abaqus中UMAT子程序编写方法.docx

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