abaqus中UMAT子程序编写方法.docx
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abaqus中UMAT子程序编写方法.docx
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abaqus中UMAT子程序编写方法
UMAT
Usersubroutinetodefineamaterial'smechanicalbehavior.
Product:
Abaqus/Standard
Warning:
Theuseofthissubroutinegenerallyrequiresconsiderableexpertise.Youarecautionedthattheimplementationofanyrealisticconstitutivemodelrequiresextensivedevelopmentandtesting.Initialtestingonasingle-elementmodelwithprescribedtractionloadingisstronglyrecommended.
References
∙“User-definedmechanicalmaterialbehavior,”Section25.7.1oftheAbaqusAnalysisUser'sManual
∙“User-definedthermalmaterialbehavior,”Section25.7.2oftheAbaqusAnalysisUser'sManual
∙*USERMATERIAL
∙“SDVINI,”Section4.1.11oftheAbaqusVerificationManual
∙“UMATandUHYPER,”Section4.1.21oftheAbaqusVerificationManual
Overview
UsersubroutineUMAT:
∙canbeusedtodefinethemechanicalconstitutivebehaviorofamaterial;
∙willbecalledatallmaterialcalculationpointsofelementsforwhichthematerialdefinitionincludesauser-definedmaterialbehavior;
∙canbeusedwithanyprocedurethatincludesmechanicalbehavior;
∙canusesolution-dependentstatevariables;
∙mustupdatethestressesandsolution-dependentstatevariablestotheirvaluesattheendoftheincrementforwhichitiscalled;
∙mustprovidethematerialJacobianmatrix,
forthemechanicalconstitutivemodel;
∙canbeusedinconjunctionwithusersubroutineUSDFLDtoredefineanyfieldvariablesbeforetheyarepassedin;and
∙isdescribedfurtherin“User-definedmechanicalmaterialbehavior,”Section25.7.1oftheAbaqusAnalysisUser'sManual.
Storageofstressandstraincomponents
InthestressandstrainarraysandinthematricesDDSDDE,DDSDDT,andDRPLDE,directcomponentsarestoredfirst,followedbyshearcomponents.ThereareNDIdirectandNSHRengineeringshearcomponents.Theorderofthecomponentsisdefinedin“Conventions,”Section1.2.2oftheAbaqusAnalysisUser'sManual.Sincethenumberofactivestressandstraincomponentsvariesbetweenelementtypes,theroutinemustbecodedtoprovideforallelementtypeswithwhichitwillbeused.
Defininglocalorientations
Ifalocalorientation(“Orientations,”Section2.2.5oftheAbaqusAnalysisUser'sManual)isusedatthesamepointasusersubroutineUMAT,thestressandstraincomponentswillbeinthelocalorientation;and,inthecaseoffinite-strainanalysis,thebasissysteminwhichstressandstraincomponentsarestoredrotateswiththematerial.
Stability
Youshouldensurethattheintegrationschemecodedinthisroutineisstable—nodirectprovisionismadetoincludeastabilitylimitinthetimesteppingschemebasedonthecalculationsinUMAT.
Convergencerate
DDSDDEand—forcoupledtemperature-displacementandcoupledthermal-electrical-structuralanalyses—DDSDDT,DRPLDE,andDRPLDTmustbedefinedaccuratelyifrapidconvergenceoftheoverallNewtonschemeistobeachieved.Inmostcasestheaccuracyofthisdefinitionisthemostimportantfactorgoverningtheconvergencerate.Sincenonsymmetricequationsolutionisasmuchasfourtimesasexpensiveasthecorrespondingsymmetricsystem,iftheconstitutiveJacobian(DDSDDE)isonlyslightlynonsymmetric(forexample,africtionalmaterialwithasmallfrictionangle),itmaybelessexpensivecomputationallytouseasymmetricapproximationandacceptaslowerconvergencerate.
AnincorrectdefinitionofthematerialJacobianaffectsonlytheconvergencerate;theresults(ifobtained)areunaffected.
Specialconsiderationsforvariouselementtypes
Thereareseveralspecialconsiderationsthatneedtobenoted.
Availabilityofdeformationgradient
Thedeformationgradientisavailableforsolid(continuum)elements,membranes,andfinite-strainshells(S3/S3R,S4,S4R,SAXs,andSAXAs).Itisnotavailableforbeamsorsmall-strainshells.Itisstoredasa3×3matrixwithcomponentequivalenceDFGRD0(I,J)
.Forfullyintegratedfirst-orderisoparametricelements(4-nodequadrilateralsintwodimensionsand8-nodehexahedrainthreedimensions)theselectivelyreducedintegrationtechniqueisused(alsoknownasthe
technique).Thus,amodifieddeformationgradient
ispassedintousersubroutineUMAT.Formoredetails,see“Solidisoparametricquadrilateralsandhexahedra,”Section3.2.4oftheAbaqusTheoryManual.
Beamsandshellsthatcalculatetransverseshearenergy
IfusersubroutineUMATisusedtodescribethematerialofbeamsorshellsthatcalculatetransverseshearenergy,youmustspecifythetransverseshearstiffnessaspartofthebeamorshellsectiondefinitiontodefinethetransverseshearbehavior.See“Shellsectionbehavior,”Section28.6.4oftheAbaqusAnalysisUser'sManual,and“Choosingabeamelement,”Section28.3.3oftheAbaqusAnalysisUser'sManual,forinformationonspecifyingthisstiffness.
Open-sectionbeamelements
WhenusersubroutineUMATisusedtodescribethematerialresponseofbeamswithopensections(forexample,anI-section),thetorsionalstiffnessisobtainedas
whereJisthetorsionalconstant,Aisthesectionarea,kisashearfactor,and
istheuser-specifiedtransverseshearstiffness(see“Transverseshearstiffnessdefinition”in“Choosingabeamelement,”Section28.3.3oftheAbaqusAnalysisUser'sManual).
Elementswithhourglassingmodes
Ifthiscapabilityisusedtodescribethematerialofelementswithhourglassingmodes,youmustdefinethehourglassstiffnessfactorforhourglasscontrolbasedonthetotalstiffnessapproachaspartoftheelementsectiondefinition.Thehourglassstiffnessfactorisnotrequiredforenhancedhourglasscontrol,butyoucandefineascalingfactorforthestiffnessassociatedwiththedrilldegreeoffreedom(rotationaboutthesurfacenormal).See“Sectioncontrols,”Section26.1.4oftheAbaqusAnalysisUser'sManual,forinformationonspecifyingthestiffnessfactor.
Pipe-soilinteractionelements
Theconstitutivebehaviorofthepipe-soilinteractionelements(see“Pipe-soilinteractionelements,”Section31.12.1oftheAbaqusAnalysisUser'sManual)isdefinedbytheforceperunitlengthcausedbyrelativedisplacementbetweentwoedgesoftheelement.Therelative-displacementsareavailableas“strains”(STRANandDSTRAN).ThecorrespondingforcesperunitlengthmustbedefinedintheSTRESSarray.TheJacobianmatrixdefinesthevariationofforceperunitlengthwithrespecttorelativedisplacement.
Fortwo-dimensionalelementstwoin-planecomponentsof“stress”and“strain”exist(NTENS=NDI=2,andNSHR=0).Forthree-dimensionalelementsthreecomponentsof“stress”and“strain”exist(NTENS=NDI=3,andNSHR=0).
Largevolumechangeswithgeometricnonlinearity
Ifthematerialmodelallowslargevolumechangesandgeometricnonlinearityisconsidered,theexactdefinitionoftheconsistentJacobianshouldbeusedtoensurerapidconvergence.Theseconditionsaremostcommonlyencounteredwhenconsideringeitherlargeelasticstrainsorpressure-dependentplasticity.Intheformercase,total-formconstitutiveequationsrelatingtheCauchystresstothedeformationgradientarecommonlyused;inthelattercase,rate-formconstitutivelawsaregenerallyused.
Fortotal-formconstitutivelaws,theexactconsistentJacobian
isdefinedthroughthevariationinKirchhoffstress:
Here,Jisthedeterminantofthedeformationgradient,
istheCauchystress,
isthevirtualrateofdeformation,and
isthevirtualspintensor,definedas
and
Forrate-formconstitutivelaws,theexactconsistentJacobianisgivenby
Usewithincompressibleelasticmaterials
Foruser-definedincompressibleelasticmaterials,usersubroutineUHYPERshouldbeusedratherthanusersubroutineUMAT.InUMATincompressiblematerialsmustbemodeledviaapenaltymethod;thatis,youmustensurethatafinitebulkmodulusisused.Thebulkmodulusshouldbelargeenoughtomodelincompressibilitysufficientlybutsmallenoughtoavoidlossofprecision.Asageneralguideline,thebulkmodulusshouldbeabout
–
timestheshearmodulus.Thetangentbulkmodulus
canbecalculatedfrom
IfahybridelementisusedwithusersubroutineUMAT,Abaqus/StandardwillreplacethepressurestresscalculatedfromyourdefinitionofSTRESSwiththatderivedfromtheLagrangemultiplierandwillmodifytheJacobianappropriately.
Forincompressiblepressure-sensitivematerialstheelementchoiceisparticularlyimportantwhenusingusersubroutineUMAT.Inparticular,first-orderwedgeelementsshouldbeavoided.Fortheseelementsthe
techniqueisnotusedtoalterthedeformationgradientthatispassedintousersubroutineUMAT,whichincreasestheriskofvolumetriclocking.
IncrementsforwhichonlytheJacobiancanbedefined
Abaqus/StandardpasseszerostrainincrementsintousersubroutineUMATtostartthefirstincrementofallthestepsandallincrementsofstepsforwhichyouhavesuppressedextrapolation(see“Procedures:
overview,”Section6.1.1oftheAbaqusAnalysisUser'sManual).InthiscaseyoucandefineonlytheJacobian(DDSDDE).
Utilityroutines
SeveralutilityroutinesmayhelpincodingusersubroutineUMAT.Theirfunctionsincludedeterminingstressinvariantsforastresstensorandcalculatingprincipalvaluesanddirectionsforstressorstraintensors.Theseutilityroutinesarediscussedindetailin“Obtainingstressinvariants,principalstress/strainvaluesanddirections,androtatingtensorsinanAbaqus/Standardanalysis,”Section2.1.11.
Usersubroutineinterface
SUBROUTINEUMAT(STRESS,STATEV,DDSDDE,SSE,SPD,SCD,
1RPL,DDSDDT,DRPLDE,DRPLDT,
2STRAN,DSTRAN,TIME,DTIME,TEMP,DTEMP,PREDEF,DPRED,CMNAME,
3NDI,NSHR,NTENS,NSTATV,PROPS,NPROPS,COORDS,DROT,PNEWDT,
4CELENT,DFGRD0,DFGRD1,NOEL,NPT,LAYER,KSPT
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