Explicit Dynamics With LS-DYNA

Maurício Michelon Bernard Patury 08.08.09

September 2013

 Introduction;

 Comparison of explicit and implicit time integration;

 Time step control;

 Program execution syntax;

 Description of keyword input;

 Element library;  Hourglass control;  Material models;  Boundary conditions;  Initial conditions;  Loads;  Sets;  Contacts;  Rigid bodies;  Damping;  Output control;  Restart;  Static prestress;  Units;

 Recommendation for control settings.

Introduction

Introduction

• Explicit Finite Element Program:

• This means: FEM-Program with explicit time integration.

• This also means: only transient dynamic analysis are possible.

• There is also an implicit part in LS-DYNA (several things already possible, but still under development):

• Implicit static.

• Implicit transient dynamics.

• Modal analyses (determination of eigen frequencies and eigen modes). • Structural analyses are main field of application:

• Coupling with temperature dependent problems possible.

• Also fluid-structure interaction (FSI) with eulerian formulation possible (e.g. aquaplaning, airbag inflation, tank sloshing).

• Topic of this training is 3D structural analyses with explicit time integration.

What is LS-DYNA:

Introduction

• LS-DYNA is developed by LSTC (Livermore Software Technology Corporation) and has its roots in DYNA3D/2D from LLNL (Lawrence Livermore National Laboratories); both are and have been developed by Dr. John Hallquist.

• LS-DYNA is a pure solver, therefore needs an input file in a specific format and produces results in form of binary and ASCII data.

• Input file is generated using a pre processor, e.g. LS-PrePost, FEMB, ANSA, ANSYS/LS-DYNA (Classic or LS-DYNA Export), EASi-Crash, FEMAP, HyperMesh, Medina, Oasys Primer, Patran. All pre processors have in common, that they produce a Keyword text file as a input file for LS-DYNA.

Introduction

• LS-PrePost version 3.0 can read IGES- and VDA-Files and mesh them with a surface mesh, moreover simple geometric entities can also be generated.

• Post processing for binary and also ASCII data is typically done using LS-PrePost; other post processors are also avaliable e.g. Animator Evaluator (GNS), ANSA, HyperMesh, ANSYS/LS-DYNA, Oasys D3PLOT.

• LS-DYNA also comes with LS-OPT for optimization using the successive response surface method.

Introduction

Characteristics of LS-DYNA:

Large Element library: - Simple and fast elements for standard applications. - High-order elements available, but costly.

Wide choice of material laws:

. plasticity: - Kinematic and isotropic hardening. - Strain rate dependency.

- Temperature dependency. - Failure.

- Anisotropic plasticity. . Foam.

. Composite material: - anisotropic combined with failure. . Rubber.

. Viscous. . Fluid.

Introduction

Contact-Algorithm: - With friction.

- Contact of deformable with rigid bodies in any combination. - Single surface contact.

- Contact with analytical surfaces. - Contact Rigid-Body and Rigid-Body. - Definition quite simple.

- Very fast.

Rigid Body Dynamics: - Definition of rigid bodies with elements or nodes.

- Joints between rigid bodies.

- Deformable to rigid material switching at any time.

Models for gas inflow and gas outflow of airbags.

Possibilities to increase the time step (reduce calculation time):

Mass Scaling: Local increase of mass, minor changes of the total mass. Subcycling: Grouping of elements according to their time step size.

Fields of application for explicit FE programs

STATIC

QUASI STATIC

DYNAMIC

Typical application for explicit FE programs

• Simulation of short time dynamic problems where the frequencies of interest are high (e.g. impact analyses), so that small time steps are also necessary in case of implicit calculation.

• Simulation of highly nonlinear problems, which require small time increments

(because of contact, large deformations), especially for large model sizes, therefore also for quasi-static problems.

Crash- analyses Metal forming Turbine

• Railway construction; • Aerospace industry; • Drop tests.

• Automobile (component- and complete models); • Automobile (side-impact);

1 DOF System – Equation of motion

Equation of motion depends on time discretization necessary! 2 possibilities: implicit or explicit time integration

)

(

p

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u

K.

)

(

.

u

C.

)

(

..

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M.

:

motion

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Equation

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t



t



t

K.u

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force

Elastic

.

u

C.

:

force

Damping

..

u

M.

:

force

Inertia

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(

:

m

Equilibriu

 









s

f

d

f

i

f

t

p

s

f

d

f

i

f

Comparison explicit vs. implicit

Implicit time integration

:

e.g. Newmark-method

The equations of motion are evaluated at time t_n+1 (i.e. at the end of the current time step):

Explicit time integration

: e.g. Central difference scheme

The equations of motion are evaluated at time t_n (i.e. at the begin of the current time step):

Newmark method / linear acceleration method (implicit)

Equation of motion at time t_n+1: Displacement at time t_n+1:

Problem: stiffness matrix K on left hand side Equilibrium iteration for nonlinear problems necessary, costly solving of system of equation.

1 .. u 6 .. u 3 . u u 1 u : nt Displaceme 1 .. u 2 .. u 2 . u 1 . u : Velocity on accelerati in change linear : Assumption 2 2                 n t n t t n n n n t n t n n ) 1 ( 1 1 ) . 2 .. 2 3 ( ) .. 2 . 3 6 ( 1 1 ). 1 1 3 1 6 ( 2 2                         n u n K n K n u n u t n u t n C n u n u t n u t n M n p n u n K n C t n M t

Central Difference method (explicit)

Equation of motion at time t_n:

Displacement at new time t_n+1:

If M and C are diagonal, no matrix inversion is necessary, solution is simple and fast! ) 2 / 1 . u 2 / 1 . u ( 1 .. u : on Accelerati ) u 1 u ( 2 / 1 1 2 / 1 . u : Velocity on accelerati in change linear : Assumption            n n n t n n n n t n 1 ) 2 1 1 ( ) 2 ( 1 ). 2 1 1 ( 2 2 2            _t Mn _t Cn un pn Kn _t Mn un _t Mn _t Cn un

Comparison explicit vs. implicit

Implicit time integration

:

e.g. Newmark-method

Explicit time integration

: e.g. Central difference scheme

The equations of motion are evaluated at time t_n+1 (i.e. at the end of the current time step)

The equations of motion are evaluated at time t_n (i.e. at the begin of the current time step)

Characteristics: - Equilibrium must be satisfied at time t_n+1.

- Thus necessary to solve a large system of equations. - Iteration within time step, convergence may be a problem. - Few but large time steps.

- Time step size depending on frequencies of interest. - CPU time per time step depends on equation solver. - One step method, self starting.

Characteristics: - Equilibrium at time t_n, non-equilibrium at time t_n+1.

- Accelerations calculated to shift the system towards balance. - No large system of equations to solve.

- Usually no problems with convergence.

- Only conditional stable, time step must be small enough:

Time step size depends on highest natural frequency. - Many but very small time steps.

Implicit vs. Explicit time integration

Implicit

Explicit

• The integration method is always stable; independently of the time step used.

• Usually the time step has to be adapted according to the expected results (eigen frequencies of interest).

• In case of nonlinearities the time step must be small enough in order to obtain Convergence.

• The integration method is only stable if the time step is smaller as the so called critical time step (conditional stable). The critical time step is correlated with the highest eigen frequency of the system and reads for linear systems without viscous damping.

for nonlinear system the time step might be significantly smaller! max 2  







crit

t

t

Control of time step size

• LS-DYNA calculates the time step size for each element at each time step automatically (Courand-Levy-Stabilitycriterion):

Global time step = Minimum (all element time steps).

• The smallest time step size will be used (might change from time step to time step). • The user can reduce the time step size:

• By changing the scaling factor (default: 0.9), which is used in the program to multiply the actual time step size:

*CONTROL_TIMESTEP (Control Card 1, tssfac).

• By defining a load curve containing the maximum allowed time step size: *CONTROL_TIMESTEP (Control Card 1, lctm).

Time step control / stability aspects

Stable time integration:

tssfac -> Time step scaling factor.

Instable time integration:

values bigger than 1.0 will lead to instability of the time integration procedure *CONTROL_TIMESTEP $ dtinit tssfac 0.9 *CONTROL_TIMESTEP $ dtinit tssfac 1.5

Control time step

- The time step size is calculated based on wave propagation in the material:

Courand-Levy-Stabilit Criterium

- Distinguish between:

Solid, Shell and Beam Elements or Discrete Elements

Solid-Elements:

9

.

0

c

l

t





l characteristic length of the element c speed of sound

depends on element type tssfac

l minimum length of the element

density

Mass

ratio

Poisson

Modulus

s

Young'

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1

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1

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Control time step

Solid-Shell-Elements: Warped Shell-Elements: Shell-Elements:

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1

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2

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element max max

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- with *CONTROL_TIMESTEP , isdo

area

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max e, e 2 max e, e

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Control time step

Beam-Elements:

In general:

- Shorter element-edges. - Lower mass density. - Added stiffness.

Reduce time step size by modelling.

• Create mesh as uniform as possible

• Mesh refinement increases calculation time

Two options to increase the time step size or to reduce calculation time:

- Mass Scaling; - Subcycling.



E

c



Mass scaling

- User defines the desired time step size: *CONTROL_TIMESTEP, dt2msf

- Program changes the mass density of all elements in such way, that the step size for all elements is equal to the given one.

Not useful for dynamic analyses; generally not recommended!

- Using a negative value for the time step size, will only change mass density for those elements, whose step size is smaller than the desired one:

Also useful for dynamic analyses; Check added mass carefully!

Element l₁ l2 l3

Mass scaling

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l

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2 2 n 2 specified n 2 n.min specified



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





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

Subcycling

- The time step size is always limited by a single element in the finite element mesh, e.g. due to a small element size, a low mass density or a high Young’s modulus.

- In using Subcycling the elements are sorted based on their time step size into

groups whose step size is some even multiple of the smallest element step size. Then each group is calculated with its own time step size.

*CONTROL_SUBCYCLE

- Only recommended for models with very different sizes of elements (mesh refinement) or with extremely different material values (e.g. steel and foam).

- Grouping is possible for the following element and contact formulations:

• Solid-Elements, Shell-Elements, Beam-Elements, Solid-Shell-Elements; • Penalty-Contacts;

• not for Discrete-Elements (spring and damper).

Subcycling

Exemple Subcycling :

E₁ = 4 E₂ A₁ = A₂ ρ₁ = ρ₂

• material 1 is four times stiffer than material 2 • because of : and



E

c



c

l

T





The time step size of material 2 is twice the time step size of material 1.

Consequently elements with material 2 are only calculated every second time step

Scheme of explicit FE program

Loop over all time steps:

loop over all integration points IP

calculation of strains at IP via deformed geometry (strain tensor at IP from current node position)

calculation of stresses at IP with constitutive equation calculation of nodal force contribution of IP

contact algorithm: loop over all contact partners

- calculation of penetrations and resulting contact forces

sum of all nodal forces including external forces and contact forces) - system of nodes with concentrated masses

determined by integration and nodal forces

loop over all nodes: explicit time integration in order to determine the primary variables, i.e. displacements, velocities and accelerations

Hourglassing is a state of strain, which is free of energy (ZEM: Zero Energy

Mode) and can emerge in case of one-point-integrated solid- (hexahedrons) and shell elements.

Hourglass modes are mostly caused by: - concentrated loads

- contact (contact force at several nodes )

Hourglass control

In LS-DYNA there are 2 possibilities to prevent Hourglassing:

using the automatic stabilization against this deformation with -*HOURGLASS (input for each part) or

- *CONTROL_HOURGLASS (global control) using a fully integrated element type

disadvantages: - more computation time

Hourglass control

Recommendation for *HOURGLASS and. *CONTROL_HOURGLASS

for shell elements ihq=4 (stiffness form, default settings) for solid elements (in general) ihq=5 (stiffness form, default settings) for solid elements (foam) ihq=3 (viscous form, default settings) for solid elements (elastic) ihq=6,qm=1.0 (stiffness form)

for solid elements (plastic) ihq=6,qm=0.01-0.001 (stiffness form) For solid elements (rubber, viscoel) ihq=6,qm=1, qw=1 (stiffness form) Note: ihq=6 is a special solid element formulation according to Belytschko-Bindeman

Program execution syntax (SMP)

With the call of LS-DYNA up to 19 parameters can be declared. For a standard execution the following are important:

lsdyna i=input file memory=number_words ncpu=number_processors

The file input file must contain a complete input data for LS-DYNA. There are two

possible formats for the input file:

• structured input: - the input data file is structured in using lines and columns - the sequence of input data must be kept

- this format is old and not recommended • keyword input:

- the input data are described by keywords - the sequence of the data is arbitrarily

- in each line the data can be defined either in a tabular format or in a free format (separated by commas)

Program execution syntax (SMP)

The parameter memory defines the size of the working memory for the program.

Number_Words describes the working memory in words.

On most platforms the default is Number_Words = 8500000, this is approx. 32 MB.

Define e.q. memory=80m to have approx. 305 MB of working memory. An automatic allocation of memory is also possible by definition of an environment variable

(LSTC_MEMORY = auto).

Use Number_Processors to define the number of CPU’s for parallel processing.

Defining Number_Processors as a negative number induces, that the calculation is done in such way that the results are independent of the number processors used (this is related to a somewhat lower performance (see also *CONTROL_PARALLEL).

For Distributed-Memory-Paralelisation (MPP) another executable is necessary as well as a different start procedure.

Program execution syntax (MPP)

The Distributed-Memory-Version of LS-DYNA, MPP-DYNA, is started using a

MPIprogram. Thereby slight changes in the argument list compared to SMP is needed. On a linux cluster the program execution could be as follows:

mpirun –np ncpu mppdyna i=Inputfile memory=number_words memory2=number_words

p=pfile

ncpu is the number of CPUs used

The parameter memory defines the memory in word for the first processor. The first processor has to do the domain decomposition and therefore needs more memory compared to the other CPUs. The parameter memory2 defines the memory for the remaining processors. In case that memory2

is not given, then all processors will allocate the memory given with memory.

An automatic allocation of memory through the definition of an environment variable is also possible (LSTC_MEMORY = auto).

The so called pfile defines specific control options for MPP-DYNA. Since the same options are in meantime possible to define in the keyword file directly (*CONTROL_MPP) the pfile is less

1 - Choose LS-DYNA Solver at Simulation Environment.

Select the License.

Mechanical APDL Product Launcher:

3 - Browse working directory 2 - Choose Analysis Type

5 - Run 4 - Browse keyword file If HPC license is available

It’s possible to set the number of CPU’s.

Parallelization

Shared Memory Parallelization

(SMP)

Massive Parallel Programming

(MMP)

• shared memory

• good speed-up for few CPUs

• no domain decomposition necessary • few new coding necessary

• distributed memory

• domain decomposition necessary (controlling is possible)

• Extraordinary scalability

SMP

Process Elements Contact Constraints Update Nodes Main Loop / Time Step

MPP

Communication Process Elements Contact Constraints Update Nodes Main Loop / Time Step

Using LS-DYNA interactive, the run can be controlled with the following key combination: ^C (Control-C)

This sends an interrupt to LS-DYNA and the user is prompted to input a sense switch code:

sw1 - A restart file is written and LS-DYNA terminates;

sw2 -LS-DYNA responds with time and cycle numbers;

sw3 -A restart file is written and LS-DYNA continues;

sw4 -A plot state is written and LS-DYNA continues;

swa -Flush ASCII file buffers. This can be used to stop the

calculation at arbitrary time and to continue (restart) later.

If the job runs in the back

ground, one has to generate a file d3kil in the working

directory. The file contains then the above mentioned sense switches. In the next time step LS-DYNA reads the file, deletes it and does the corresponding action.

Description of keyword Input

The Keyword input file starts with the line

*KEYWORD, followed by all input data in an arbitrary order.

A data block begins with a keyword followed by data pertaining to the keyword. Each keyword is started with an “*” in the first column of the line. The keywords are

described in the LS-DYNA Users Manual in alphabetic order.

General Card format – Keyword input

For each keyword the required cards have to be defined. Each card is defined in its rigid format form and is shown as a number of fields in an 80 character string.

Most cards are 8 fields with a length of 10. An typical description in the Users Manual is shown below:

The type is the variable type and is either ‘F’ for floating point or ‘I’ for integer. The default value is set, if zero is specified, the field is left blank or the card is not defined. In case the card format differs from eight fields of length 10, it is indicated above the card (e.g.*NODE).

Free formats may be used with the data separated by commas. When using comma format, the number of characters used to specify a number must not exceed the number which would fit into the equivalent rigid format field. Rigid and free formats can be mixed throughout the deck but not within a card.

Part definition – *PART

Part *PART Section *SECTION_ Hourglass *HOURGLASS_ Material *MAT_ Section ID

Element-formulation Cross-section-_{Definition for} SHELL and BEAM Elements (form,integration) ) Material ID Material information Hourglass ID Hourglass-Control-Typ

Part definition – *PART

in LS-DYNA each element has only one attribute: the PART ID

the PART is defined with the Keyword *PART. It contains at least the ID of a material definition (*MAT) and a section definition (*SECTION); optional an equation-of-state ID (*EOS) and a hourglass ID (*HOURGLASS) can be given

the section definition includes the element formulation as well as the cross section description in case of shell and beam elements

Element Library – *SECTION_SHELL

SECTION_SHELL: preferred element type

Shell element:

with the nodes I,J,K,L

Triangular

Shell element:

Shell thickness:

- the shell thickness is defined in *SECTION_SHELL, t1 until t4 - additional input is possible in the element card, with

*ELEMENT_SHELL_THICKNESS; this overwrites the thickness from section definition - in order to consider thickness change of the shell due to membrane straining one has to set *CONTROL_SHELL, istupd (e.g. for sheet metal forming).

Element Library – *SECTION_SHELL

Number of integrations points:

- most shell elements (other than type 6, 7 and 16) have 1 integration point in plane, shell element types 6, 7 and 16 have 4 integration points in plane

- The number of the integration points across the thickness is variable and must be defined in *SECTION_SHELL, nip

Default is nip=2, which is not sufficient for most applications.

- use the following rules to define the number of integration points throughout thickness:

• for membranes 1 integration point

• for linear material 2 integration points sufficient

Attention: stress output not accurate on shell top- and bottom surface • in case of non-linear material 3 until 5 (or more) integration points are needed

- with *DATABASE_EXTENT_BINARY; maxint, declare the number of

integration points, for which LS-DYNA writes results to the binary database

For maxint =3 (default) the results are written for the middle and the two

outermost integration points, available as middle, lower and upper surface.

NIP=5 ; MAXINT=3 NIP=5 ; MAXINT=5 Shell normal

Element Library – *SECTION_SHELL

GAUSS integration points across the thickness

- usually the Gauss integration rule is used for thickness integration

- although the outer integration points are not located on the surface, this method gives accurate results and is commonly used.

- thickness integration can be switched from Gauss to Lobatto integration by setting

*CONTROL_SHELL, intgrd=1

In this case the inner and outer integration points are located on the shell surface. This feature is only available for 3-10 integration points throughout the thickness

Element Library – *SECTION_SHELL

Elements formulation in LS-DYNA:

EQ.1: Hughes-Liu

EQ.2: Belytschko-Tsay -> default

EQ.3: BCIZ triangular shell

EQ.4: co-rotational C0, triangular shell

EQ.5: Belytschko-Tsay membrane EQ.6: S/R Hughes-Liu

EQ.7: S/R co-rotational Hughes-Liu

EQ.8: Belytschko-Leviathan shell

EQ.9: fully integrated Belytschko-Tsay membrane

EQ.10: Belytschko-Wong-Chiang

EQ.11: fast (co-rotational) Hughes-Liu

EQ.12: plane stress (x-y plane) EQ.13: plane strain (x-y plane)

EQ.14: axisymmetric solid (y-axis of symmetry) – area weighted EQ.15: axisymmetric solid (y-axis of symmetry) – volume weighted

EQ.16: fully integrated shell element with EAS-formulation (very fast)

EQ.17: fully integrated DKT, triangular shell element

EQ.18: fully integrated linear DK quadrilateral/triangular shell

EQ.20: fully integrated linear assumed strain C0 shell EQ.21: fully integrated linear assumed strain C0 shell

EQ.43: Mesh-free plane strain EQ.44: Mesh-free axisymmetric

Only for 2D analysis

Only for linear implicit Only for 2D EFG

Element technique – reduced/selective reduced integration

Shear Locking and Hourglassing:

(a) true material behavior

(b) fully integrated linear element (shell 4, solid 8 integration points)

(c) fully integrated quadratic Element (shell 9, solid 27 integration points) (d) reduced integrated linear Element (shell 1, solid 1 integration points) (e) reduced integrated quadratic Element (shell 4, solid 8 integration points)

Element Library – *SECTION_SHELL

Belytschko-Tsay-Shell (Type 2):

- standard element with one point integration - very fast

- problems in case of warping and large shear deformation

-very efficient: moderate accuracy (often sufficient) in combination with high speed

C0 Triangular shell (Type 4):

- special triangular element, because degenerated quad elements are very bad

- in setting *CONTROL_SHELL, esort=1, all triangular elements use this formulation automatically -only a small number of triads recommended in a quad dominated mesh

Fully integrated shell (Type 16):

- fully integrated element with EAS-formulation and without Hourglass modes - very fast for a fully integrated element (2.5 times more expensive than type 2) - new standard element of Belytschko-Tsay group for increased accuracy

-Bathe/Dvorkin behavior for improvement of transversal shear

DKT Triangular Shell (Typ 17):

- fully integrated Discrete Kirchhoff Dreieck-Element

- better than type Typ 4 triangular, especially in bending; but twice calculation time - appr. 1.9-times calculation time compared to type 2; additionally appr. twice elements

Element Library – *SECTION_SHELL

Belytschko-Wong-Chiang (Type 10):

- slightly slower than type 2 (1.2 times more expensive than type 2) -little bit better results as type 2, especially for warped elements

Belytschko-Leviathan (Type 8):

- calculation time and accuracy comparable to type 10 (ca. 1.4 times more expensive than type2) - physical Hourglass control, i.e. no input of Hourglass parameters needed

-for linear material it should be as accurate as an fully integrated element

Hughes-Liu-Shell (Type 1):

- developed from continuum model, one point integration - high accuracy (also in case of twisted elements )

-highly expensive (2.5 times more expensive than type 2)

selective reduced Hughes-Liu-Shell (Type 6,7):

- most costly shell element (10–20 times more expensive than type 2)

- only shear part with reduced integration, otherwise 4 integration points in plane thus only one Hourglass mode

Element Library – *SECTION_SHELL

Belytschko-Tsay- Membrane (Type 5):

- membrane element without bending stiffness, only 1 integration point throughout the thickness

-one integration point in the element plane (Hourglass modes possible)

Fully integrated Belytschko-Tsay- Membrane (Type 9):

Element Library – *SECTION_SOLID

SECTION_SOLID: Hexahedron: (favoured solid element) Tetrahedron:

(created by free mesh, less accuracy)

Tetrahedron:

- 4-noded without rotation: very stiff, only used for foams

- 4-noded with rotation: compromise between effort and accuracy

- 10-noded very accurate but also

Element Library – *SECTION_SOLID

Elements formulation in LS-DYNA:

EQ.1: constant stress hexahedron element (default) EQ.2: fully integrated S/R hexahedron

EQ.3: fully integrated quadratic 8 node hexahedron with nodal rotations EQ.4: S/R quadratic tetrahedron element with nodal rotations

EQ.5: 1 point ALE hexahedron EQ.6: 1 point Eulerian hexahedron

EQ.7: 1 point Eulerian ambient hexahedron EQ.8: acoustic hexahedron

EQ.9: 1 point corotational hexahedron for *MAT_MODIFIED_HONEYCOMB EQ.10: 1 point tetrahedron

EQ.11: 1 point ALE multi-material element, hexahedron

EQ.12: 1 point integration with single material and void, hexahedron EQ.14: 8 point acoustic hexahedron

EQ.15: 2 point pentahedron element

EQ.16: 5 point 10 noded quadratic tetrahedron with mid side nodes

EQ.18: 8 point enhanced strain hexahedron element for linear statics only EQ.31: 1 point Eulerian Navier-Stokes

EQ.32: 8 point Eulerian Navier-Stokes EQ.41: Mesh-free solid - EFG

Element Library – *SECTION_SOLID

standard element (Type 1):

- 8-node hexahedron solid element with tri-linear shape functions

- reduced integration, i.e. stresses are calculated only in one integration point in the middle of the element

-Hourglass modes possible

fully integrated quadratic element (Type 2):

- 8-node hexahedron solid element with tri-linear shape functions - fully integrated with 8 integration points

- no Hourglass modes

- 2-3 times more expensive than type 1 - helpful, if Hourglass modes are a problem

- handicap: lower deformations obtained as with type 1

-uses B-bar-method to overcome transversal shear locking 8 integration points

fully integrated quadratic 8 node element with nodal rotations (Type 3):

- 8-node hexahedron solid element with quadratic shape function - 6 degrees-of-freedom per node: translations and rotations

- 14 integration points

- not useful for plasticity or material with Poisson ratio close to 0.5 - very expensive in cpu time (3 times more expensive than type 2)

Element Library – *SECTION_SOLID

Solid element - (type 8):

- for acoustic simulation (sound distribution within fluids) - nodes only have a pressure degree of freedom

1 point corotational for *MAT_MODIFIED_HONEYCOMB (Type 9):

- special hexahedron element for extra large deformations in combination with foam material law 126 (*MAT_MODIFIED_HONEYCOMB)

Pentahedron element (Type 15):

- 6-noded element with trlinear displacement behavior and 2 integration points

- element typically is generate when triangular surface element is extruded into the depth

- with the input:

*CONTROL_SOLID, esort=1

Element Library – *SECTION_SOLID

Tetrahedron element (Type 10):

- 4-nodes tetrahedron element with tri-linear shape functions and 1 integration point - in general much too stiff

- often used in combination with foam material, then realistic results expected

S/R quadratic tetrahedron element with nodal rotations (Type 4):

- 4-node tetrahedron solid element with quadratic shape functions - 6 degrees-of-freedom per node: translations and rotations

- 5 integration points

- very expensive in cpu time (5 times more expensive than type 10)

- accuracy better than tetrahedron type 10, but less than hexahedron type 2

- accurate tetrahedron elements must have midside nodes, but impracticable for explicit computations

10-noded tetrahedron element (Type 16):

- tetrahedron element with midside nodes and quadratic displacement behavior - 4+1 integration points

- needs approx. The same computation time as Type 4 but time step is halfed - for post processing only a constant stress within element available

Element comparisson

- typical bending application modelled with different element formulations

- in case of hexahedrons, 4 elements are used across the height

- in case of tetrahedrons only 1 element is used across the height

Element Library – ALE-formulation in Section_Solid;Shell

Eulerian- formulation:

- is used in fluid mechanics

- mesh of elements is fixed in space - material ‘flows’ through the elements

-variable boundary conditions are complicated

Lagrangian- formulation:

- is used in structure mechanics

- material and elements are bonded together -large deformation induces element distortion

ALE: Arbitrary- Lagrangian- Eulerian:

- both formulations in combination, may be alternated by time - two possible kinds of applications:

REZONING: large deformation in structure mechanics; mesh must be corrected

Element Library – *SECTION_SOLID

Solid element - ALE (type 5):

- 8-node hexahedron element with trilinear displacement behavoir with reduced integration

- ALE = Arbitrary Lagrangian Eulerian

coupling of lagrangian and eulerian formulation - Eulerian: materials flow through elements

- useful for simulations with large element distortion

Solid element - (type 6 and 7):

- represent fluid elements within an ALE formulation

Solid element - (type 11 and 12):

- admit within ALE formulation different materials in one fluid element

- use in combination with *ALE_MULTI-MATERIAL_GROUP (11) or in combination with void-definition (12)

Element Library – *SECTION_BEAM

SECTION_BEAM:

except for Type 3, 6 and 9 all beam elements need a third node K, which defines the orientation of the local coordinate system.

element formulation in LS-DYNA:

EQ.1: Hughes-Liu with cross section integration (default) EQ.2: Belytschko-Schwer resultant beam

EQ.3: truss (resultant)

EQ.4: Belytschko-Schwer full cross-section integration

EQ.5: Belytschko-Schwer tubular beam with cross-section integration EQ.6: discrete beam/cable

EQ.7: 2D plane strain shell element (xy plane)

EQ.8: 2D axisymmetric volume weighted shell element (xy plane) EQ.9: spot weld beam

Element Library – *SECTION_BEAM

Belytschko-Schwer-Beam (Type 2):

- efficient in computation

- only valid for linear material and for resultant material formulation (plastic hinges) -cross section of the beam is described by area and moments of inertia

Hughes-Liu-Beam (Type 1):

- expensive in computation - also valid for plastic material

- predefined circular and rectangular cross section definition - arbitrary cross section with user defined integration rule (*INTEGRATION_BEAM)

Truss-Element (Type 3):

- simple element for tension and compression only - described by cross section area

Element Library – *SECTION_BEAM

Discrete beams (Type 6):

- not really a beam, but a stiffness in all 6 directions between two nodes - beam nodes should have (and may have) the same coordinates

- element length does not influence the time step - element formulation only for material law 66-68

- *MAT_LINEAR_ELASTIC_DISCRETE_BEAM

- *MAT_NONLINEAR_ELASTIC_DISCRETE_BEAM

- *MAT_LINEAR_PLASTIC_DISCRETE_BEAM

- local beam coordinate system available - input same as beam, output same as beam

Cable-Element (Typ 6):

- same input as in discrete 3D-beam, but with element length important - acts as a rod, which can only transmit axial tensile forces

- element formulation is exclusively for material law 71:

- *MAT_CABLE_DISCRETE_BEAM

Spot weld beam (Type 9):

- good for description of elastic spot welds

alternative to rigid spot welds (*CONSTRAINED_SPOTWELD)

- often used in combination with *CONTACT_SPOTWELD to define mesh independent spot welds - only available in combination with the material law 100 (*MAT_SPOTWELD)

- discrete springs / damper with linear and non-linear characteristic and single mass points

-define springs and dampers with *ELEMENT_DISCRETE

Those elements do not yet have a mass, the user must take care that the adjacent elements and nodes have sufficient mass

- define mass-points with *ELEMENT_MASS and *ELEMENT_INERTIA (in order to represent components which are not modelled in the model)

Element Library – *SECTION_DISCRETE

SECTION_DISCRETE:

Spring

Damper:

Mass:

Material definition

• description of a material with *MAT_...

• the corresponding material ID is then referenced in the corresponding part definition • it should be noted that not all materials are available for each element type

• the information, for which elements a material law is valid, is stated in the Keyword Manual in the description of *MAT

• often used material laws are:

Type 1: *MAT_ELASTIC linear elastic

Typ 3: *MAT_ELASTIC_PLASTIC plasticity (iso/kin) Type 9: *MAT_NULL no effect

Type 20: *MAT_RIGID rigid

Type 24: *MAT_PIECEWISE_LINEAR_PLASTICITY standard for plasticity Type 123: *MAT_MODIFIED_PIECEWISE_LINEAR_ PLASTICITY improved for shells Type 57: *MAT_LOW_DENSITY_FOAM foam

A FORTRAN interface is available to integrate own material routines. For this material numbers 41-50 are reserved (*MAT_USER_DEFINED).

Material definition – Plasticity

*MAT_ELASTIC or *MAT_001:

• simple material law for linear elastic behaviour of material, available for (almost) all element types Example input : MID: Material ID RO: Density E: E-Modulus PR: Poisson ratio

Material definition – Plasticity

*MAT_PLASTIC_KINEMATIC (*MAT_003) • material law to describe isotropic materials with plastic hardening behavior (isotropic or kinematic hardening)

• strain rate effects can be considered • available for Shells, Solids, Beams

Example input :

MID: Material ID SIGY: Yield strength FS: Failure strain RO: Density ETAN: Tangent-modulus

E: E-modulus BETA: Hardening parameter iso/kin PR: Poisson ratio SRC/SRP: Strain rate parameters

Material definition – Plasticity

*MAT_PIECEWISE_LINEAR_PLASTICITY or *MAT_024:

• standard material law to describe an elastic-plastic material behavior

• the stress-strain curve is either bilinear with a yield stress (sigy) and the tangent

modulus (etan) or can be specified with an input table of a stress-strain curve (either in the fields eps{n} and es{n} or as a load curve lcss with *DEFINE_CURVE

• the true stress in relation to the logarithmic plastic strain must be entered Example input :

Material definition – Engineering X True

nominal strain: nominal stress: 0 0

A

F

L

L

eng eng











Logarithmic strain (natural strain) engineering incremental With integration plas el tot











0

L

L

eng







E

tot plas













_eng



L L

L

L

L

L

L

L

L

L

dL

_



_















_

_

























ln

ln

ln

ln

ln

1

0 0 0 0 log 0







L

L



true stress

true stress belongs to true strains Constant volume

A

F







L

₀

L



A

₀

L

₀

V

₀

A

V













_eng



_eng



_eng



eng

A

F

A

F

A

L

L

L

A

A































1

1

1

1

0 0 0 0 0

Material definition – Plasticity

*MAT_PIECEWISE_LINEAR_PLASTICITY or *MAT_024: •To enter strain rate effects for plasticity:

a) constants C and P for Cowper&Symonds b) TABLE-input via lcss

c) Load-Curve (lcsr) defining yield stress scaling factor vs. strain rate Example input for TABLE-Option: Important for TABLE-Input:

-lcss is a TABLE-ID

- for any strain rate in the TABLE a *DEFINE_CURVE must follow immediately

Material definition – Plasticity

Specific load curves (*DEFINE_CURVE), which are used in material models, LS-DYNA does an internal rediscretisation of the input curve. Thereby the new curve is described with 100 x-y pairs, which have the same increment on the abscissa.Starting from the smallest input value to the largest value, the

internal used increment on the abscissa is:

Using internally a strain increment of 0.01 for the hardening curve, one has to define in *DEFINE_CURVE for the first strain value 0 and for the last 0.99.

99

/

)

(

x

_end

x

_in

x







Material definition – Plasticity

This is done for stress-strain curves e.g. in:

*MAT_024 and *MAT_123 (both only in case of TABLE input) *MAT_120 (always)

This is done for almost all force curves of discrete beams: *MAT_..._DISCRETE_BEAM

It is not done for stress-strain curves e.g. in:

*MAT_024 and *MAT_123 (both only if no TABLE input is used) *MAT_36 (always)

It is not done for all force curves in discrete elements: *MAT_SPRING_..

Recommendation: Largest value on abscissa as small as possible; material curves will be linearly extrapolated. End values must be chosen in such way that important inner pairs are well represented.

Material definition – Plasticity

Many plasticity material models allow the usage of a viscoplastic formulation, activated with the input: VP=1

This feature needs some more computation time, but leads to a smoother and more realistic stress curve. It is generally recommended.

In the standard strain rate formulation (VP=0), the effective strain rate is calculated once based on the components in the current strain rate tensor.

In the viscoplastic strain rate formulation (VP=1), the effective strain rate is calculated only based on the plastic part of the strain rate tensor. In this formulation you need to do iteration on the effective plastic strain rate during the corrector state of the

Material definition – Plasticity

*MAT_MODIFIED_PIECEWISE_LINEAR_PLASTICITY or *MAT_123:

• description of an elastic-plastic material behaviour; same as Type 24, but with extended failure criteria

• only available for shell elements Exemple input:

Material definition – Null

*MAT_NULL or *MAT_009:

-shell elements and beam elements with this material definition neither have a stiffness nor need any significant computation time

-application:

- “Null shells” for description of contact surfaces on solid elements or between beams

- “Null beams” for description of contact edges with

*CONTACT_AUTOMATIC_GENERAL

- visualisation of stonewalls, springs or draw beads (for invisible elements)

- in combination with solid elements also for fluids in tanks, when the mass of the fluid is relevant. An additional *EOS definition is necessary. The mass of the fluid comes from

Material definition – Rigid

Type 20 (*MAT_RIGID):

• with this material any element can become a rigid body

• the Young's modulus, which should be in the same order than the surrounding material, is used only to compute the contact stiffness if the rigid body interacts in a contact definition; neither element length nor material data have an influence on the time step size

• a part with MAT_RIGID is one rigid body and has only 6 degrees of freedom for calculation • elements of one rigid body must not be connected. Nevertheless they move like a single body (Attention !). For independent rigid bodies different parts are necessary and must be defined • nodes connected with rigid bodies may have no additional boundary conditions or constraints • define boundary conditions for rigid bodies in the material definition, this applies to the centre of gravity

• the centre of gravity, the mass and the moments of inertia are calculated by the shape of the elements, this can be overwritten by

*PART_INERTIA

Material definition – Foams

Fundamental Behavior

1. Cell walls carry loads: ~linear elastic (first region) 2. Cell walls buckle:

- few stress increase (horizontal plateau) - air in pore carry little load or decelerates - with or without failure

3. Material is compacted: significant stress increase; densification is obtained

Material definition – Foams

Material definition – Foams

Material models available in LS-DYNA:

• elasto-viscoplastic material models with failure (so-called crushable foams) • Viscoelastic formulation for foams with hysteretic behavior

• Isotropy or anisotropy Differences of the models:

• Input of curves for stress-strain relationship • Input of material parameters

• Consideration of strain rate effects Similarities of the models:

• Material behavior is controlled with volumetric strain • Stresses and strains input is positive for compression • Elastic foam has no transverse contraction

Material definition – Foams

Overview Elastic Foams: distinction in strain rate effect

*MAT_057 - viscoelastic with one term (most simple model) *MAT_073 - viscoelastic with 6 terms (seldom used)

*MAT_083 - table input of stress strain curves; not viscoelastic but rate dependent (often used)

Overview Crushable Foams: distinction in anisotropy and plasticity

*MAT_026 - for strongly anisotropic foams (Honeycomb), one-dimensional uncoupled plasticity

*MAT_126 - modification of MAT_026, one-dimensional uncoupled plasticity *MAT_063 - isotropic, one-dimensional plasticity (principal stresses)

*MAT_163 - isotropic, one-dimensional plasticity (principal stresses); strain rate dependent

*MAT_075 - isotropic, three-dimensional plasticity *MAT_142 - anisotropic, three-dimensional plasticity

Material definition – Elastic foam

*MAT_LOW_DENSITY_FOAM or *MAT_057

• For highly compacted foams with low densities (e.g. seat cushion) • Very stable, viscoelastic formulation (no permanent deformation) • Similarities to a Kelvin element

• Input of engineering strains and -stresses • Unloading with hysteretic option (HU)

• Form and amount of unloading hysteresis controlled with parameters (HU and SHAPE)

• Most simplest strain rate dependency(1 parameter); corresponds to a Maxwell element

• Optional tension cut off for tensile stress; otherwise linear elastic behavior with E-Modulus without transverse contraction under tensile loading

• Optional input of reference geometry in order to calculate the initial stress stress state

• The time step is calculated based on the steepest tangent in the stress strain curve under consideration of the CURRENT density

Material definition – Elastic foam

Type 57 (*MAT_LOW_DENSITY_FOAM):

- simple material law for highly compressible low density foams - for compression a stress-strain-curve has to be defined

- in tension linear behaviour up to failure Exemple input:

Material definition – Elastic foam

Determination of the stress strain curve from quasi-static or dynamic compression tests. Needed values: engineering stresses over strains (strain measure depends on used material model)

In order to avoid localization, the stress strain curves have to fulfill the following conditions:

0

0

0

0 . 0 2 0 0 2 0 0































For each stress strain curve

For a bunch of stress strain curves in a TABLE definition

Material definition – Elastic foam

*MAT_LOW_DENSITY_FOAM or *MAT_057:

• influence of HU (hysteretic unloading parameter)

Material definition – Elastic foam

Material definition – Elastic foam

*MAT_LOW_DENSITY_VISCOUS_FOAM or *MAT_073

• Enhancement to *MAT_LOW_DENSITY_FOAM

• For highly compressible low density foams with large strain rate effects • Input of engineering stresses and strains for strain rate Independent part • Extensive viscoelastic formulation

• Strain rate effect either determined with a relaxation curve or with pairs of shear modulus and exponent (Prony-Serie) > those input parameters are typically not easy to determine, consequently seldom used.

Material definition – Elastic foam

*MAT_FU_CHANG_FOAM or *MAT_083

• For foams with low density

• Input of engineering stresses and strains

• Consideration of strain rate effects using a TABLE definition (simple input if experimental data are available, therefore often used)

• Optional input of engineering strain rate or logarithmic strain rate (SFLAG) • Optional input of stress strain relation or linear behavior for tensile (TFLAG) • Calculation type of strain rate can be changed (RFLAG)

• Additional input of load curves to define the hydrostatic compression over volumetric strain (PVID)

• Hysteretic behavior during unloading

• Time step calculated from Ed; if Ed=0 then from E; time step does not follow the steepest tangent > E or Ed must be large enough

density change is not considered for calculating the time step

> Attention: for highly compacted foams and used mass scaling large increase in mass might occur.

Material definition – Elastic foam

*MAT_CRUSHABLE_FOAM or *MAT_063

• For foams with failure and permanent deformations • Isotropic, one-dimensional plastic formulation

• Plasticity uncoupled in terms of principal stresses, yield surface is a cube • Unloading with elastic E-modulus

• Input of unaxial stress over volumetric strain

*MAT_MODIFIED_CRUSHABLE_FOAM or *MAT_163

• Same model as *MAT_063

• Additional strain rate dependency: input with TABLE option for different stress strain curves for different strain rates

Material definition – Plastic foam

*MAT_BILKHU/DUBOIS_FOAM or *MAT_075

• For foams with failure and permanent deformation • Isotropic 3D plasticity formulation

• Unloading with elastic E-modulus

• Input of unaxial stress over volumetric strain (from uniaxial experiment) • Input of pressure at yield over volumetric strain (from triaxiality experiment) • Elliptical yield surface i.e. 3D plasticity

Material definition – Honeycomb

*MAT_HONEYCOMB or *MAT_026

• For Honeycomb materials with highly anisotropic behavior • One dimensional formulation with permanent deformations • Plasticity uncoupled for the single material axes

• Unloading with elastic E-modulus

• Input of stress volumetric strain curves for each material direction; also for shear components

*MAT_MODIFIED_HONEYCOMB or *MAT_126

• For honeycomb materials with highly anisotropic behavior • One dimensional formulation with permanent deformations • Plasticity uncoupled for the single material axes

• Unloading with elastic E-modulus

• Input of stress volumetric strain curves for each material direction; also for shear components

• Small strain option available • Option for 3D plasticity available

Material definition – Honeycomb

Input of material direction is done with AOPT

definition on material card:

AOPT=0.0:

local orthotropic material cosy defined by the element node numbering; only useful for structured meshes with equal or predefined orientation of element cosy

AOPT=1.0:

local orthotropic material cosy defined by element center and vector to origin P; only for solid elements

AOPT=2.0:

global orthotropic material cosy defined by two vectors a and d; only useful for flat or minimal curved structures (plates)

AOPT=3.0:

local orthotropic material cosy defined by element

normal and vector v; also useful for curved structures AOPT=4.0:

local orthotropic cylindrical material cosy defined by point P and vector v; only for solid element

Boundary conditions

• boundary conditions are used to fix displacements or rotations of nodes • boundary conditions can be defined in two different ways

> - at the end of the lines in the nodes definition (*NODE)

- this boundary condition always acts in the global coordinate system - it is not possible to output the corresponding reaction forces

> - with *BOUNDARY_SPC_...

- this boundary condition may act in an arbitrary coordinate system (the coordinate system „0“ is the global coordinate system)

- the reaction forces are print to the ASCI file spcforc

• nodes connected to rigid bodies may not get such boundary conditions

> define boundary conditions for rigid bodies at their centre of gravity in the material description (*MAT_RIGID) or define a joint

(*CONSTRAINED_JOINT)

Initial conditions

- for time transient calculations initial conditions for displacements and velocities are necessary, default is zero for all

- the acceleration is set to zero at time t=0

- initial velocities can be set with *INITIAL_VELOCITY,

-for rigid bodies define initial velocities in the part definition with *PART_INERTIA

> but then, all mass parameters of the rigid body (centre of gravity, mass, moments of inertia) must be defined too

- to define initial displacements (e.g. for a prestressed structure) different ways are possible

a) calculation of prestress deformation with LS-DYNA using dynamic relaxation b) define initial displacements (for beams and shells also initial rotations) for

each node from a external file (may be created by an implicit code like ANSYS)

> define *CONTROL_DYNAMIC_RELAXATION, idrflg =2

(initialisation to a prescribed geometry) and set m=filename as parameter on the command line to start LS-DYNA

c) run the prestress calculation in LS-DYNA using the implicit solver - initial temperatures can be defined in the same way as initial displacements - initial stresses and initial strains can be defined in the same way as initial

Loads

possible loads:

-- nodal forces (*LOAD_NODES ; *LOAD_RIGID_BODY)

> defines concentrated forces on nodes or on the centre of gravity of rigid bodies

> possibility to modify the force direction with the deformation (follower forces), e.g. shell with water loading

-- element pressure (*LOAD_SEGMENT)

-- prescribed displacements, velocities or accelerations (*BOUNDARY_PRESCRIBED_MOTION_...)

> defines the displacement, the velocity or the acceleration as a function of time

> for rigid bodies only displacements or velocities at centre of gravity can be defined

> the use of prescribed velocity is recommended to get a smooth process > the reaction forces are reported to the ASCII file bndout

Loads

-- acceleration field (e.g. gravitation) (*LOAD_BODY)

> this describes an acceleration of the ground

-- the quantity of the load is generally provided as a function of time

by pairs {time; value} in form of so-called “load curves“: *DEFINE_CURVE -- load curves are also used for many other reasons:

> e.g. for the input of a time-dependent damping

> for the input of stress-strain-relation in the material description > for the input of time dependent output frequency

> for the input of an arbitrary line in case of generating a axisymmetric body as geometric contact entities

Sets

-SETS are needed to define contact, loads, boundary conditions or initial velocities, where a number of nodes, elements or parts must be specified

-a set describes a group of nodes, parts, elements or segments with the reference of a set ID

- *SET_BEAM_OPTION (options: GENERATE ; GENERAL)

- *SET_DISCRETE _OPTION (options: GENERATE ; GENERAL)

- *SET_NODE _OPTION (options: LIST; COLUMN; LIST_GENERATE; GENERAL)

- *SET_PART _OPTION (options: LIST; COLUMN; LIST_GENERATE)

- *SET_SEGMENT _OPTION (options: GENERAL)

- *SET_SHELL _OPTION (options: LIST; COLUMN; LIST_GENERATE; GENERAL)

- *SET_SOLID _OPTION (options: GENERATE ; GENERAL)

- *SET_TSHELL _OPTION (options: GENERATE ; GENERAL)

- possible options are: GENERATE - generate a block of entities between a starting nodal ID and an ending nodal ID number

GENERAL - combine a series of options, see Keyword-Manual

LIST - define a list of entities

LIST_GENERATE - generate a block of entities between begin and end

Contact

- the contact algorithm prevents the penetration of nodes into element (contact) segments

- contact segments can be element faces of solid elements or the element area of shell elements; if necessary together with an offset of half the shell thickness

- for a contact definition, parts of the model coming in contact must be described as so-called master and slave side. If it is not possible to describe two contacting model parts a single surface contact can be used instead and only a slave side has to be defined

Contact

- the contact partners can be defined by direct input of the nodes and segments or by a list of PART numbers and geometric box dimensions

- internally LS-DYNA uses always nodes and segments, where segments are element areas (shell elements or faces of solid elements)

-in some contact types the normal direction of the contact plane is important. In solid elements the normal is always outward directed, for shell elements the element normal is used

-> it is generally recommended to create connected meshes with uniform normal orientation

Contact

3 Types of Contact:

1) Sliding Interfaces (*CONTACT_...) 2) Stonewalls (*RIGIDWALL)

3) Geometric Contact Interfaces(*CONTACT_ENTITY) 1) Sliding Interfaces (*CONTACT_...)

- this is the most general formulation for contact between rigid and deformable bodies in arbitrary combination

- in most cases a penalty-method is used, i.e. inner pairs of forces are applied

at those locations where penetrations are observed

- the pair of forces are calculated based on penetration depth and contact stiffness

Contact – Contact stiffness

- penalty force: F = k ×g with k - contact stiffness g - penetration depth - for shell elements the contact stiffness is determined by:

k = slsfac × sf ×K×A/ d

With: slsfac - global scale factor given in *CONTROL_CONTACT sf - local scale factor given in *CONTACT_, Card 3 (sfs,sfm) K - bulk modulus

A - element area

d - thickness or shortest diagonal and for solid elements:

k = slsfac × sf ×K×A² /V

With: slsfac - global scale factor given in *CONTROL_CONTACT sf - local scale factor given in *CONTACT_, Card 3 (sfs,sfm) K - bulk modulus

A - segment area

Contact – Contact stiffness

- according to this, the contact formulation is identical to a spring under compression

- the contact stiffness is computed for each segment on the master and slave side; in case of contact the smaller value is used

- if these two values differ about a factor of more than 100, the mean value is computed and a warning message is given

-the biggest disadvantage of the penalty method is, that a contact stiffness has to be defined, which might be not optimal for all cases:

> if the stiffness is too low, the penetration will be too high

> if the stiffness is too high, high frequency vibrations are activated and the explicit time integration procedure may become unstable