RADIOSS for Impact Analysis

Copyright © 2008 Altair Engineering, Inc. All rights reserved. Altair Proprietary and Confidential Information

RADIOSS IMPACT INTRODUCTION

Introduction to Explicit and Large

Displacement Analysis

Rev.: May 2009


Radioss Basic Training Schedule

8:30 - 8:45 Introduction

8:45 – 9:15 RADIOSS Tools + Process Example

9:15 - 9:30 Break

9:30 – 10:30 Elements

10:30 – 11:00 Hands on Twisted Beam

11:00 – 11:30 Common Features

11:30 – 12:30 Lunch

12:30 – 1:00 Time Step Control

1:00 – 1:30 Time Step Demo with an Example

1:30 - 2:15 Materials

2:15 - 2:30 Break

2:30 - 3:15 Hands on Tensile Test

3:15 – 3:45 Interfaces

3:45 - 4:30 Hands on Boxtube


Chapter 1: RADIOSS Introduction

Application Fields

Modeling A Physical Problem

Formulations

Time Integration

Explicit and Implicit Method


Structural Mechanics

Fluid-Structure interaction

Material characterization

Application Fields


Stamping Safety

Composite shell

Application Fields


Computational Fluid Dynamics

Computational Aero Acoustics

Noise Vibration Harshness

Centrifugal Fan Noise

Centrifugal Fan Noise

Application Fields


1. Geometry (Physical model)

• 1D, 2D or 3D ? [ Beam, Shell or Solid ?

2. Physical laws (conservation)

• Physical laws (conservation)

• Mass conservation

• Energy conservation

• Momentum conservation (equilibrium)

3. Formulation:

• Choice of time and space discretizations

• Lagrangian

• Eulerian

• Arbitrary Lagrangian Eulerian (ALE)

4. Space Discretization:

• Finite Element (FE)

5. Time Integration:

• Newmark schemeExplicit formulation

Implicit formulation

simple form + Central Difference Method

Modeling A Physical Problem


How to combine time and space discretization?

1. Lagrangian Formulation (Structural Analysis)

• The mesh points coincide with the material points

• Elements are deformed with material

• Element deformation = Material deformation

2. Eulerian Formulation (CFD - fluid)

• Nodes fixed in space, Material goes through the mesh

• Fixed nodes a No degradation of mesh in large deformation problems

3. ALE: Arbitrary Lagrangian Eulerian Formulation (Impact - missile)

• Between two previous formulations

• Internal nodes move to minimize element distortion

Formulations


Formulations

Fluid flow for three kinds of formulations


Newmark scheme

Time Integration

Explicit formulation

Implicit formulation

simple form + Central Difference Method

ttn-1 tn

tn+1

2

1nx

2

1nx

1nxnx1nx

nx

txxx nnn

21

21

txxxnnn

211

xn+1 is obtained with a precision 2t


Explicit Flow Chart

Time integration

ttt

extF •Loop over elements

i

j

j

iij

x

v

x

v

2

1

)( ijij f

tttt ijijij

•Assemble hrgFF ,intcontF

iii mFv

intF

txxx nnn

21

21

txxxnnn

211


Implicit Newmark Flow Chart

CMK ,, Form

000 ,, Initialize UUU

1..7i a det. then , t,Select i

; ;1

;2 ;1

;1 ;

; ;

76

254

21

31

2

11

0 2

tata

aa

aa

aa

t

t

tt

CMKK 10ˆ Form aa

TLDLKK ˆ:ˆ izeTriangular

UUUCUUUMRR tttttttttt

541320 aaa aaa ˆ

Rtttt ˆ Solve ULDLT

UUUU

UUUUU

tttttt

ttttttt

aa

aaa

76

320


Velocity

Non Linearity

Static Dynamic

Rupture

Damage

Buckling

Plasticity

Elasticity

Explicit

Explicit 1 Implicit

Implicit


Complexity

Cost (CPU)

Static / Elastic Nonlinear Dynamic

Implicit

Explicit

Explicit 1 Implicit


Explicit Implicit(-) Conditional stability (+) Always stable

(-) Small (+) Large

(+) Precision (+) Precision

(+) [M]-1 (diagonal matrix) (-) ([M]+ [K])-1 (non diagonal)

(+) Low memory (10 MW) (-) High memory (6000 MW)

(+) Dynamic and Shock problems (+) Dynamic and Static problems

(+) « Element-by-Element » method

• Local treatment

(-) Global resolution

•Need of convergence at each step

(+) High Robustness

• High and Coupled nonlinearities

(-) Low Robustness

• Null pivots, Divergence, …

(+) Relatively low cost

• « Low » CPU, « Low » Memory

(-) Too expensive

• High CPU, High Memory

ctt

t )( s t )(ms

2t

2t

Advantages / Disadvantages


Chapter 2: RADIOSS Tools

RADIOSS Tools

Pre-Processor HyperMesh and HyperCrash

RADIOSS Solver (Start and Engine)

Pos-Processor HyperView and HyperGraph

RADIOSS Files


Access Radioss from HyperWorks 10.0 Suite:

Radioss Tools

Launch Radioss

Radioss Manuals


Pre-Processor - HyperMesh


HyperCrash

Databases

. properties

. materials

• RADIOSS Input (fixed/block)

• NASTRAN Format

• Universal Format (IDEAS)

• Ls-Dyna Format

• Pam 2G Format

• RADIOSS 4.1 block and Fixed Formats

• RADIOSS 4.1, 4.4 & 51 Block Formats

• Nastran Format

• Universal Format (Ideas)

• Ls-Dyna Format

•Pam 2G Format

Create / Modify a RADIOSS

model from a FE mesh

Pre-Processor - HyperCrash

• RADIOSS 4.1 block and Fixed Formats

• RADIOSS 4.1, 4.4 & 51 Block Formats

• Nastran Format

• Universal Format (Ideas)

• Ls-Dyna Format

•Pam 2G Format


HyperCrash

Quality

MenuModel Checker

Menu

Connection

Menu

Mesh Editing

Menu

Loadcase

Menu

Safety

Menu

Pre-Processor - HyperCrash


ENGINE

_0000.rad / D00

_0000.out / L00

_0000.rst / R00

_0001.rst / R01

_0001.out / L01 A01-Ann T01

_0001.rad / D01

Input Deck (ASCII)

Listing File (ASCII)

Restart File (BINARY)

Restart File (BINARY)Engine File (ASCII)

Listing File

(ASCII)

Animation File

(Binary)TH File (Binary)

Processor – RADIOSS Computation

STARTER


• Checks consistency of the model

• Gives you warning and errors

• Generates R00 file for engine

Listing File (ASCII)Restart File (BINARY)

Input Deck (ASCII)

STARTER

RADIOSS Starter

_0000.rad / D00

_0000.rst / R00 _0000.out / L00


• Generates output files (Annn Tnnn)

• Details the computation (Lnn)

• Generates Rnn file for restart

Restart File

(Binary)

TH File

(Binary)

_0001.rst / R01

ENGINE

Restart File (Binary)Engine File (ASCII)

Listing File

(ASCII)

Animation File

(Binary)

T01 A001-Annn 0001.out / L01

_0000.rst / R00

RADIOSS Engine

_0001.rad / D00


• Reads animations (Annn)

• Displays selected variables (Von Mises Stress, Plastic

Strains, etc.

Post-Processor–HyperView


• Reads Time history (Tnn)

• Plots selected variables (Energies, Nodal, Element, and etc.)

Post-Processor – HyperGraph


File Description Read by Written by Format

_0000.rad

D00 (V4) Input RADIOSS File

Starter/ HyperMesh

HyperCrash

HyperMesh

HyperCrashASCII

_0001.rad

D01 (V4) Engine input Engine

HyperCrash

/Text EditorASCII

_000n.out

L00, Lnn (V4)List files Text Editor Starter/Engine ASCII

_000n.rst

R00, Rnn (V4)Restart files Engine Starter/Engine

Binary

(by default)

Annn Animation files HyperView Engine Binary

Tnn Time history file HyperGraph EngineBinary

(by default)

RADIOSS Files


Exercise 2.1: First run with Radioss


Chapter 3: Elements

Stress/Strain

Hourglass

Element Library (Solid, Shell, Beam, Truss, Spring, etc.)

Element Capabilities


Stress/Strain - Definitions

• Logarithmic TRUE STRAIN tensor

• Cauchy TRUE STRESS tensor

engtruel

l1lnln

0

engengtrue 1


• Usually used for small deformation simulations :

• Linear elastic studies

• Usually not used for crash analysis

• Sometimes used to resolve some special numerical problems :

• Large mesh distortion due to large deformations

• Decrease of time step due to decrease of element length

• Negative volume of brick elements due to large deformation

Stress/Strain – Small strain option


• Under Integrated Elements (1 IP)

• Efficiency

• Constant Stress over Elements

• Hourglass mode exists

• Zero energy deformation

• Strain and stress are zero

1 2

X

Y34

IP

0xd 0xx 0xx

8 Nodes SOLID

4 Nodes SHELL

Hourglass Formulation


• Additional internal forces are required to maintain the

deformation stability of the element

• Resistance forces [ Generate an ARTIFICIAL energy

f1f21 2

X

Y

f3f4 34

IP

Hourglass - Control


• 12 translational modes:

• 3 rigid body modes (1, 2, 9)

• 6 deformation modes (3, 4, 5, 6, 10, 11)

• 3 hourglass modes (7, 8, 12)

• 12 rotational modes:

• 4 out of plane rotation modes (1 [ 4)

• 2 deformation modes (5, 6)

• 2 rigid body or deformation modes (7, 8)

• 4 hourglass modes (9 [ 12)

Hourglass – Shell Modes


• 4 modes for each directions:

• 12 hourglass modes for a brick element

Hourglass – Brick Modes


• For the Model: HE/IE < 10%

• Plot Global Hourglass for the model in HyperGraph

• For each Subset/Part: HE/IE < 10%

• Select PARTS for Output in the D00 file

• Plot Hourglass for selected Parts in HyperGraph

• Check Hourglass with HyperView

• Add the command below in the Engine file

• /ANIM/ELEM/HOURG

• Display Hourglass contour over Elements

Hourglass - Checking


3D – Solid - Hexahedron

• A simple Brick element:

• 8 nodes with Linear interpolation

• Integration :

• Reduced [ 1 POINT (DEFAULT)

• Full [ 8 POINT

• Characteristic length

•

s

t

r

1 2

65

34

78

areafacelargest

Volumelc


Put nodes of the same edge together to obtain other shapes

Use of a normal

tetra element is

recommended

Degenerated Solid Elements


• Element symmetry must be respected

• Not recommended elements:

Not Rec’d Element Degenerations


3D – Solid - Tetrahedron

• 4 nodes solid tetrahedron

• Linear shape functions

• Integration:

• 1 POINT

• No HOURGLASS

• Shear Locking

• Low convergence


• aalc 816.03

2


3D – Solid - Tetrahedron

• 10 nodes solid tetrahedron

• Quadratic shape functions

• Integration :

• 4 POINTS

• No HOURGLASS

• Low time step

• No shear locking

• High convergence


.0 ac

2al 2646

5

a


Quadratic 4 nodes tetra element

• Quadratic 4 nodes tetra element

• 4 nodes tetra element with enriched nodal variables (6 DOF per each node)

• 4 integration points

• Displacement of the dummy nodes is computed on the basis of rotational DOF

• Advantages

• High time step versus 10 nodes tetra element with same accuraccy

• Shear locking effect low or negligible (it may appear in bending)

• Compatibility with shells


• Other solid elements:

• HA8: 8 node linear brick with variable integration schemes from 2x2x2 to 9x9x9

• HEPH: 8 node linear brick with 1 integration point , Elastic-plastic physical stabilization method

• BRICK20: 20 node quadratic brick with reduced 2x2x2 or full 3x3x3 integration schemes

• SHELL16 : Thick shell element

1 2

3

5

6

78

9

10

1314

1517

18

19

20

4 1112

1 2

356

78

9

1013

14

15

16

3D – Other Elements


• Isolid: Solid & Hourglass formulations

• Default = 0 [ 1 IP

• 12 [ 8 IP

• 24 [ HEPH

• Ismstr: Small Strain control

• Default = 0 [ Large Strain

• 1 [ Small Strain from t = 0

• 2 [ Small Strain if criteria

reached

3D – Solid Control Card


• Bushings

• Inserts

• Barriers

• Bumpers

• Dummies

• Seat

3D – Solid - Applications


2D – Shell Q4 Formulations

• Crashworthiness simulations: Over 90% shell elements BT

• Four Node Quadrilateral Elements (Q4)

• Belytshko & Tsay (BT) formulation (DEFAULT)

• 1 Integration Point [ Hourglass

• Unphysical Hourglass Control

• QEPH

• 1 Integration Point [ Hourglass

• Physical Hourglass Control

• BATOZ

• 4 Integration Point [ No hourglass


2D – Shell Q4 - BT

• 1 Integration point over the surface

• Low cost elements to save CPU time

• Four non-coplanar nodes

• Normal constant over the element

(without curvature)

• The local z axis is the vector product of two element diagonals

• For warped surfaces [ precision m

• Drawbacks: Hourglassing, flat element and cannot couple

bending & membrane behavior

z

N1

N2

N3

N4

4231 NNNNze

4231 NNNN


2D – Shell Q4 - QEPH

• Four-node curved element

• Four independent normals at nodes

• Hourglass physical Stabilization

N1

N2

N3

N4n1

n2

n3

n4


• Fully Integrated Elements: 4 Gauss point over the element

• More Expensive Today 3*CPU cost

• Variable Stress over Elements

• No Hourglass

X

Y

IP IP

IP IP

1 2

34

0xd 0xx 0xx

2D – Shell Q4 - Batoz


• BT

• Use of Q4BT (Belytschko Tsay) : robust, CPU cost effective

• Popular + Compatible + Cannot couple bending-membrane behavior

• Best choice for coarse mesh

• QEPH

• 15% CPU > BT + Sensitive to mesh quality + Avoid hourglassing

• Good trade off quality/cost

• BATOZ

• No Hourglass + Good curvature + Couples bending-membrane

behavior

• Best choice for fine mesh

2D – Shell Q4 - Conclusion


2D – Shell Q3 – C0

• Q3

• A flat facet element

• No HOURGLASS

• Too stiff

• Degenerated Q4 (Not Recommended)

• Q4 [ T3

• Non homogenous mass

• distribution

m/4m/4

m/4m/4

x

y

z


2D- Shell Q3 – DKT18

• DKT18: Batoz Triangle:

• Three in-plane integration points with Hammer scheme

• No hourglass

• Good bending behavior but high cost element

• Globally, twice more expensive than C0 element

x

y

z


• Global Integration (DEFAULT)

• Average value is computed

• Bad strain/stress computation for the bending out of plane

• Integration Points

• From 1 to 5

• 1 IP gives no out of plane stiffness

• Use 5 for a good accuracyz

N1

N2

N3

N4

2D – IP Through Thickness


• Iterative algorithm:

• Use Newton-Raphson method

• CPU k, precision k

• Two methods :

• Radial return (IPLAS = 2)

• Iterative algorithm (IPLAS = 1)

• Radial return:

• CPU m, precision m

Iterative Plasticity

Iplast = 1

Plastically Admissible Stresses


• By default Radioss considers a constant thickness through the

element:

• Ithick = 0

• To take the thickness changes into account :

• Ithick = 1

Thickness Changes

Ithick = 1

Thickness Variation


• Ishell: Shell & Hourglass

• formulations

• Default = 0 [ BT

• 4 [ BT with improved Hourglass

• 12 [ BATOZ

• 24 [ QEPH

• Ismstr: Small Strain control

• Default=0 [ Large Strain

• 1 [ Small Strain from t = 0

• 2 [ Small Strain if criteria

reached

2D – Shell Control Card


Manufacturing Automotive

2D – Shell - Applications


1D – Beam Element

• A standard Euler-Bernouilli beam

• Element with three nodes

• Third node to define the orientation of the cross-section

L

x

yz

1

2

3

y

z

1, 2 3


1D – Beam Element

• Beam inputs:

• A : cross section area

• Ix : moment of inertia of cross section about local x axis

• Iy : moment of inertia of cross section about local y axis

• Iz : moment of inertia of cross section about local z axis

• Recommendations:

• Time Step:

AL 44 10121.0 AIIA zy

100/01.0 zy II )(2)(5.0 zyxzy IIIII

)3/,12/1,4min(5.0 BBa

cLat Ecwith

),max(/2zy IIALB


1D – Beam Control Card


1D – Truss Element

• A standard two node element

• Material law:

• Type 1 : Linear Elastic

• Type 2 : Elastic Plastic

• Property set:

• A : Cross section area

• Time Step:

N1 N2

c

tLt

)(L(t) : Current Truss length

Ec


• Suspensions, Supports …

1D – Beam/Truss–Applications


• Type 4

• Spring with 1 d.o.f.

• Type 8

• Mathematical spring

• Type 12

• Pulley type

• Type 13

• Beam type

1D – Springs


+

=

• Simple physical spring with a dashpot

•

• 1 d.o.f spring:

• Tension-Compression behavior

• The nodal forces are always collinear

• Time step is depending on the spring

mass, its stiffness and its damping

•

M

CCKMdt

2

xckxF

1D – Spring Type 4


1D – Spring Type 8, 12, 13

• Type 8:

• Mathematical def. having 6 DOF’s total; L > 0

• Not enough DOF’s to represent Rigid Body Motion

• Global momentum not respected

• Type 12:

• 3 Nodes to define pulley

• Deformable rope with friction at node 2

• Sliding is locked when node 1 or 3 touches node 2

• Type 13:

• Works like a Beam element (bending & shear coupled); L > 0

• 12 DOF’s to represent Rigid Body Motion

• 3 nodes, 2 to define axis of spring and 3rd for local frame


Linear Spring Non linear Elastic Spring H=0 Non linear Elastic-Plastic Spring

With Isotropic Hardening H=1

Non Linear Elastic-Plastic Spring

With uncoupled hardening H=2


With kinematic hardening H=4


With nonlinear unloading H=5

F

F

0l

F

0l

resid

F

0l

F

0l

F

0l

f2

f1

0l

1D – Spring Property Set


F

dtd /

• Dashpot behavior

• Multidirectional Failure Criteria

DX

D

Y

Dyp

Dyn

DxpDxn

1D – Spring Property


1D – Spring Control Card


• Joints

• Rivets

• Spotwelds

• Pretension

• Retractors

• …

1D – Spring Applications


Fixed format number Description Keywords

0 Void element TYPE0, VOID

1 Shell element TYPE1, SHELL

2 Truss element TYPE2, TRUS

3 Beam element TYPE3, BEAM

4 Spring element TYPE4, SPRING

5 Old rivet TYPE5, RIVET

6 Orthotropic solid element TYPE6, SOL_ORTH

8 General spring element TYPE8, SPR_GENE

9 Orthotropic shell element TYPE9, SH_ORTH

10 Composite shell element TYPE10, SH_COMP

11 Sandwich shell element TYPE11, SH_SANDW

12 3 nodes spring element TYPE12, SPR_PUL

13 Beam type spring element TYPE13, SPR_BEAM

14 General solid element TYPE14, SOLID

PROPERTY SET LIST

Element Compatibility


MATERIAL LAWS DESCRIPTION

Law Type Description

34 BOLTZMAN Viscoelastic Boltzman

25 COMPSH Elastic plastic orthotropic Composite shell

14 COMPSO Elastic plastic orthotropic Composite material

24 CONC Elastic plastic brittle Reinforced concrete

22 DAMA Elastic plastic Ductile damage

21 DPRAG Elastic plastic Drücker-Prager Law for rock or concrete, hydrodynamic behaviour is given by a function

1 ELAST Elastic Linear elastic model

19 FABRI Shell orthotropic Linear elastic orthotropic

33 FOAM_PLASTIC Viscous plastic Closed cell, elasto-plastic foam

35 FOAM_VISCOUS Viscous elastic Generalized Kelvin-Voigt

32 HILL Elastic plastic orthotropic Hill’s model

43 HILL_TAB Elastic plastic orthotropic Tabulated Hill model

28 HONEYCOMB Orthotropic Honeycomb material

4 HYD_JCOOK Johnson Cook Strain rate and temperature dependent yield stress

6 HYD_VIS Hydrodynamic Viscous Turbulent viscous flow

3 HYDPLA Elastic plastic hydrodynamic Von Mises isotropic hardening, polynomial pressure

40 KELVINMAXWELL Viscous elastic Generalized Maxwell - Kelvin law

10 LAW10 Elastic plastic Drücker-Prager Law for rock or concrete, hydrodynamic behaviour is polynomial

23 LAW23 Elastic plastic Ductile damage

42 OGDEN Hyperelastic Ogden - Mooney-Rivlin

27 PLAS_BRIT Elastic plastic brittle Brittle shell (aluminum, glass)

2 PLAS_JOHNS Elasto plastic (Johnson Cook) Von Mises isotropic hardening

36 PLAS_TAB Elastic plastic Piecewise linear

2 PLAS_ZERIL Elastic plastic (Zerilli-Armstrong) Von Mises isotropic hardening

29 USER1 User’s

30 USER2 User’s

31 USER3 User’s

38 VISC_TAB Viscous elastic Foam (Tabulated law)

0 VOID Void material Fictitious



Law 2D QUAD 3D BRICK SHELL TRUSS BEAM

34 BOLTZMAN yes yes

25 COMPSH yes

14 COMPSO yes yes

24 CONC yes yes

22 DAMA yes yes yes

21 DPRAG yes yes

1 ELAST yes yes yes yes yes

19 FABRI yes

33 FOAM_PLASTIC yes yes

35 FOAM_VISCOUS yes yes yes

32 HILL yes

43 HILL_TAB yes

28 HONEYCOMB yes yes

4 HYD_JCOOK yes yes

6 HYD_VIS yes yes

3 HYDPLA yes yes

40 KELVINMAXWELL yes yes

10 LAW10 yes yes

23 LAW23 yes yes

42 OGDEN yes yes

27 PLAS_BRIT yes

2 PLAS_JOHNS yes yes yes yes yes

36 PLAS_TAB yes yes yes

2 PLAS_ZERIL yes yes yes

29 USER1 yes yes yes



38 VISC_TAB yes yes

0 VOID yes yes

ELEMENT COMPATIBILITY



Exercise 3.1: Hands on Twisted Beam


Chapter 4: Common Features

Interfaces

Rigid Bodies

Monitored Volumes

Boundary Conditions

Loads

General Features


• The interfaces solve the contact between two parts

• Different kinds of interfaces exist depending on the contact

Surface 2

Surface 1

Interfaces


• Four kinds of rigid walls are available

• Infinite plane

• Cylindrical rigid wall

• Spherical rigid wall

• Parallelogram

• Each wall can be fixed or moving

• A rigid wall is defined by a Master Node and a group of slave

Nodes

• The group of Slave Nodes is defined by an explicit list

and/or by a “distance for slave search”

• A rigid wall is a Kinematic Condition

Rigid Wall


Diameter

M

Slave Nodes

M1M0

Plane Rigid Wall

SphericalM

M1 Cylindrical

Slave Nodes

Rigid Wall


• A Rigid Body is an underformable structure

• A Rigid Body is defined with a set of slave nodes and a

master node

• A kinematic condition is applied on each node and for all

directions

• By default, the master node is moved to the center of mass

Input master node

localization

Rigid body center of mass

Rigid Body


Rigid Parts (Undeformable parts, walls

engine, battey) Connections between Parts

Rigid Body


• Simulate a volume of gas or fluid

• Requirement

• The surface defined must be closed

• The shell normal must be oriented outward the volume

• Only 3 or 4 shell elements sets

• 5 types of monitored volume

• Type 3 for tire and fuel tank

• For simple unfolded airbag use monitored volume type 4

• For chambered airbag use type 5

Monitored Volumes


Tire

Tank

Airbag

Deploying

Monitored Volumes


• A boundary condition is a constraint on node degrees of

freedom

• A boundary condition is a kinematic condition

• 6 degrees of freedom :

• X translation

• Y translation

• Z translation

• X rotation

• Y rotation

• Z rotation

#-BOUNDARY CONDITION:

#--1---|---2---|---3---|---4---|---5---|

/BCS/1

boundary_condition

#trarot nskew gr_node

101 110 0 1004

# BCS NODE GROUP

/GRNOD/NODE/1004

group_of_nodes

207

#--1---|---2---|---3---|---4---|---5---|

Boundary Conditions


• Initial velocity: defined by a value in each direction and a

group of nodes

• Imposed velocity: defined by a function, a direction and a

group of nodes

• Imposed displacement (Block only): same as Imposed Velocity

Velocity & Imposed Displacements


Concentrated load Pressure load

Gravity load

F P

g

Loads & Gravity


• An added Mass is a mass which is added on a group of

nodes

• The mass is equally divided among the nodes in the group

or is added to each node of the list

#-ADDED MASS:

#--1---|---2---|---3---|---4---|---5---|

/ADMAS/1/1

BOAT

#- Mass| Node|

0.5 1000

/GRNOD/NODE/1000/

ADDED MASS

207

Added Masses


• SKEW FRAMES are used to define local directions

• Two types of skew frames are available in RADIOSS

• Fixed skew frame

• Moving skew frame

Moving skew frame (defining by 3 nodes)

Ys

Zs

Xs

Fixed skew frame

Skew Frames


• A section is a cut in the structure where forces and

moments will be stored in TH files

• A section is defined by a group of element, a group of nodes

and a skew defined by three nodes

Sections


Chapter 5: Time Step Control

Critical Time Step

Stability Condition

Characteristic length of elements

Time Step Control in Radioss

Hints and Remarks


• Explicit Scheme:

• Conditionally stable

• If Stable scheme

• Unstable case:

• If information passes across more than one element per time step

• Stability Condition depends on two factors:

• Size of the smallest element [ Numerical

• Sound propagation speed [ Physical

criticaltt

Fext(t)L

Stability of Time Integration


• Courant’s stability condition


• It depends on the shape of the element:

c

lt c c : Speed of sound in the material

lc : Characteristic element length

l

lcl cl

l

l

lD

DAlclc = 0.707 l lc = 0.866 l

Courant’s Stability Condition


• In principle, no need of user intervention (automatic)

• The time step is calculated using two methods:

• Element time step

• Nodal time step

• The time step is influenced by existence of interfaces

• Interface time step

Time Step Control in Radioss


Element Time Step Control

• For the smallest element, the following relation must be

verified:

• Scale Factor:

• To ensure the stability

• To introduce the nonlinearity in Courant’s condition

• Particular cases:

• One element mesh [ Sf = 0.1

• Foams (high nonlinearity) [ Sf = 0.67

c

lSt fe Where Sf is the Scale Factor

[ et[ [

c

E

ce

llt


Nodal Time Step Control

• For any node, the following relation must be verified:

• For a regular mesh:

• For an irregular mesh (generally):

m : nodal mass

k : equivalent stiffness of nodek

mtn

2

en tt

en tt


• The interface time step depends on the type of interface

used:

• Type 2:

• Just a kinematic condition [ No need of time step condition

• Types 3, 4, 5 and 8:

• A small stiffness is used [ Stable with Sf = 0.9 or less

• Types 7, 10 and 11:

• A variable stiffness is used

• May be large enough compared to element stiffness

[ A stability condition must be established

k

mti

2

Interface Time Step


RADIOSS Input for Time Step Control

Time Step Control in Engine (0001.rad) file

/DT

Tsca Tmin

/DT/BRICK

/DT/SHELL

/DT/QUAD [ Element Time Step Control

/DT/SH_3N

/DT/BEAM

…

/DT/INTER [ Interface Time Step Control

/DT/NODA [ Activate Nodal Time Step Control

[ Larger Time Step for non-optimized mesh


• /DT/Keyword2

Tsca Tmin

Keyword 2: Brick, Quad, Shell, Sh3n, Truss, Beam, Spring, Airbag, Inter, Noda

• /DT/Keyword2/Keyword3

Tsca Tmin

Keyword 2: Stop, Del, Cst

• Delete Option

/DT/BRICK/DEL

/DT/SHELL/DEL

…

/DT/INTER/DEL

• DEL option [ Mass / Volume is lost [ Change of the physics

To delete Elements where mintte

To remove nodes from interface where mintti



• Constant Option:

/DT/NODA/CST

/DT/INTER/CST

• To apply a constant time step

• Radioss adds mass to the model to satisfy the nodal stability condition

• Increase of kinetic energy

• The added mass should be checked by user to ensure the validity of

results

/DT/BRICK/CST

/DT/SHELL/CST

• Switch an element to small strain formulation [ time step is then

independent of the size of the element



• Many time step options influence the results:

• Keep the numerical model close to the physical problem

• Small Time Step for:

• Stiff material: [

• Light material: [

• Small element: [

• For mild steel:

• Remove details to save CPU time

• More than 1 Million elements are needed to mesh a complete car

model with 5x5mm2 elements

E

l

t

t

t

(For crash problems)

With E

e

l

c

lt

Characteristic length

for elementsmml 5min

smc /5000

st 1

Remarks on Time Step Control


• Default values:

• Scale factor = 0.9

• Minimum time step = 0

• By default if te < tmin :

• Radioss deletes the shell element which control the time step

• Radioss stops calculation if a brick element control the time step

• The /DT/INTER concerns only the interface type 7

Remarks on Time Step Control


• Take a simple Tensile Test model

• Case 1: Run it with Natural Time Step (No Time Step Commands)

• Time Step is 2.164E-4

• Total Number of Cycles = 55467 Cycles

• Case 2: Add Command:

/DT/NODA

0.9 0

• Time Step = 2.2521E-4

• Total Number of Cycles = 53291 Cycles

• This proves that Nodal Time Step > Element Time Step

• Case 3: Add Command:

/DT/NODA/CST

0.9 3E-4

• Time Step = 3E-4 Must be input after reviewing Nodal Time Step in Starter Listing File

• Total Number of Cycles = 40001 Cycles with 2.19% Added Mass 28% Faster Computation

• This explains why we add mass to the models For Faster Computation Time

• In Dynamic Analysis, it’s recommended not to add more that 2% Mass

Demo of Time Step Control in RADIOSS


Exercise 5.1: Time Step Demo with an Example


Chapter 6: Materials

Material Laws

Failure Models

Law 2 - Johnson-Cook and Zerilli-Armstrong

Law 27 - Elastic-Plastic Brittle

Law 28 - Honeycomb

Law 36 - Elastic-Plastic Tab.


Material Laws In RADIOSS

Type Description Model Law (MID)

Isotropic

Elasticity

Linear elastic model Hook (1)

Hyper elastic Ogden-Mooney-Rivlin (42)

Composite

and

Orthotropic

materials

Linear elastic for orthotropic shells Fabric (19)

Nonlinear pseudo-plastic orthotropic

solids without strain rate effect

Honeycomb (28)

Nonlinear pseudo-plastic orthotropic

solids with strain rate effect

Crushable foam (50)

Elastic-plastic orthotropic shells

Hill (32)

Hill (tabulated) (43)

Elastic-plastic orthotropic composites

Composite Shell (25)

Composite Shell with

Chang-Chang failure

(15)

Composite Solids (14), (53)




Elastic-

plasticity of

Isotropic

Materials

von Mises hardening

without damage

Johnson-Cook (2)

Zerilli-Armstrong (2)

Zhao (48)

Cowper-Symonds (44)

Piecewise linear (36)

Drucker-Prager for rock or concrete (10), (21)

von Mises hardening

with brittle damage

Aluminum, glass, etc. (27)

Predit rivets (54)

Reinforced concrete (24)

von Mises hardening

with ductile damage

Ductile damage for solids and shells (22)

Ductile damage for solids (23)

von Mises with

viscoplastic flow

Ductile damage for porous materials,

Gurson

(52)




Viscous

Materials

Visco-elastic

Boltzmann (34)

Generalized Kelvin-Voigt (35)

Tabulated law (38)

Generalized Maxwell-Kelvin (40)

Visco-plastic Closed cell, elasto-plastic

foam

(33)

Hydrodynamic

Strain rate and temperature

dependence on yield stress

Johnson-Cook (4)

Turbulent viscous flow Hydrodynamic viscous (6)

Elastio-plastic hydrodynamic von Mises isotropic

hardening with polynomial

pressure

(3)

Elastio-plastic hydrodynamic with

thermal softening

Steinberg-Guinan (49)

Void Void material Fictitious (0)


Failure Models In RADIOSS

• Independent and can be coupled with compatible material laws

• /FAIL/TYPE/MAT_ID


• Law 2: Elastic Plastic Isotropic (Von Mises)

• Law 27: Elastic Plastic Brittle

• Law 28: Honeycomb Material

• Law 36: Elastic Plastic Isotropic Piecewise Linear

Materials discussed in this class


• Elastic for stresses lower than the yield stress

• Plastic when the stress reaches the yield stress

• Available for brick, shell, beam and truss elements

• Two plasticity models:

• Johnson-Cook

• Zerilli Armstrong

Material Law 2: Elastic-Plastic


Stress-Strain relation:

)1)(ln1)(( *

0

mnp Tcba

Influence of temperature change

Influence of strain rate

Influence of plastic strain

p

a

b

= Stress level

= Plastic strain

= Yield stress

= Hardening modulus

n = Hardening Exponent

c = Strain rate coefficient

0= Strain rate

= Reference strain rate

Material Law 2: Johnson-Cook


Stress-Strain relation:

Influence of temperature change and strain rate

Influence of plastic strain

p

= Stress level

= Plastic strain

C0 = Yield stress

n = Hardening Exponent

0

= Strain rate

= Reference strain rate

npCTCTCCC 54310

0lnexp

Material Law 2: Zerilli-Armstrong


• Element rupture if the plastic strain is larger than max

• For shell elements:

• Ruptured element is deleted

• For solid elements:

• Deviatoric stress tensor is set to zero

• The element is not deleted

Material Law 2: Element Rupture


Layer crackingCrack orientation

1

2

• Only for shell elements

• The isotropic elastic-plastic computation and modeling is the same as for law 2

• Law allows material damage and brittle failure

• Glass, aluminium, …

• Brittle failure is modeled by the introduction of a crack

• Crack throughout the element thickness for type 1 elements (regular shell)

• Crack in the layer that the material is applied for type 11 elements (composite shell with variable layers)

Material Law 27: Elastic-Plastic Brittle


• Damage effected material

• Nominal and effective stress:

• Linear damage:

• Linear stress:

t1 = Tensile rupture strain in direction 1

m1 = Maximum strain in direction 1

dmax1 = Maximum damage in direction 1

f1 = Maximum strain for element

deletion in direction 1

y

E

pt t m

Linear damage

Linear stress

deffn 1 d : damage factor 0 < d < 1

tm

td

p

t

tm

mE

Material Law 27: Damage Model


• Typical honeycomb, crushable foams

• Only for solid elements

• Two drawbacks:

• No viscous effect

• Plastic behavior

• Material behaves as three independent membrane spring:

• Hook’s law

• For an isotropic material

s

t

r

1

5

2

6

34

78

31

23

12

33

22

11

31

23

12

33

22

11

31

23

12

33

22

11

00000

00000

00000

00000

00000

00000

G

G

G

E

E

E

332211 EEE 231231211E

GGGand

Material Law 28: Honeycomb


• Plasticity is represented by independent stress-strain curves

• Material behavior is always orthotropic

• The input yield stress is always positive

• Volumic strain or strain dependent yield curve (user’s choice)

• The failure plastic strain is input for each direction

• If the failure strain is reached in one direction, the element is deleted

User defined

yield curve ij

ij

10

ijor

Material Law 28: Honeycomb


• Isotropic elastic-plastic material

• User defined function for the stress-strain curve

• Available for brick and shell elements

• Elastic portion of material stress-strain curve defined by

Young modulus and Poisson’s ratio

• Material plasticity curves can be given for an arbitrary

number of strain rates

• Linear interpolation of strain-stress curve

• For a given strain rate

• For a given plastic strain011

p

Mat. Law 36: Elastic-Plastic Tab.


Exercise 6.1: Hands on Tensile Test


Chapter 7: Interfaces

Contact Interfaces in Radioss

Contact Treatment

Contact Modeling

Description of commonly used Interfaces


For beams, bars or springs

Edge-to-edge impact (7+11)Impact between two lines11

Tied After impact with or without

reboundLike type 7 but with a tied contact10

Good contact at all speedsGeneral purpose contact impact between 2

parts7

User defined contactContact between two rigid bodies6

Not recommended anymoreContact for a single part4

Use of type 7 is recommendedContact between 2 parts3 & 5

Change of mesh density (solid)Tied interface, No sliding2

Fluid structure interactionFor Radioss ALE1 & 9

CommentsDescriptionType

Interfaces in RADIOSS


Radioss/Madymo CouplingEllipsoidal surfaces to segments contact15

Radioss/Madymo CouplingEllipsoidal surfaces to nodes contact14

ALE or Euler or Lag.Connects 2 fluid meshes with free, tied or

periodic options12

CommentsDescriptionType

Fluid-structure inetractionsCEL Lagrange / Euler interface18

Meshes with 8- or 16-node thick-

shell or 20 bricks

Contact between nodes to quadratic shape

solids and solid-shells or between quadratic

shapes

16 / 17

Interfaces in RADIOSS

19 Slave and Master Surfaces Combination of Type 7 and

Type11

21 Rigid master surface/slave surface Fast interface for Stamping


• The interfaces solve the contact between several parts of the

model

• Contact modeling:

• Type 7:

• Node-to-surface contact

• Symmetric Node-to-Surface contact

• Self-contact Node-to-Surface

• Generalized Node-to-Surface contact

• Type 11:

• Edge-to-Edge contact

• Contact treatment:

• Kinematic master-slave formulation

• Penalty method

Contact Modeling & Treatment


The velocity and displacement of the slave nodes are

controlled by the master segments in order to satisfy the

kinematic contact conditions

Slave nodes

Master surface

Nodes-to-Surface Contact


• The nodes of each surface are treated as slaves

• Each surface is treated as a master surface

Slave + Master

Slave + Master

Symmetric Nodes-to-Surface


Self-contact of a single surface due to buckling ...

Slave node + Master surface

Self-contact Nodes-to-Surface


• A node may be master and slave at the same time

• Slave nodes may belong to different surfaces

Slave Nodes

Master nodes

Master surface

Generalized Nodes-to-Surface


Limitation of Nodes-to-surface


For contacts between beams, bars, springs or the edges of

shells

Edge-to-Edge Contact


• Penalty method:

• A spring is added between a slave node and a master segment

• Each contact is treated as an element

• The kinematic continuities are not directly respected

• The energy conservation is verified

• The stiffness of the spring is very important

• Too stiff [ Numerical instabilities

• Too flexible[ Large penetration, kinematic discontinuity

Vm VsMm Ms

Interface Spring

Contact treatment in RADIOSS


• Type 2: Tied interface

• Type 7: General contact

• Type 11: Edge-to-Edge interface

Interfaces discussed in this class


• Tied interface is a kinematic condition

• Applications:

• To connect a fine and a coarse solid lagrangian mesh

• To connect spring elements to shell surfaces for spotweld or rivet

modeling

Shell elements (master segments)

Spotwelds modeled by spring elements (slave nodes)

Type 2: Tied Interface


• Tied interface formulation:

• Masses and forces of the slave nodes are added to the master

nodes

• Accelerations and velocities of the master nodes are computed with

the added masses and added forces

• Kinematic constrains are applied to all slave nodes in order to keep

them on the initial position with respect to their master segments

Type 2: Tied Interface


• For all types of impact between a set of nodes and a master

surface

• A node can impact on several master segments

• A node can impact on the edge of a master segment

• Direct search of the closest segment

• No search limitation

• Only edge-to-edge contacts are not solved

• Possible to put a slave node on the master surface

• Impact is possible on the two sides of segments

• Variable interface stiffness is used to avoid penetration larger than

gap

• A time step is computed to insure the stability

Interface Type 7


Type 7: Search Algorithm

Fast Sorting Method


• A gap is used to:

• Give a physical thickness to the

surface

• Allows to distinguish the

impacts on the top or the lower

part from the facet

• The contact is activated if:

• The node penetrates inside the

gap

• Distance Between Node to

Surface < Gape

P

Master gap

Type 7: Detection of Penetration


• Physical value for constant Gap:

• GAP = 1/2 (thickness1+thickness2)

• Default value for GAPmin (used if no constant gap is given)

• GAPmin= min (lmin/10 , t , l/2)

• lmin : the smallest side length of the master brick element

• l : the side length of the element brick

• t : thickness of the master shell

e1

e2

Type 7: Constant Gap


• Possible to use a different gap value for each interface segment

• The gap is computed for each impact as:

• Gap = Gapm+ Gaps (m: master s: slave)

• Gapm= ½ shell thickness or zero for brick elements

• Gaps = ½ largest thickness of the elements connected to the slave node

• or zero for a node connected to a brick or spring elements

• or ½ (beam cross-section)1/2 for beam elements

• If the slave node is connected to multiple elements, the largest Gaps is

used

• The minimum value of Gap is given by Gapmin as it is explained

previously

Type 7: Variable Gap


F

)(5.0pg

gsEtKCPKF s

dt

dps

Where E and t are the young modulus and the

thickness of the master surface

S is a scale factor (1 by default)

Type 7: Penalty Force


Type 7: Time Step

• A kinematic time step is applied to prevent large penetrations

• If dp/dt > 0

• For a crash problem:

• The nodal time step is computed as following:

p

g-pg

With

ssmm

mmt 100

)/5000(2

1

dtdp

pgt

/5.0

K

Mt

2elementsInterface KKK


• Initial penetration is not allowed for interface type 7

• The node is deactivated from interface when:

• node to element mid-plane distance is smaller than 10-10*Gap

• For self impacting surfaces, use the following recommended

value:

• Gap < (smallest segment edge) / 2

• For impact between stiff and soft materials the stiffness

factor has to be adjusted

• S = Eslave*Thickslave / Emaster*Thickmaster

Type 7: Hints and Remarks


Contacts between a soft and a rigid part (foam/steel or

tire/structure)

Rigid Soft

SlaveMaster

K1=Eslave / Emaster K2 = Eslave / Emaster = 1 / K1

2 interfaces

Rigid Soft

MasterSlave



• Deep penetrations are not tolerated

• Deep penetration leads to:

• high penalty forces

• small time step

• infinite loop message

• large contact force vectors in post-processing

• Deep penetrations are caused by:

• Initial penetrations of adjacent plates

• Edge impacts

• Full local collapse

• Rigid body impact on another rigid body or on fixed nodes or on very stiff part

• Impact between heavy stiff structures

• High impact speed

• Small gap



• Time step reduces for high speed impacts or small gaps

• To avoid time step problems:

• Increase gap, but check if no initial penetration is resulted

• Increase stiffness factor STFAC

• Some ENGINE options can be used but attention should be paid to

the quality of results:

• /DT/INTER/DEL

• Some nodes will be allowed to pass through the impacted surface

• /DT/INTER/CST

• Nodal masses will be modified to maintain a constant time step



• Initial penetrations:

• are generally due to the discretization

• result in high initial contact forces

• should be avoided

• Remedies:

• Modify node coordinates

• Reduce gap

• For small penetrations

• Deactivate node stiffness

• Simple approach

• Option used after geometry adjustments

Initial penetration



• Simulates impacts between two

lines

• Lines: Beams, Bars, Springs, Edge

of shell elements

• Works as the interface type 7:

• Penalty formulation

• Same search method

• In association with interface type

7, the edge-to-edge impacts can

be simulated

Interface Type 11


Exercise 7.1: Hands on Boxtube

RADIOSS for Impact Analysis

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Transcript of RADIOSS for Impact Analysis