ExplicitSTR140L06MaterialModelsWord格式文档下载.docx
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ExplicitSTR140L06MaterialModelsWord格式文档下载.docx
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EModelingProvidedByEngineeringData
ClassofMatal
MaterialElTects
Metals
ElasticityIPlasticityIsotropicStrainHardngKinnaticStrainHarddng
IsotropicStrainRateHarddngIsotropicThτnalSoftngDuctileFracture
BrittleFracture(FrareEnergybase
DynancFailure(SpaU)
ConcreteIRock
Elasticity
PorousCompaction
Plllü
city
StrainHardng
StrainRateHardinginCompression
StrainRateHardinginTsion
oessureDepdtPlasticityLodeAngleDepdPlasticityShearDamageIFracture
TsileDamageIFracture
SoillSand
Plasticity
oessureDepdtPlasticity
ShearDamageIFracture
RubbersIPolners
I
lI:
nu:
fJslidty
Orthotropic
OrthotropicElasticity
Explosives
DetonationIExpansion
3(Q2011ANSYSInco
March82012
MaterialDeformation
Materialdeformationcanbesplitintotwoindependentparts
•VolumetricResponse‐changesinvolume(pressure)
–Equationofstate(EOS)
•DeviatoricResponse‐changesinshape
–Strengthmodel
Also,itisoftennecessarytospecifyaFailuremodelasmaterialscanonlysustainlimitedamountofstress/deformationbeforetheybreak/crack/cavitate(fluids).
Changein
Volume
Shape
PrincipalStresses
Astressstatein3Dcanbedescribedbyatensorwithsixstresscomponents
•Componentsdependontheorientationofthecoordinatesystemused.
Thestresstensoritselfisaphysicalquantity
•Independentofthecoordinatesystemused
Whenthecoordinatesystemischosentocoincidewiththeeigenvectorsofthestresstensor,thestresstensorisrepresentedbyadiagonalmatrix
whereσ1,σ2,andσ3,aretheprincipalstresses(eigenvalues).
Theprincipalstressesmaybecombinedtoformthefirst,secondandthirdstressinvariants,respectively.
Becauseofitssimplicity,workingandthinkingintheprincipalcoordinatesystemisoftenusedintheformulationofmaterialmodels.
ElasticResponse
•Forlinearelasticity,stressesaregivenbyHooke’slaw:
whereλandGaretheLameconstants(GisalsoknownastheShearModulus)
•Theprincipalstressescanbedecomposedintoahydrostaticandadeviatoriccomponent:
wherePisthepressureandsiarethestressdeviators
•Then:
Non‐linearResponse
•Manyapplicationsinvolvestressesconsiderablybeyondtheelasticlimitandsorequiremorecomplexmaterialmodels
Hooke’sLawGeneralizedNon-Linear
Response
f
EquationofState
StrengthModel
FailureModelσi(max,min)=
ModelsAvailableforExplicitDynamics
AUTODYNEquationofStateStrengthModelFailureModel
ElasticConstants
ShearModulus
Young’sModulus
Poisson’sRatio
BulkModulus
Shear
ModulusG
E
2(1+n)
3EK
9K-E
3K(1-2n)
2(1+n)
Young’s
ModulusE
2G(1+n)
9KG
3K+G
Poisson’s
Ration
E-2G
2G
3K-2G
2(3K+G)
3K-E
6K
Bulk
ModulusK
GE
3(3G-E)
3(1-2n)
PhysicalandThermalProperties
Density
•Allmaterialmusthaveavaliddensitydefinedfor
ExplicitDynamicssimulations.
•ThedensitypropertydefinestheinitialMass/
unitvolumeofamaterialattimezero
–Thispropertyisautomaticallyincludedinallmodels
SpecificHeat
•Thisisrequiredtocalculatethetemperatureusedinmaterialmodelsthatincludethermalsoftening
–Thispropertyisautomaticallyincludedinthermalsofteningmodels
IsotropicElasticity
•Usedtodefinelinearelasticmaterialbehavior
–suitableformostmaterialssubjectedtolowcompressions.
•Propertiesdefined
–Young’sModulus(E)
–Poisson’sRatio(ν)
•Fromthedefinedproperties,BulkmodulusandShearmodulusarederivedforuseinthematerialsolutions.
•Temperaturedependenceofthelinearelasticpropertiesisnotavailableforexplicitdynamics
•Usedtodefinelinearorthotropicelasticmaterialbehavior
–suitableformostorthotropicmaterialssubjectedtolowcompressions.
–Young’sModulii(Ex,Ey,Ez)
–Poisson’sRatios(νxy,νyz,νxz)
–ShearModulii(Gxy,Gyz,Gxz)
•Temperaturedependenceofthepropertiesisnotavailableforexplicitdynamics
Viscoelastic
•Representsstrainratedependentelasticbehavior
•LongtermbehaviorisdescribedbyaLongTermShear
Modulus,G∞.
–SpecifiedviaanIsotropicElasticitymodelorEquationOFState
•ViscoelasticbehaviorisintroducedviaanInstantaneous
ShearModulus,G0andaViscoelasticDecayConstantβ.
•Thedeviatoricviscoelasticstressattimen+1iscalculatedfromtheviscoelasticstressattimenandtheshearstrainincrementsattimen:
•Deviatoricviscoelasticstressisaddedtotheelasticstresstogivethetotalstress
ε=Constant
σ=Constant
Stress
Strain
Time
StressRelaxationCreep
Severalformsofstrainenergypotential(Ψ)areprovidedforthesimulationofnearlyincompressiblehyperelasticmaterials.
Formsaregenerallyapplicableoverdifferentrangesofstrain.
6.00
5.00
Tensiletestsonvulcanisedrubber
Mooney-Rivlin
Arruda-Boyce
Eng.Stress(MPa)
4.00Ogden
TreloarExperiments
3.00
2.00
1.00
0.00
012345678
Eng.Strain
Needtoverifytheapplicabilityofthemodelchosenpriortouse.
Currentlyhyperelasticmaterialsmayonlybeusedforsolidelements
ExamplesofHyperelasticity
Ifamaterialisloadedelasticallyandsubsequentlyunloaded,allthedistortionenergyisrecoveredandthematerialrevertstoitsinitialconfiguration.
Ifthedistortionistoogreatamaterialwillreachitselasticlimitandbegintodistortplastically.
InExplicitDynamics,plasticdeformationiscomputedbyreferencetotheVonMisesyieldcriterion
(alsoknownasPrandtl–Reussyieldcriterion).Thisstatesthatthelocalyieldconditionis
whereYistheyieldstressinsimpletension.Itcanbealsowrittenas
or
)
(since
Thustheonsetofyielding(plasticflow),ispurelyafunctionofthedeviatoricstresses(distortion)anddoesnotdependuponthevalueofthelocalhydrostaticpressureunlesstheyieldstressitselfisafunctionofpressure(asisthecaseforsomeofthestrengthmodels).
IfanincrementalchangeinthestressesviolatestheVonMisescriteriontheneachoftheprincipalstressdeviatorsmustbeadjustedsuchthatthecriterionissatisfied.
Ifanewstressstaten+1iscalculatedfromastatenandfoundtofalloutsidetheyieldsurface,itisbroughtbacktotheyieldsurfacealongalinenormaltotheyieldsurfacebymultiplyingeachofthestressdeviatorsbythefactor
Byadjustingthestressesperpendiculartotheyieldcircleonlytheplasticcomponentsofthestressesareaffected.
Effectssuchasworkhardening,strainratehardening,thermalsoftening,e.t.c.canbeconsideredbymakingYadynamicfunctionofthese
BilinearIsotropic/KinematicHardening
•Usedtodefinetheyieldstress(Y)asalinearfunctionofplasticstrain,εp
•Propertiesdefined
–YieldStrength(Y0)
–TangentModulus(A)
•IsotropicHardening
–Totalstressrangeistwicethemaximumyieldstress,Y
•KinematicHardening
–Totalstressrangeistwicethestartingyieldstress,Y0
–ModelsBauschingereffect
–Oftenrequiredtoaccuratelypredictresponseofthinstructure(shells)
IsotropicvsKinematicHardening
σ2σ2
CurrentYieldsurface
σ1σ1
InitialYieldsurface
IsotropicHardening(σ3=0)KinematicHardening(σ3=0)
MultilinearIsotropic/KinematicHardening
•Usedtodefinetheyieldstress(Y)asapiecewiselinearfunctionofplasticstrain,εp
–Uptotenstress‐strainpairs
•IsotropicHardening
–Totalstressrangeistwicethemaximumyieldstress,Y
•KinematicHardening
–Totalstressrangeistwicethestartingyieldstress,
Y0
–Canonlybeusedwithsolidelements
JohnsonCookStrength
•Usedtomodelmaterials,typicallymetals,subjectedtolargestrains,highstrainratesandhightemperatures.
–Definestheyieldstress,Y,asafunctionofstrain,strainrateandtemperature
εp=effectiveplasticstrain
εp*=normalizedeffectiveplasticstrainrate(1.0sec‐1)
TH=homologoustemperature=(T-Troom)/(Tmelt-Troom)
•Theplasticflowalgorithmusedwiththismodelhasanoptiontoreducehighfrequencyoscillationsthataresometimesobservedintheyieldsurfaceunderhighstrainrates.Afirstorderratecorrectionisappliedbydefault.
•Aspecificheatcapacitymustalsobedefinedtoenablethecalculationoftempe
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