2025年LSDYNA材料模型及参数

目录

1基本的状态方程.................................................

1.1EOS」WL..................................................................................................

2.2EOS_GRUNEISEN...............................................................................

2.3EOS_LINEAR_POLYNOMIAL...........................................................

2.材料模型.......................................................

2.1MAT_HIGH_EXPLOSIVE_BURN.....................................................

RDX........................................................................................................

HMX.......................................................................................................

TNT.........................................................................................................

1.2MAT_NULL............................................................................................

空气.....................................................

水.......................................................

1,3MAT_J0HNS0N_C00K.....................................................................

紫铜.....................................................

钢.......................................................

1.4MAT_PLASTIC_KINEMATIC............................................................

钢.......................................................

高导无氧铜..............................................

土壤.....................................................

1.5MAT_STEINBERG...............................................................................

高导无氧铜..............................................

1.6MAT_J0HNS0N_H0LMQUIST_CERAMICS................................

B4c陶瓷................................................

1.7MAT_JOHNSON_HOLMQUIST_CONCRETE................................

混凝土..................................................

3其它材料参数...................................................

LY12CZ铝合金...............................................

重要材料模型及参数

1基本的状态方程

1.1EOS_JWL

5678

VariableEOSIDABRIR2OMEGEOvo

Type1FFFFFFF

Remarks:

TheJWLequationofstatedefinesthepressureas

andisusuallyusedfordetonationproductsofhighexplosives.

2.2EOS_GRUN曰SEN

5

VariableFfKIDC9133GAMAOAFO

TypeFFFFFFF

Cafd2

VanabkVO

TypeF

TheGruneiseiequationofstatewithcubicshockveliKity-particlevelocitydefinespressure

forcompressedmaterialsas

p=+(力+”)£

[1-(5,-l)p-5,餐-S'局]

andforexpandedmaterialsas

C>+(y+^)£.

p=po0

whereCistheinterceptofthevx-vpcurve;S卜S?.andS3arethecoefficientsof(heslopeof(hev、・

Vpcurve:is〔heGruneisengamma:aisthefirstordervolumecorrectionto第上andp=­-1.

P。

2.3EOS_LINEAR_POLYNOMIAL

(对EOS_GRUNEISEN进夕亍线性化)

Remarks:

1.Thelinearpolynomialequationofstateislinearininternalenergy.Thepressureisgivenby:

++++G/)R

wheretermsC9p-andC6H2aresettozeroifp<0,/y=­-1,and-is(heratioofcurreni

A.P”

densitytoinitialdensity.

2.材料模型

2.1MAT_HIGH_EXPLOSIVE_BURN

CardFormut

Ca(dI12345678

VanjMcMIDRODPCJBETAKGSIGY

Type1FFFFFFF

Burnfractions,F、whichmultiplytheequationsofstalesforhighexplosives,controlthe

releaseofchemicalenergj-forsimulatingdetonations.Atanytime,thepressureinahighexplosive

elemeniisgivenby:

P=FPAV'E)

whereisthepressurefromtheequationofstate(eithertypes2or3),Vistherelativevolume,

andEistheinternalenergydensityperunitinitialvolume.

Intheinitializationphase,alightingtimet]iscomputedforeachelementbydividingthe

distancefromthedetonationpointtothecenteroftheelenientbythedetonationvelocityD.IfmuItipIe

detonationpointsaredefined,tl)eclosestdetonationpointdetenninestjThebumfraction/'istakenas

themaximum

2(，-。)人

if/>/>

3匕

6=

0if

whereVCJistheChapman-Jouguetrelativevolumeandtiscurrenttime.If/exceeds1,itisresett(

I.Thiscalculationofthebumfractionusuallyrequiresseveraltimestepsfortoreachunity,thereby

spreadingtheburnfrontoverseveralelements.Afterreachingunity,/isheldconstant.Thisburi

fractioncalculationisbasedonworkbyWilkins[1964]andisalsodiscussedbyGiroux[1973].

Ifthebetaburnoptionisused,BETA=1.0,anyvolumetriccompressionwillcausedetonation

and

andisnotcomputed.

Ifprogranunedburnisused,BETA=2.0,theexplosivemode)willbehaveasanelastic

perfectlyplasticmaterialifthebulkmodulus,shearmodulus,andyieldstressaredefined.

Therefore,withthisoptiontheexplosivematerialcancompresswithoutcausingdetonation.

Asanoption,thehighexplosivematerialcanbehaveasanelasticperfectly-plasticsolidprior

todetonation.Inthiscaseweupdatethestresstensor,toanelastictrialstress.

whereGistheshearmodulus,andisthedeviatoricstrainrate.ThevonMisesyieldconditionis

givenby:

(7*

i-胃

wherethesecondstressinvariant.isdefinedintermsofthedeviatoricstresscomponentsas

/_1

4=2Vi/

andtheyieldstressisat.Ifyieldinghasoccurred,i.e.,(/>>0,thedeviatorictrialstressisscaledto

obtainthefinaldeviatoricstressattimen+l:

If040.then

Beforedetonationpressureisgivenbytheexpression

whereKisthebulkmodulus.Oncetheexplosivematerialdetonates:

andthematerialbehaveslikeagas.

RDX

密度：1.69E+3k°/n】3；D:8310m/s；Pci:30.45Gna

A:850Gi)a；B:18Goa；Ry4.6；R1:1.3；\\@38；Eq：10N4J/ke

For(g-cm-us):

*MAT_HIGH_EXPLOSIVE_BURN

11.698.3100.30150

♦EOSJWL

18.500.184.61.3038IOe-021.00

HMX

衡度：1.891E+3ka，'m]D：9910m/s,Pci：42Gpa.

A：778.3Gr>a；B：7.1Gna；Ri：41：R?：LOO：\v°：30：Eo：l().5MJ/ki

For(g-cm-us):

*MAT_HIGH_EXPLOSIVE_BURN

I1.899.9100.420

*EOS_JWL

17.7830.0714.21.00.3010.5e-021.00

TNT

密度：1.63E+3kHm'；D：6930m/s；Pci：27Gpa：

A：371.2Goa：B：11；Ri：4.15；R2：0.95；Wo：30

For(g-cm-us):

*MAT_HIGH_.EXPLOSIVE_BURN

11.636.9300.270

*EOSJWL

13.7130.07434.150.950.307.0e-021.00

1.2MAT_NULL

GirdI

VariableMIDROPCMUTERODCERODYMPR

%1FFFFFFF

Defaallsnotenone0.00。0.00.00J00.0

].Thenullmaterialmustbeusedwithanequationof-state.Pressurecutoffisnegativeintension.

A(deviatoric)viscousstressoftheform

F/Vl「NTil

万'1工

iscomputedfornonzero口whereisthedeviatoricstrainrate.〃isthedynamicviscosity

withunitof|Pascal*second|.

2.Thenullmaterialhasnoshearstiffnessandhourglasscontrolmustbeusedwithgreatcare.In

someapplications,thedefculthourglasscoefficientmightleadtosignificantenergylosses.In

generalforfluid(s),thehourgkisscoefficientQMshouldbesmall(intherange1.OE-4toI.OE-

6intheSIunitsystemfor:hestandLirddefauItIHQchoice).

3.TheNullmaterialhasnoyieldstrengthandbehavesinafluid-likemimner.

4.Thepressurecut-off.PC,mustbedefinedtoallowforamaterialto“numerically”cavitate.In

otherwords,whenamaterialundergoesdilatationabovecertainmagnitude,itshouldnolonger

beabletoresistthisdilatation.Sincedilatationstressorpressureisnegative,settingPClimitto

averysmallnegativenumberwouldallowforthematerialtocavitateoncethepressureinthe

materialeoesbelowIhisneealivevalue.

空气

*MAT_NULL

RO=1.25ke/m3.PC=-LODa(vO),­(动力粘性系数)

*EOS_LINEAR_POLYNOMIAL

1.OGna.OGna.OGpa.0.0.4.S4.1)

253312.5，1.0

For(g-cm-us):

*MAT_NULL

30.125e-02-1.0E-I21.749E-7(X)O(X)0000(X)0()

*EOS_GRUNEISEN

30.3444(X»0()(X)0()(XX)(X)1.4000(X)

00

/萃匕USLINEARPOLYNOMIAL

300000.40.40

2.5OOOE-61

水

*MATJNULL

LRO998.21ke/ni',PO-10.0oa,0,0,0,0

("4X()ni、.SI:2.56.S2:-1.986.S3：().2268.丫:0.4934.A:0.47.1吧:()

Vfld.

For(g-cm-us):

*MAT_NULL

I0.998-l.OE-ll0.8684E-50000000000000

*EOSGRUNEISEN

I1.651.92-0.0960000()0.3500000

00

1.3MAT_JOHNSON_COOK

Can1112345678

VariaNcMIDROGEPRDTFVP

Type1FFFFFF

Defaultnonenonenonenonenone().00.0

CanJ2

VariableABNcMTMTREPSO

TypeFFFFFFFF

Defaultnone().00.00.0nonenonenonenone

Caid3

VariableCPPCSPALLrrDID2D3D4

TypeFFFFFFFF

Defaultnone0.02.00.00.00.00.00.0

eninrkr

JohnsonandCookexpresstheflowstressas

/4+〃「)(l+olne”)("7*")

where

A,B,C,n,andm=inputconstants

effectiveplasticstrain

r

e*=-effectiveplasticstrainratefore。=1s

T-J

T'=homologoustemperature=

乙-T…

Constantsforavarietyofmaterialsareprovidedin[JohnsonandCook1983].Afiillyviscoplastic

formulationisoptional(VP)whichincorporatestherateequation?withintheyieldsurface.An

additionalcostisincurredbutheimprovementisresultscanbedramatic.

Duetononlinearityinthedependenceofflowstressonplasticstrain,anaccuratevalueofthe

flowstressrequiresiterationfartheincrementinplasticstrain.However,byusingaTaylorseries

expansionwithlinearizationa?outthecurrenttime,wecansolveforOywithsufficientaccuracylo

avoiditeration.

Thestrainatfractureisgivenby

紫铜

EX=1.19

*MAT_JOHNSON_COOK

18.960000.46

0.900E-032.920E-030.3100.250E-011.090.1356E+042100.100E-05

O.383E-O5-9.00E+003.000.003.000.000.000.00

0.00

*EOSGRUNE1SEN

10.3941.4890.(X)0.002.020.470.00

1.00

钢

EX=2.0

*MAT_JOHNSON_COOK

29.960000.46

0.900E-032.920E-030.3100.25E-011.090.I36E+042100.100E-05

O.383E-O5-9.00E+003.000.0()3.000.000.000.00

0.00

*EOSGRUNEISEN

10.3941.4890.000.002.020.470.00

1.00

1.4MAT_PLASTIC_KINEMATIC

Card112345678

VariableMIDROEPRSIGVETANBETA

Type1FFFFFF

Defaulttonenonenoocnoocnon:0.00.0

Card2

VariableSRCSRPFSVP

TypeFFFF

Dcfaukn<tusednotusednotused0.0

Remarks:

StrainrateisaccountedforusingtheCowperandSymondsmodelwhichscalestheyield

stresswiththefactor

c

whereeisthestrainrate.AfiillyviscoplasticformulationisoptionalwhichincorporatestheCowper

andSymondsformulationwithintheyieldsurface.Anadditionalcostisincurredbutthe

improvementisresultscanbedramutic.ToignorestrainraleeffectssetbothSRCandSRPtozero.

Kinematic,isotropic,oracombinationofkinematicandisotrapichardeningmaybespecified

byviirying任between0andI.Forp'equalto0andI,respec:ively,kinematicandisotropic

hardeningareobtainedasshowninFigure20.2.Forisotropichardening.B'=I.MaterialModel12.

KMAT_ISOTROPIC_ELASTIC_PLASTIC,requireslessstorageandismoreelTicient.Whenever

possible.Material12isrecommendedforsolidelements,butforsheIelementsitislessaccurateand

thusmaterial12isnotrecommendinthiscuse.

Figure20.2.Elastic-plasticbehaviorwithkinematicandisotropichardeningwhere1（）andIare

undeformedanddeformedlengthsofuniaxialtensionspecimen.Etistheslopeof

thebilinearstressstraincurve.

钢

*MAT_PLASTIC_KINEMATIC

47.832.070.3000.400E-025.00E-021.00

0.000.000.0()

高导无氧铜

*MAT_PLASTIC_KINEMATIC

18.931.170.3500000.400E-020.100E-021.00

0.000.()00.00

土壤

*MAT_PLASTIC_KINEMATIC

17.802.10.3000.0230.0240.1.00

000

1.5MAT_STEINBERG

*MAT_STEINBERG

ThisisMaterialType11.Thismaterialisavailableformodelingmaterialsdeformingatveryhigh

strainrales(>1O5)andcanbeusedwithsolidelements.Theyieldstrengthisafunctionof

temperatureandpressure.Anequationofstatedeterminesthepressure.

Cwd3

VanaNcPCSPALLRPFLAGNtMNMMX卜（（）HI

T,pcFFFFFFFF

CURJ4

VanaNcEC2EC3EC4EC5EC6EC7EC8

T)pcFFFFFFFF

MDMuteriu!idaitifkaKion.Auniquenumberhuxtobechoien.

ROMUKKdensity.

GOBasicshearmodulus.

SIGO，>,seedefiningequalicnx

MMA,seedefiningequations.

Nn、MWdefiningequations.

GAMA节.mittalplasticstrain,redefiningequalions.

SIGM0m.secdefiningequations.

Bb.secdefiningequations.

PCf\uib•，(default=*l.e4X)|

RPh\wedefiningc!t|untinn«.

SHALL^paiitype:

EQ.0.0:<kfuuMs«t0-2.(r.

Hh.secdefiningequations.EQ.IQ:p々PE.

EQ.2X>:if<rn&x2Rsekmenl»palbandtension,p<0.Btew

Ff.seedefiningequations.alowed.

EQ.3.0:p<-pevtelementandicmion.p<0.isneveralk>ved.

AAtomicweight(if■0.0.R'mustbedefined).

RPR'IfR"*0.0.Aitnotdefined.

TMOTmo*definingequatiors.FLAGSetto1QforpcocHktenufortheccWcsgrtMionenef^'HLDehukfoT

GAMOKxsecdefiningequations

MMNPta^orHmm-Optionalpor11minimumYidue.

SAa.seedefiningequations.MMXPMMarHnm-Optionalparv)mAtimumvalue.

PCpailor-Of(de«mll=・l.s3D)BC8.EC9Coldcompressionenerg)-coeftkients<op<ic«ial).

UserswhohaveaninterestinthismodelareencouragedtostudythepaperbySteinbergand

Guinanwhichprovidesthetheoreticalbasis.AnotherusefulreferenceistheKOVECuser'smanual.

Intermsoftheforegoinginputpiiramelers.wedefinetheshearmodulus.G.beforethe

materialnieltsiis:

G=G。]彳:「300)e

wherepisthepressure,Vistherelativevolume,Risthecoldcampressionenergy:

900Rexp(ar)

€(-«)=1/>dx-

x=I-V,

andEmisthemeltingenergy:

Em(X)=Ec(x)+3RTm(x)

whichisintermsofthemeltinglemperatureTm(x):

7；,exp(2〃r)

乙(”=

andthemeltingtemperatureatp=po,Tmo.

IntheabuwcqualimiRzisdeHncxlby

A

whereRisthegasconstanlandAistheatomicweight.IfR'isnotdefined.LS-DYNAcomputesit

withRinthecm-grain-microsecondsystemofunits.

Theyieldstrengthayisgivenby:

%=d]+3所川^^__300)卜”/

高导无氧铜

*MAT_STEINBERG

28.930.4770.120E-0236.00.4500.000.640E-02

2.832.830.377E-030.100E-0263.50.179E+042.021.50

-9.003.000.000.000.000.000.000.00

0.000.000.000.000.000.000000.00

*EOSGRUNEISEN

20.3941.490.000.002.020.4700.00

1.00

1.6MAT_JOHNSON_HOLMQUIST_CERAMICS

ThisisMaterialType110.ThisJohnson-HolmquistPlasticityDamageModelisusefulformodeling

ceramics,glassandotherbrittlematerials.Amoredetaileddescriptioncanbefoundinapaperby

JohnsonandHolmquist[1993|.

Card1I2345678

VariableMIDROGABCMN

Type1FFFFFFF

Card212345678

VariableEPSITSFMAXHELPHELBETA

TypeFFFFFF

Caid312345678

VariableDID2KIK2K3FS

TypeFFFFFF

MIDMaterialdenliftculion.Auniquenumberh笛tobechosen.EPS1Referencestrainrate.

RODeniityTNtixiinumtensilestrengih.

GShearmnduluxSFMAXMuinwmnormalizedI'rucluredurength(ifEq.0,defaulttole20).

AIntactnormali/al%trenjthpanmeterHH.HugonidelaMlk:limtf.

BFmcturcdnomulizcdstrengthpammeterPHELRre^sirecompcxienlattheHupxiitMebMiclimit.

CStrengthFurameter(forstrainraledependence>BETARuctionofelasticenergylossconvertedtohxxlrmtaticenetjy.

MFwturedstrengthparameterorewureexponent)DIParameterforpbsticstraintofracture.

NIntactstrengthpurameier(pn*nun»exponent).D2Krameterforphstn:straintofracture(exponent).

KIFifs<pres