ansys autodyn- chapter 9: material models

9-1ANSYS, Inc. Proprietary© 2009 ANSYS, Inc. All rights reserved.

February 27, 2009Inventory #002665

Chapter 9

Material Models

ANSYS AUTODYN

Material Models



Training ManualMaterial Models in Explicit Dynamics (ANSYS)

Failure Model

Strength Model

Equation of State

AUTODYN

Material Models



Training ManualAUTODYN Material Models• An AUTODYN material model consists of 3 components

– Equation of State (EOS)

– Strength Model

– Failure ModelEOS Strength Failure

Models Also Available in Explicit Dynamics (ANSYS)

Material Models



Training ManualAUTODYN Additional Material Models

• Ideal Gas Equation of State

• Two Phase Equation of State

• SESAME Tables

• Cumulative Damage Model

• Beam Resistance Model

• Fragment Analyzer

• Rigid Materials (specification is different in AUTODYN)

• Orthotropic Materials

– Orthotropic Solids

– Composite Shells

• High Explosives (HE)

– Detonation – Expansion of detonation

products (gases)– After-burn– Ignition and Growth

• Slow-burning Explosives

• User Material Models

Material Models



Training Manual

• Energy dependant EOS

γ = ideal gas constant, Gammaρ = density,

e = specific internal energy

• Adiabatic Constant, C– Enter non-zero value to calculate adiabatic

response

P/ργ = C• Pressure shift

– Lets you subtract atmospheric pressure

( ) e1P +ρ−γ=

Ideal Gas Equation of State

Material Models



Training Manual

• Used to model the expansion and vaporization of superheated liquids– e.g. a reactor coolant

• Used together with a compression EOS

• A Gruneisen EOS is used for the single phase region– Saturation curve is the reference curve

• The saturation curve for the material is defined in user subroutine EXTAB– The saturation curve for water is provided with AUTODYN

Two Phase Equation of State

Specific Volume

Single phaseLiquid region

Two phaseLiquid and Vapour region

Single phaseVapour region

Pressure

Material Models



Training ManualSesame Library• The Sesame library is not an EOS but a table

format for storing state data

– Contains data for over 200 materials including metals, minerals, polymers and mixtures

– Most of the tables have data for very wide ranges of density and internal energy, but were developed for particular applications where a particular range was required

– Use with caution

• The Sesame Library is US export-controlled

– Not included in standard distribution

– Library can be obtained from ANSYS if required permissions are provided

– Can also be obtained directly from LANL

Material Models



Training Manual

• Allows progressive degradation of the strength of a material•

• Early model developed to represent brittle materials under crushing

– Predates the Johnson-Holmquist Model

• First developed using User Subroutines

– Good example of the effective combination of multiple user subroutines

Cumulative Damage Failure Model

Material Models



Training Manual

• Strength data for the beam-resistance model is defined using four 10 point piecewise linear curves

– Axial Force vs. Axial Strain along axis 11– Moment vs. Curvature about axis 11– Moment vs. Curvature about axis 22– Moment vs. Curvature about axis 33

• Load-deflection data from experiments on reinforced concrete beams fed directly into beam resistance model to obtain realistic structural response

• There is no inter-dependence between the four piecewise curves defining the axial, torsional and bending response of the elements

Beam Resistance Model

Material Models



Training Manual

Courtesy of AWE (A), UK

Beam Resistance Model

• Example: 1/3 Scale Pullover Tests

– Experiment

• Failure Load: 86kN ± 4KN

– Simulation

• Failure Load: 83kN ± 5KN

Material Models



Training Manual

Courtesy Sandia National Lab.

• View and Tabulate the fragments formed during an analysis• Example: Out-of-barrel Bullet Deflagration

Fragment Analyzer

Material Models



Training Manual

• Select “EOS Rigid” in the standard material input

• Fill any Unstructured Part with a rigid material

– Not available for Structured Parts

• Elements filled with a Rigid material will act as a single rigid body with mass / inertia

• Mass / inertia is defined by

– Material density and volume of filled elements

– Explicitly in the material definition

• You can use more that one Rigid material to define multiple rigid bodies

Rigid Materials

Material Models



Training Manual

Deformable Projectile Rigid Projectile

• Example: 3D Oblique Impact

Rigid Materials

Material Models



Training Manual

• Example: Sheet Metal Forming– Rigid Punch and Die

– Unstructured Shell (Quad dominant) Work Piece

Punch

Work Piece

Die

Rigid Materials

Material Models



Training Manual

• AUTODYN has extensive capabilities for modeling orthotropic materials under a wide range of loading conditions

– Orthotropic linear-elastic response (structural loading)• Orthotropic elastic stiffness matrix

– Linear volumetric response

– Orthotropic elastic response coupled with a non-linear equation of state (transient shock loading)

• Modified orthotropic elastic stiffness matrix– Non-linear volumetric response

– Orthotropic plasticity• Generalized quadratic plasticity surface

– Orthotropic failure• Damage model

• Brittle Failure

Orthotropic Materials

Material Models



Training Manual

Orthotropic EOS

Orthotropic Softening

Orthotropic Yield

Orthotropic Materials• Use Orthotropic EOS, Yield and Softening models to obtain fully response

Material Models



Training Manual

12

3

Represented by a continuum with equivalent orthotropic material

properties - individual layers not represented explicitly

Laminated Composite

• Orthotropic materials are represented using solid continuum elements


OR

Material Models



Training Manual

S = C-1 =C =


• Orthotropic Linear-elastic Response

– Linear Equation of State implicitly assumed for the volumetric response

Material Models



Training ManualOrthotropic Materials• Orthotropic elastic response coupled with a non-

linear equation of state

– Polynomial– Shock– Porous

Material Models



Training Manual

– Shape of the surface defined by coefficients, aij

– Hardening defined by the parameter, k

– General form reduces to

• Hills orthotropic yield function

• Von-mises yield function

kaa

aaa

aaaaf ij

=+

+++

++++=

21266

23155

22344331113332223

22111223333

22222

21111

22222

2)(

σσ

σσσσσ

σσσσσσ


• Orthotropic Plasticity

– Uses Generalized quadratic plasticity surface

Material Models



Training Manual

• Orthotropic Failure : Brittle Failure

– Three orthotropic brittle failure initiation models are available

• Material Stress

• Material Strain

• Material Stress / Strain

– These allow different tensile and shear failure stresses and/or strains to be specified for each of the principal material directions


Material Models



Training ManualOrthotropic Materials

• OrthotropicFailure : Damage Model

– The failure initiation criteria (surfaces) for this model are

Material Models



Training ManualOrthotropic Materials• OrthotropicFailure : Damage Model

– Once failure is initiated, a damage tensor is computed and used to soften the failure surfaces

Material Models



Training Manual

• Static Tensile Test results for KEVLAR®-epoxy


Material Models



Training Manual

• Example: Impact of a fragment onto a GFRP target


Material Models



Training Manual

• Layered Composite Shells– Intended for thin composite structures

under structural (rather than shock) type loading

– Layered composite shells are defined during the “Fill” of the shell part

• Select the Composite button

• Lay-up’s are applied to the mesh along with the normal initial conditions

– Any number of lay-up’s can be defined, stored and selected

• Each layer can be an isotropic or orthotropic material

– For orthotropic materials, you must specify the 11 direction

• Each layer is assigned a thickness

• Each layer can be viewed independently


Material Models



Training Manual

• Layered Composite Shells– Material models

• Models compatible with standard shells can be applied to individual layers of composite shell elements

• Orthotropic material models can also be used– Material directions need to be define

• Tsai-Wu, Hoffman and Tsai-Hill failure criteria can be applied– Including both compressive and tensile failure strengths– Bulk failure only

– Material Directions• 11 and 22 always in plane of shell

• 33 always through thickness

• Material Axes Options– I-J-K (recommended)

• Default 11 : direction of increasing K lines• Set θ to rotate 11 about centre of element• 22 always perpendicular to 11 in plane of element

– X-Y-Z


Material Models



Training Manual

• Example: Bird Strike on Aircraft Wing (Composite Shell used for wing)


Material Models



Training Manual

• Detonation process

– Burn on time

• Initiation points / planes

– Burn on compression

• Not recommended

– Insufficient physics

– Use ignition and growth model instead

• Expansion of detonation products (gases)

– JWL Equation of State (Jones, Wilkins, Lee)

High Explosives

Material Models



Training Manual

Detonation Fronts

Initiation Node

Cell

T1

T2

S1

S2

T1 = S1 / DT2 = S2 / D

• Burn on Time– Detonation is initiated at a node or plane

(user defined)

– Detonation front propagates at the Detonation Velocity, D

– Cell begins to burn at time T1

– Burning is complete at time T2

– Chemical energy is released linearly from T1to T2

• Burn fraction increases from 0.0 to 1.0 over this time

– Element Variable alpha–

= -T1, T<T1

= Burn fraction, T>T1

High Explosives – Detonation Process

Material Models



Training Manual

• Burn on Time

– Direct Path detonation

• Detonation paths are computed by calculating a straight line from the detonation node to each cell center (not necessarily through explosive regions)

– Indirect Path detonation

• Detonation paths are computed by finding either a direct path through explosive regions or by following straight line segments connecting centres of cells containing explosives

High Explosives – Detonation Process

Good use of direct path detonation

Bad use of direct path detonation

Material Models



Training ManualHigh Explosives – Detonation Process• Burn On Time

– Indirect path with multiple initiation points

• Detonation in the shadow zone is calculated accurately only if point #2 is defined

Material Models



Training Manual

Direct Path

Indirect Path 1 det. point

Indirect Path 2 det. points

Indirect Path 3 det. points

High Explosives – Detonation Paths

Material Models



Training Manual

• JWL EOS

– Used to model the rapid expansion of high explosive detonation products (gases)

– The JWL EOS is empirical and the data required is derived from fitting numerical experiments to physical experiments

– Data for a wide range of high explosives is available

– The pressure for the expanding gas is given by

– where A, B, R1, R2, ω are empirically derived constants and ρ = density, ρ0 = reference density, η = ρ / ρ0, e = specific internal energy

eeR

1BeR

1AP21 R

2

R

1

ωρ+⎟⎟⎠

⎞⎜⎜⎝

⎛ ωη−+⎟⎟

⎠

⎞⎜⎜⎝

⎛ ωη−= η

−η

−

log p

High Explosives – Expansion of Detonation Products

log v

Material Models



Training ManualHigh Explosives – Expansion of Detonation Products

• JWL EOS

– Input parameters include

• EOS parameters

• Detonation Velocity

• Chemical Energy / unit volume

– Data for most High Explosives are included in the standard material library distributed with AUTODYN

– Burn on compression fraction and Pre-burn bulk modulus

• Not recommended, leave zero

– Auto-convert to Ideal Gas

• Recommended for accuracy

Material Models



Training Manual

nm Padtd )1( λλ

−=

whereQ = additional specific energy,a = energy release constant,m = energy release exponent,n = pressure exponent


VQEe

VRBe

VRAP VRVR )()1()1( 21

21

λωωω ++−+−= −−

• JWL EOS – Miller Extension

– Non-ideal explosives, containing Aluminum (Al) or Ammonium Perchlorate (AP) can release substantial amount of energy from burning Al and AP particles after detonation

– Miller extension models this energy release

Material Models



Training ManualHigh Explosives – Expansion of Detonation Products

• JWL EOS - Energy release extension

– Thermobaric explosives produce more explosive energy than conventional explosives

• Typically achieved by inclusion of Aluminum

• Undergoes combustion with atmospheric oxygen after detonation (after-burning)

– Additional Energy option in JWL EOS lets you model this time-dependent energy release

• Energy deposition over specific time interval

Material Models



Training Manual

0

2000

4000

6000

8000

10000

12000

14000

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Time (ms)

Pres

sure

(KPa

) TNT + additional Energy

TNT

0

100

200

300

400

500

600

700

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Time (ms)

Impu

lse

(Pa

S)

TNT + additional energy

TNT


• JWL EOS - Energy release extension

– Effect of adding 2.15MJ/kg between 0.12 and 0.55 msec. to a spherical charge of 10kg TNT

– Longer pulse duration and increased impulse

Material Models



Training Manual

• Lee-Tarver Ignition & Growth Model

– Equation of State used for High Explosive (HE) initiation studies

– Assumes ignition starts at local hot spots and grows outward from these sites

– Consists of three basic parts:

• An equation of state for the inert explosive (a choice between a Shock form or a JWL form)

• JWL equation of state for the reacted detonation products

• Reaction rate equation to describe, ignition, growth and completion of burning

High Explosives

Material Models



Training Manual

0.5 km/s 0.7 km/s 1.0 km/s

High Explosives• Lee-Tarver Ignition & Growth Model

– Example: Sympathetic Detonation

Material Models



Training Manual

• Powder Burning Model– Simulates combustion of materials where

dominant physical characteristic is deflagration (incendiary devices, munitions)

– Two phase model

• Gas and solid present in a cell at the same time

• Solid Phase: Linear/Compaction EOS

• Gas Phase: JWL/Exponential

– Burn velocity, c, dependant on gas pressure, Pg

– Burn rate dependent on gas pressure , Pg and burn fraction, F

– Formulation: A Atwood, EK Friis and JF Moxnes, A Mathematical Model for Combustion of Energetic Powder Materials, 34th International Annual Conference of ICT, June 24-27, 2003, Karlsruhe Federal Republic of Germany

Slow-burning Explosives

GasSolid Particles

Numerical Cell of Volume V

Material Models



Training ManualSlow-burning Explosives• Powder Burn Model Model

– Example: Sabot and projectile inside gun chamber

Material Models



Training Manual

• A collection of published material models and data is supplied with AUTODYN

• Accessed through ‘Material’, ‘Load’

• Materials can be sorted by Name, EOS, Strength or failure model

• All materials have an EOS defined, most a strength model and only a few have a failure model defined

• You can add to or modify data in the supplied library or create new libraries

• Data is converted into current units when it is retrieved

Material Libraries

Material Models



Training ManualWhat Material Models to use?• How do we choose a set of material modelling options for a particular

material ?

– In terms of material itself, it is relatively easy to identify the basic category that a material lies in

• Liquid or Solid?• Isotropic or Anisotropic/Orthotropic ?• Inert or Reactive?• Porous or Not ?• Ductile or Brittle ?• Pressure Dependant Strength (cohesive) or not ?

– The actual set of models used however are highly dependant on the application and the available material data

– Start with simple models and progress, as required, to more complex models

• Lets you understand how parameters influence response and which parameters are critical for good results

Material Models



Training Manual

Erosion criteriaMDERO_USER_1

Failure criteriaMDFAI_USER_1

Strength (Yield and/or Shear) ModelMDSTR_USER_1

Equation of stateMDEOS_USER_1

• Modularized Material Modeling Routines let you:

– Build an input GUI

– Check the consistency of input parameters

– Map input parameters to solver parameters

– Write the solver equations

• Written in Fortran 90

User Subroutines for Material Modeling

Material Models



Training Manual

• Example Layout : Strength Model– Module STR_USER_1

• Declare scalar and array variables used in the model here

– INIT_STR_USER_1• Define input parameters and create a menu to

read them in

– SET_STR_USER_1• Copy input parameters to solver scalar/array

variables

– CHECK_STR_USER_1• Check that input parameters are valid

– SOLVE_STR_USER_1• Strength model solver

Material Models



Training ManualGlobal and Material Erosion• Erosion is a numerical mechanism for the

automatic removal (deletion) of elements during a simulation.

– Removes very distorted elements before they become inverted (degenerate).

– Ensures time step remains reasonably large.– Ensures solutions can continue to the End Time. – Can be used to allow simulation of material fracture, cutting

and penetration

• In Explicit Dynamics (ANSYS), an erosion model can be specified globally

– Covered in the Explicit Dynamics training course

• In AUTODYN, an Erosion model can be specified for each material

– Erosion is not a physical effect (or material property). It is amechanism to combat mesh distortion

• There are five options available to initiate erosion of elements in AUTODYN

– Geometric Strain– Plastic Strain– Timestep– Failure– User Erosion

• Program user subroutine EXEROD

ansys autodyn- chapter 9: material models

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