrangian.Abaqus/Explicit will recognize surface-type and point or edge constraints automatically and will createan appropriate Lagrangian boundary region for each type, asexplained in the following subsections.

Input File Usage: *BOUNDARY, REGION TYPE=LAGRANGIAN

Abaqus/CAE Usage: Boundary regions de ned using boundary conditions are not supported inAbaqus/CAE.

Surface-type constraints applied using boundary conditions

Although boundary conditions are always applied to individual nodes in Abaqus/Explicit, they oftenrepresent physical constraints on surfaces. For example, symmetry conditions, where nodes areconstrained to move in a plane, are actually surface constraints. A fully clamped (ENCASTRE)condition along a boundary can also be considered a surface constraint. (During adaptive meshing it ismeaningful to allow nodes to move along a fully clamped edge.)

Abaqus/Explicit will examine an adaptive mesh boundary andtry to create regions that arecoincident with the applied boundary conditions. Currently, Abaqus/Explicit can create boundaryregions for surface-based constraints on:

# symmetry planes,# fully clamped planes, and# planes on which a uniform motion is prescribed.

Figure 12.2.2"2 shows an example in which boundary regions are created by applying surface-typeboundary conditions. This gure shows a block of material with a crack and three symmetryplanes(therefore, three Lagrangian boundary regions). Materialwill not ow across any symmetry plane, yet

12.2.218


adaptive meshing can be performed within each Lagrangian boundary region. This exibility is oftenhelpful in problems that have signi cant deformation.

Point or edge constraints applied using boundary conditions

Some boundary conditions represent point or edge constraints. For example, a displacement can beprescribed at a node. The boundary regions associated with such nodes are exactly the same as thosecreated by concentrated loads.

Defining a sliding boundary region using a boundary conditi on

A sliding boundary region associated with a boundary condition can move according to the adaptivemeshing algorithm. Since this behavior is probably not physically meaningful, the edges of a slidingboundary region are usually xed in the direction tangential to the surface using adaptive meshconstraints. This approach can be used, for example, to simulate frictionless contact between a rigidpunch and a deformable body, as shown in Figure 12.2.2"10.

sym

met

ry

node set CONTACT

N

sym

met

ry

N

(a) effect of punch modeled with contact

=

zero-displacement adaptive mesh constraint applied tonode N in direction 1

sliding boundary region created by velocity-type boundarycondition applied to node set CONTACT

(b) effect of punch modeled with boundary conditions applied to sliding boundary region

material flows past node N

V

y

x

Figure 12.2.210 Contact simulation using a sliding boundary region.

In this example the punch is replaced by a sliding boundary region with a constant velocity boundarycondition applied in the area of contact.! A tangential mesh constraint is applied to the edge ofthe boundary region at node N (the other edge is constrained by the Lagrangian boundary regioncreated automatically on the symmetry plane). This problemde nition allows material to ow radiallyunderneath the punch! while retaining the original size and location of the contact! area.

Abaqus/Explicit makes no distinction between surface-type constraints and point or edge constraintsfor sliding boundary regions.

To allow the boundary condition to slide freely over the material, create a sliding boundary region.

12.2.219


Input File Usage: *BOUNDARY, REGION TYPE=SLIDING


Defining an Eulerian boundary region using a boundary condi tion

To decouple the boundary region from the material motion, create an Eulerian boundary region and applyspatial mesh constraints normal to the surface. If no mesh constraints are applied, the mesh will behavelike a sliding boundary region (no material will ow through the surface).

As an example, the mass ow rate at an Eulerian in ow boundary can be prescribed by de ning anEulerian boundary region using a boundary condition.

Abaqus/Explicit makes no distinction between surface-type constraints and point or edge constraintsfor Eulerian boundary regions.

Input File Usage: *BOUNDARY, REGION TYPE=EULERIAN


Overlapping boundary regions

A Lagrangian boundary region can overlap any number of otherLagrangian or sliding boundaryregions (see Figure 12.2.2"11). If two boundary regions partially overlap, three regions are formed: theoverlapping region and the two initial regions minus the overlapping region. A sliding boundary regionis formed when a Lagrangian and a sliding boundary region overlap.

An Eulerian boundary region can never overlap a Lagrangian or sliding boundary region.Furthermore, an Eulerian boundary region can never share a boundary with or overlap a nonadaptiveregion. Because in nite elements are nonadaptive, this latter restriction implies that in nite elementscannot be used to simulate ambient conditions at an out ow boundary.

Coincident edges

Edges shared by different types of boundary regions are subject to the following rules:

# An edge shared between a Lagrangian and a sliding boundary region will be Lagrangian.# An edge shared between a Lagrangian and an Eulerian boundaryregion will be sliding.# An edge shared between a Lagrangian and a nonadaptive boundary region will be nonadaptive.# An edge shared between a sliding and a nonadaptive boundary region will be nonadaptive.# An edge of an Eulerian boundary region can never be coincident with an edge of a nonadaptive

region.

Predefined fields

There are no restrictions on applying prescribed temperatures or eld variables in an adaptive meshdomain, but these nodal values are not remapped when adaptive meshing is performed. Therefore,prede ned elds that are not spatially uniform may not be meaningful within an adaptive mesh domain.

12.2.220


L

L

L

S

S S

L

E

L = Lagrangian boundary regionS = Sliding boundary regionE = Eulerian boundary region

Lagrangian edgeSliding edgeLagrangian corner

Figure 12.2.211 Overlapping boundary regions.

(Time-varying, spatially uniform prede ned elds are acceptable, since adaptive meshing is applied atdiscrete instances in time.) However, if temperature or eld variable data are collected from a spatialframe of reference, it may make physical sense to apply a spatially varying eld for an Eulerian domainin which the mesh does not move. Abaqus/Explicit does not perform any checks or calculations onprede ned elds for adaptive meshing; you must ensure that the prede ned elds are meaningful.

Materials

All material models and behaviors, except brittle cracking( Cracking model for concrete,!Section 23.6.2), fabric ( Fabric material behavior,! Section 23.4.1), and low-density foam( Low-density foams,! Section 22.9.1) materials, can be used in an adaptive mesh domain.

For domains modeled with hyperelastic or hyperfoam materials the usefulness of adaptive meshingis limited. The recommended enhanced hourglass method ( Section controls,! Section 27.1.4), whichwill generally predict a much better return to the original con guration for these materials when loading isremoved, cannot be used in an adaptive mesh domain. Therefore, for hyperelastic or hyperfoam materialsit is recommended that the analysis be run without adaptive meshing but with enhanced hourglass control.

If the porous failure model ( Failure criteria in Abaqus/Explicit! in Porous metal plasticity,!Section 23.2.9), shear failure model ( Shear failure model! in Dynamic failure models,! Section 23.2.8),tensile failure model ( Tensile failure model! in Dynamicfailure models,! Section 23.2.8), or one ofthe progressive damage models (Chapter 24, Progressive Damage and Failure!) is speci ed withinan adaptive mesh domain, Abaqus/Explicit will continuously monitor the status of elements whileperforming adaptive meshing. When elements within the domain fail, the nodes along the interface

12.2.221


between the failed and unfailed elements will become nonadaptive. This has the effect of creating amaterial boundary between the failed and unfailed zones.

When failure occurs in elements that use the shear failure, the tensile failure, or the progressivedamage models without element deletion, elements in the failure zone will not be deleted; they can carrysome states of stress. Adaptive meshing will occur within the failure zone but not along the interfacewith the unfailed material.

Elements

An adaptive mesh domain can contain only rst-order, reduced-integration, solid elements. Allelements within an adaptive mesh domain must have the same geometry (all two-dimensional,three-dimensional, axisymmetric, or plane strain, etc.).Since adaptive mesh domains are split acrosselement types, degenerate elements should be used for mixeddomains that include both triangles andquadrilaterals (or tetrahedron and bricks). All elements other than rst-order, reduced-integration, solidelements$including mass, rotary inertia, and in nite elements$are nonadaptive. These elements canbe connected to an adaptive mesh domain, but their nodes are nonadaptive. All nodes and elements ona rigid body are nonadaptive. Rebar are not supported withinan adaptive mesh domain.

Multi-point constraints and equations

As with boundary conditions, multi-point constraints ( General multi-point constraints,! Section 34.2.2)and equations ( Linear constraint equations,! Section 34.2.1) are always applied to nodes but sometimesrepresent constraints on surfaces. Abaqus/Explicit will recognize surface-type constraints when thefollowing conditions are satis ed:

# an equation, PIN MPC, or TIE MPC ties a node set to a single node; and# all the nodes involved in the MPC or equation are coplanar andlie within the boundary region.

If these conditions are satis ed, a boundary region will be associated with the node set in the MPC orequation. If the MPC is applied within a Lagrangian or sliding boundary region, a Lagrangian edge willbe created. If the MPC is applied within an Eulerian boundaryregion, no edge will be created. If theabove conditions are not satis ed, all nodes connected to the MPC or equation will be nonadaptive.

As an example, a constraint can be applied to force a plane section to remain plane in a Lagrangianadaptive mesh domain, as shown in Figure 12.2.2"12(a). In this case all nodes are constrained by anequation to lie in the same plane throughout the analysis, but adaptive meshing is allowed within theplane.

As another example, consider the out ow boundary of an Eulerian domain, as shown inFigure 12.2.2"12(b). The out ow boundary of an Eulerian domain is often assumed to be far enoughdownstream that the velocity is uniform but unknown. To model this condition, an Eulerian boundaryregion is created at the out ow boundary using a surface. An adaptive mesh constraint is used to x themesh perpendicular to the boundary, and all nodes on the plane are constrained by an equation to havethe same velocity orthogonal to the plane.

For surface-based tie constraints (see Mesh tie constraints,! Section 34.3.1), all nodes on the tiedsurfaces will be nonadaptive.

12.2.222


element setOUTFLOW

node set OUTFLOW

sym

met

ry

materialflow

zero-displacement adaptive mesh constraintsapplied to node 1 and to node set OUTFLOWin direction 1

1

node set PLANELagrangianboundaryregion

Linear constraint equation1.0u 1.0u = 0

Linear constraint equation1.0u 1.0u = 0

(a) Using an equation to force a plane section to remain a plane.

(b) Using an equation to prescribe a uniform velocity outflow condition.

1

y

x

y

x

Eulerian boundary region created using a surface defined on theS4 faces of element set OUTFLOW

PLANE

1 1

1

OUTFLOW

1 1

1

Figure 12.2.212 Using equations with adaptive meshing.

Procedures

During an adiabatic analysis temperatures will be remappedproperly in adaptive mesh domains.Adaptive meshing is not used during annealing procedures orduring geometrically linear analyses.

12.2.223


The de nitions of adaptive mesh domains, boundary regions, mesh constraints, and controls (asexplained in ALE adaptive meshing and remapping in Abaqus/Explicit,! Section 12.2.3) will propagatefrom step to step.

User subroutines

Solution-dependent state variables de ned in user subroutineVUMATwill be remapped to the new meshwhen adaptive meshing is performed.

Solution-dependent state variables that are de ned on a slave surface in user subroutinesVFRIC,VUINTER, VFRICTION, andVUINTERACTIONwill not be remapped to the new mesh when adaptivemeshing is performed. Therefore, to ensure physically meaningful results, a Lagrangian adaptive meshconstraint should be used for nodes on the contact slave surfaces with solution-dependent state variableswhere the contact constraint is de ned using these user subroutines.

Output

Since the mesh is no longer constrained to the material when adaptive meshing is performed, output atelements and nodes must be interpreted differently than in apure Lagrangian problem. See Output anddiagnostics for ALE adaptive meshing in Abaqus/Explicit,!Section 12.2.5, for details.

Input file template

To create a Lagrangian adaptive mesh domain:

* HEADING

* ELSET, ELSET=ADAPT************************** STEP* DYNAMIC, EXPLICITData line to specify the time period of the step* ADAPTIVE MESH, ELSET=ADAPT...* END STEP

To create an Eulerian adaptive mesh domain with a prescribedvelocity in ow condition and a prescribedpressure out ow condition (both in the globalx-direction):

* HEADING...* ELSET, ELSET=ADAPT...* ELSET, ELSET=OUT...* NSET, NSET=INFLOW...

12.2.224


* NSET, NSET=OUTFLOW...* SURFACE, NAME=INSURF, REGION TYPE=EULERIANData lines to de ne the surface* SURFACE, NAME=OUTSURF, REGION TYPE=EULERIANData lines to de ne the surface...* EQUATIONData lines specifying uniform velocity at the in ow************************** STEP* DYNAMIC, EXPLICITData line to specify the time period of the step* ADAPTIVE MESH, ELSET=ADAPT* ADAPTIVE MESH CONSTRAINT

INFLOW, 1, 1, 0OUTFLOW, 1, 1, 0

* BOUNDARY, TYPE=VELOCITY, REGION TYPE=EULERIANINFLOW, 1, 1, 10.0

* DLOAD, REGION TYPE=EULERIANOUT, P2, 15.0

...* END STEP

12.2.225

ALE ADAPTIVE MESHING AND REMAPPING IN Abaqus/Explicit

12.2.3 ALE ADAPTIVE MESHING AND REMAPPING IN Abaqus/Explic it

Products: Abaqus/Explicit Abaqus/CAE

References

!ALE adaptive meshing: overview," Section 12.2.1 !De ning ALE adaptive mesh domains in Abaqus/Explicit," Section 12.2.2 !Output and diagnostics for ALE adaptive meshing in Abaqus/Explicit," Section 12.2.5 *ADAPTIVE MESH *ADAPTIVE MESH CONSTRAINT *ADAPTIVE MESH CONTROLS !Customizing ALE adaptive meshing," Section 14.14 of the Abaqus/CAE User#s Manual, in the

online HTML version of this manual

Overview

ALE adaptive meshing consists of two fundamental tasks:

creating a new mesh, and remapping solution variables from the old mesh to the new mesh with a process called advection.

The success of the adaptive meshing technique depends on thechoice of the methods used for each ofthese tasks. The default methods for creating a new mesh and for remapping solution variables have beenchosen carefully to work for a wide variety of problems. However, you may wish to override the defaultchoices to balance the robustness and ef ciency of adaptive meshing or to extend the use of adaptivemeshing to more dif cult or unusual applications.

Meshing

A new mesh:

is created at a speci ed frequency for each adaptive domain; is found by sweeping iteratively over the adaptive mesh domain and moving nodes to smooth the

mesh; and

can retain the initial gradation of the original mesh.

Remapping

The methods used for advecting solution variables to the newmesh:

are consistent, monotonic, and (by default) accurate to thesecond order; and conserve mass, momentum, and energy.

12.2.31


Controlling the frequency of ALE adaptive meshing

In most cases the frequency of adaptive meshing is the parameter that most affects the mesh quality andthe computational ef ciency of adaptive meshing. A typical adaptive mesh application without Eulerianboundaries will require adaptive meshing every 5$100 increments. In contrast, adaptive meshing shouldgenerally be performed much more frequently in a steady-state process simulation using Eulerianboundaries. Thus, if a spatial adaptive mesh constraint or an Eulerian boundary region is de ned on anadaptive mesh domain, the default frequency is 1; otherwise, the default frequency is 10.

Input File Usage: Use the following option to change the frequency of adaptivemeshing:

*ADAPTIVE MESH, FREQUENCY=number of increments

Abaqus/CAE Usage: Step module:Other : ALE Adaptive Mesh Domain : Edit : toggle onUsethe ALE adaptive mesh domain below , Frequency: number of increments

Controlling the intensity of ALE adaptive meshing

During each adaptive meshing increment, the new mesh is created by performing one or more meshsweeps and then advecting the solution variables to the new mesh.

Mesh sweeps

In an adaptive meshing increment, a new, smoother mesh is created by sweeping iteratively over theadaptive mesh domain. During each mesh sweep, nodes in the domain are relocated%based on thecurrent positions of neighboring nodes and elements%to reduce element distortion. In a typical sweepa node is moved a fraction of the characteristic length of anyelement surrounding the node. Increasingthe number of sweeps increases the intensity of adaptive meshing in each adaptive meshing increment.The default number of mesh sweeps is one.

Input File Usage: Use the following option to change the number of mesh sweeps to be performedin each adaptive mesh increment:

*ADAPTIVE MESH, MESH SWEEPS=number of sweeps

Abaqus/CAE Usage: Step module:Other : ALE Adaptive Mesh Domain : Edit : toggleon Use the ALE adaptive mesh domain below , Remeshingsweeps per increment: number of sweeps

Advection sweeps

The process of mapping solution variables from an old mesh toa new mesh is referred to as an advectionsweep. At least one advection sweep is performed in every adaptive mesh increment. Ideally, anadvection sweep will be performed only once, after all mesh sweeps for the increment are complete.However, numerical stability of the advection sweep is maintained only if the difference between theold mesh and the new mesh is small. Therefore, if after a mesh sweep the total accumulated movementof any node in the domain is greater than 50& of the characteristic length of any adjacent element, anadvection sweep is performed to remap the solution variables from the old mesh to the intermediate

12.2.32


mesh. Mesh sweeps will continue until the speci ed number is reached or until the movement of anynode again exceeds the 50& threshold. At this time an advection sweep is performed again to mapvariables from the last intermediate mesh to the new intermediate mesh. The cycle will continue untilthe number of mesh sweeps reaches the speci ed number.

The number of advection sweeps per adaptive mesh increment required for each adaptive meshdomain is determined automatically by Abaqus/Explicit; you cannot override this automatic calculation.The number of advection sweeps is printed by default to the message (.msg ) le (see !Output anddiagnostics for ALE adaptive meshing in Abaqus/Explicit,"Section 12.2.5).

The computational cost of ALE adaptive meshing

The cost of adaptive meshing depends on the frequency of remeshing, the number of mesh and advectionsweeps performed, and the size of the adaptive mesh domains.When compared to a purely Lagrangiananalysis, additional computational cost is incurred only within adaptive mesh increments.

Generally, the cost of one advection sweep is several times greater than the cost of one mesh sweep.Multiple advection sweeps are triggered when adaptive meshing is performed too infrequently and/ora high number of mesh sweeps is speci ed. Performing adaptive meshing more frequently and doing1$5 mesh sweeps in each adaptive mesh increment will usuallygenerate only one advection sweep,minimizing the computational cost.

The relatively smooth mesh and improved element aspect ratios that result from adaptive meshingmay increase the stable time increment compared to a similarpure Lagrangian analysis. In some casesthis increase can offset the cost of adaptive meshing completely.

Although computational cost can vary greatly with the type of application, performing adaptivemeshing on the entire problem domain in every increment willtypically increase the cost of the analysisby 3$5 times that of a similar Lagrangian analysis. De ning adaptive mesh domains that cover only afraction of the entire problem domain will reduce the cost proportionally. Changing the frequency toevery 10$25 increments will result in CPU times that are onlymoderately higher than those for a pureLagrangian analysis.

Guidelines for controlling ALE adaptive meshing frequency and intensity

Although the default values work well for many problems, dif cult analyses may require a more frequentadaptive meshing frequency or meshing with a higher intensity.

Guidelines for transient analysis

For problems without spatial adaptive mesh constraints or Eulerian boundary regions, the defaultfrequency for adaptive meshing is 10, and the default numberof mesh sweeps is 1. The defaultvalues are usually adequate for low- to moderate-rate dynamic problems and for quasi-static processsimulations undergoing moderate deformation. If the frequency or number of mesh sweeps is toolow, excess element distortion may cause the analysis to terminate before the mesh is adapted; or,if a solution can be obtained, it may not be as accurate as the solution that could be obtained with ahigher quality mesh. In virtually all cases, however, performing adaptive meshing at any frequency will

12.2.33


reduce the distortion of elements (and, thus, improve the quality of the solution) compared to a pureLagrangian analysis.

For high-rate impact problems undergoing large amounts of deformation, it may be necessary toincrease the frequency of adaptive meshing or the number of mesh sweeps. It is generally less expensiveto increase the number of mesh sweeps slightly before increasing the frequency, as long as the numberof advection sweeps remains small.

For problems involving explosions taking place over just a few hundred increments, adaptivemeshing is usually required at every increment. It may also be necessary to increase the frequency ofadaptive meshing for quasi-static process simulations that involve large amounts of ow per increment.

For problems in which the deformation per increment is small, a high-quality mesh can bemaintained by performing adaptive meshing only every 25$100 increments. For these problems theadditional cost of adaptive meshing is negligible.

Guidelines for steady-state analysis

When an adaptive mesh domain contains Eulerian boundary regions or has spatial adaptive meshconstraints, the default frequency of adaptive meshing is 1. This default frequency is conservative andis chosen primarily because spatial mesh constraints are applied only during adaptive mesh increments.Thus, between adaptive mesh increments the mesh may drift from its prescribed location, which mayaffect the solution. However, drift from adaptive mesh constraints will always be eliminated in the nextadaptive mesh increment: it will not accumulate.

For problems in which the speed of deformation or the speed ofmaterial ow from element toelement is much less than the material wave speed, the frequency typically can be increased to 5 orhigher. This class of problems includes most steady-state process simulations, where the drift of themesh from the prescri

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