Explicit-Dynamics-Chapter-9-Material-Models

1-1ANSYS,Inc.Proprietary©2009ANSYS,Inc.Allrightsreserved.February27,2009Inventory#002665Chapter9MaterialModelsANSYSExplicitDynamicsMaterialModels1-2ANSYS,Inc.Proprietary©2009ANSYS,Inc.Allrightsreserved.February27,2009Inventory#002665TrainingManualMaterialBehaviorUnderDynamicLoading•Ingeneral,materialshaveacomplexresponsetodynamicloading•Thefollowingphenomenamayneedtobemodelled–Non-linearpressureresponse–Strainhardening–Strainratehardening–Thermalsoftening–Compaction(porousmaterials)–Orthotropicbehavior(e.g.composites)–Crushingdamage(e.g.ceramics,glass,geologicalmaterials,concrete)–Chemicalenergydeposition(e.g.explosives)–Tensilefailure–Phasechanges(solid-liquid-gas)•Nosinglematerialmodelincorporatesalloftheseeffects•EngineeringDataoffersaselectionofmodelsfromwhichyoucanchoosebasedonthematerial(s)presentinyoursimulationMaterialModels1-3ANSYS,Inc.Proprietary©2009ANSYS,Inc.Allrightsreserved.February27,2009Inventory#002665TrainingManualModelingProvidedByEngineeringDataMaterialModels1-4ANSYS,Inc.Proprietary©2009ANSYS,Inc.Allrightsreserved.February27,2009Inventory#002665TrainingManual•Materialdeformationcanbesplitintotwoindependentparts–VolumetricResponse-changesinvolume(pressure)•Equationofstate(EOS)–DeviatoricResponse-changesinshape•Strengthmodel•Also,itisoftennecessarytospecifyaFailuremodelasmaterialscanonlysustainlimitedamountofstress/deformationbeforetheybreak/crack/cavitate(fluids).MaterialDeformationChangeinVolumeChangeinShapeMaterialModels1-5ANSYS,Inc.Proprietary©2009ANSYS,Inc.Allrightsreserved.February27,2009Inventory#002665TrainingManualPrincipalStresses•Astressstatein3Dcanbedescribedbyatensorwithsixstresscomponents–Componentsdependontheorientationofthecoordinatesystemused.•Thestresstensoritselfisaphysicalquantity–Independentofthecoordinatesystemused•Whenthecoordinatesystemischosentocoincidewiththeeigenvectorsofthestresstensor,thestresstensorisrepresentedbyadiagonalmatrixwhereσ1,σ2,andσ3,aretheprincipalstresses(eigenvalues).•Theprincipalstressesmaybecombinedtoformthefirst,secondandthirdstressinvariants,respectively.•Becauseofitssimplicity,workingandthinkingintheprincipalcoordinatesystemisoftenusedintheformulationofmaterialmodels.MaterialModels1-6ANSYS,Inc.Proprietary©2009ANSYS,Inc.Allrightsreserved.February27,2009Inventory#002665TrainingManualElasticResponse•Forlinearelasticity,stressesaregivenbyHooke’slaw:wherelandGaretheLameconstants(GisalsoknownastheShearModulus)•Theprincipalstressescanbedecomposedintoahydrostaticandadeviatoriccomponent:wherePisthepressureandsiarethestressdeviators•Then:MaterialModels1-7ANSYS,Inc.Proprietary©2009ANSYS,Inc.Allrightsreserved.February27,2009Inventory#002665TrainingManualHooke’sLawGeneralizedNon-LinearResponseEquationofStateStrengthModelNon-linearResponse•ManyapplicationsinvolvestressesconsiderablybeyondtheelasticlimitandsorequiremorecomplexmaterialmodelsFailureModelσi(max,min)=fMaterialModels1-8ANSYS,Inc.Proprietary©2009ANSYS,Inc.Allrightsreserved.February27,2009Inventory#002665TrainingManualModelsAvailableforExplicitDynamicsMaterialModels1-9ANSYS,Inc.Proprietary©2009ANSYS,Inc.Allrightsreserved.February27,2009Inventory#002665TrainingManualElasticConstantsShearModulusGYoung’sModulusEPoisson’sRationBulkModulusKShearModulusYoung’sModulusShearModulusPoisson’sRatioShearModulusBulkModulusYoung’sModulusPoisson’sRatioYoung’sModulusBulkModulusPoisson’sRatioBulkModulusE-2G2GGE3(3G-E)2G(1+n)2G(1+n)3(1-2n)9KG3K+G3K-2G2(3K+G)E2(1+n)E3(1-2n)3EK9K-E3K-E6K3K(1-2n)2(1+n)3K(1-2n)MaterialModels1-10ANSYS,Inc.Proprietary©2009ANSYS,Inc.Allrightsreserved.February27,2009Inventory#002665TrainingManualPhysicalandThermalProperties•Density–AllmaterialmusthaveavaliddensitydefinedforExplicitDynamicssimulations.–ThedensitypropertydefinestheinitialMass/unitvolumeofamaterialattimezero•Thispropertyisautomaticallyincludedinallmodels•SpecificHeat–Thisisrequiredtocalculatethetemperatureusedinmaterialmodelsthatincludethermalsoftening•ThispropertyisautomaticallyincludedinthermalsofteningmodelsMaterialModels1-11ANSYS,Inc.Proprietary©2009ANSYS,Inc.Allrightsreserved.February27,2009Inventory#002665TrainingManualLinearElastic•IsotropicElasticity–Usedtodefinelinearelasticmaterialbehavior•suitableformostmaterialssubjectedtolowcompressions.–Propertiesdefined•Young’sModulus(E)•Poisson’sRatio(ν)–Fromthedefinedproperties,BulkmodulusandShearmodulusarederivedforuseinthematerialsolutions.–TemperaturedependenceofthelinearelasticpropertiesisnotavailableforexplicitdynamicsMaterialModels1-12ANSYS,Inc.Proprietary©2009ANSYS,Inc.Allrightsreserved.February27,2009Inventory#002665TrainingManualLinearElastic•OrthotropicElasticity–Usedtodefinelinearorthotropicelasticmaterialbehavior•suitableformostorthotropicmaterialssubjectedtolowcompressions.–Propertiesdefined•Young’sModulii(Ex,Ey,Ez)•Poisson’sRatios(νxy,νyz,νxz)•ShearModulii(Gxy,Gyz,Gxz)–TemperaturedependenceofthepropertiesisnotavailableforexplicitdynamicsMaterialModels1-13ANSYS,Inc.Proprietary©2009ANSYS,Inc.Allrightsreserved.February27,2009Inventory#002665TrainingManualLinearElas