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

abaqus中UMAT子程序编写方法

UMAT

Usersubroutinetodefineamaterial'smechanicalbehavior.

Product:

Abaqus/Standard

Warning:

Theuseofthissubroutinegenerallyrequiresconsiderableexpertise.Youarecautionedthattheimplementationofanyrealisticconstitutivemodelrequiresextensivedevelopmentandtesting.Initialtestingonasingle-elementmodelwithprescribedtractionloadingisstronglyrecommended.

References

“User-definedmechanicalmaterialbehavior,”Section25.7.1ofthe

AbaqusAnalysisUser'sManual

“User-definedthermalmaterialbehavior,”Section25.7.2ofthe

AbaqusAnalysisUser'sManual

*USERMATERIAL

“SDVINI,”Section4.1.11oftheAbaqusVerificationManual

“UMATandUHYPER,”Section4.1.21oftheAbaqusVerificationManual

Overview

UsersubroutineUMAT:

canbeusedtodefinethemechanicalconstitutivebehaviorofa

material;

willbecalledatallmaterialcalculationpointsofelementsfor

whichthematerialdefinitionincludesauser-definedmaterial

behavior;

canbeusedwithanyprocedurethatincludesmechanicalbehavior;

canusesolution-dependentstatevariables;

mustupdatethestressesandsolution-dependentstatevariablesto

theirvaluesattheendoftheincrementforwhichitiscalled;

mustprovidethematerialJacobianmatrix,,forthe

mechanicalconstitutivemodel;

canbeusedinconjunctionwithusersubroutineUSDFLDtoredefine

anyfieldvariablesbeforetheyarepassedin;and

isdescribedfurtherin“User-definedmechanicalmaterial

behavior,”Section25.7.1oftheAbaqusAnalysisUser'sManual.

Storageofstressandstraincomponents

InthestressandstrainarraysandinthematricesDDSDDE,DDSDDT,andDRPLDE,directcomponentsarestoredfirst,followedbyshearcomponents.ThereareNDIdirectandNSHRengineeringshearcomponents.Theorderof

“Conventions,”Section1.2.2oftheAbaqusthecomponentsisdefinedin

AnalysisUser'sManual.Sincethenumberofactivestressandstraincomponentsvariesbetweenelementtypes,theroutinemustbecodedtoprovideforallelementtypeswithwhichitwillbeused.Defininglocalorientations

Ifalocalorientation（“Orientations,”Section2.2.5oftheAbaqus

AnalysisUser'sManual）isusedatthesamepointasusersubroutineUMAT,thestressandstraincomponentswillbeinthelocalorientation;and,inthecaseoffinite-strainanalysis,thebasissysteminwhichstressandstraincomponentsarestoredrotateswiththematerial.Stability

Youshouldensurethattheintegrationschemecodedinthisroutineisstable—nodirectprovisionismadetoincludeastabilitylimitinthetimesteppingschemebasedonthecalculationsinUMAT.

Convergencerate

DDSDDEand—forcoupledtemperature-displacementandcoupled

thermal-electrical-structuralanalyses—DDSDDT,DRPLDE,andDRPLDTmust

bedefinedaccuratelyifrapidconvergenceoftheoverallNewtonschemeistobeachieved.Inmostcasestheaccuracyofthisdefinitionisthemostimportantfactorgoverningtheconvergencerate.Sincenonsymmetricequationsolutionisasmuchasfourtimesasexpensiveasthecorrespondingsymmetricsystem,iftheconstitutiveJacobian（DDSDDE）isonlyslightlynonsymmetric（forexample,africtionalmaterialwithasmallfriction

angle）,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）.Forfully

integratedfirst-orderisoparametricelements（4-nodequadrilateralsintwodimensionsand8-nodehexahedrainthreedimensions）theselectivelyreducedintegrationtechniqueisused（alsoknownasthetechnique）.

Thus,amodifieddeformationgradient

ispassedintousersubroutineUMAT.Formoredetails,see“Solid

isoparametricquadrilateralsandhexahedra,”Section3.2.4oftheAbaqus

TheoryManual.

Beamsandshellsthatcalculatetransverseshearenergy

IfusersubroutineUMATisusedtodescribethematerialofbeamsorshellsthatcalculatetransverseshearenergy,youmustspecifythetransverseshearstiffnessaspartofthebeamorshellsectiondefinitiontodefinethetransverseshearbehavior.See“Shellsectionbehavior,”Section

28.6.4oftheAbaqusAnalysisUser'sManual,and“Choosingabeamelement,”

Section28.3.3oftheAbaqusAnalysisUser'sManual,forinformationon

specifyingthisstiffness.

Open-sectionbeamelements

WhenusersubroutineUMATisusedtodescribethematerialresponseofbeamswithopensections（forexample,anI-section）,thetorsionalstiffnessisobtainedas

whereJisthetorsionalconstant,Aisthesectionarea,kisashearfactor,

andistheuser-specifiedtransverseshearstiffness（see“Transverse

shearstiffnessdefinition”in“Choosingabeamelement,”Section28.3.3

oftheAbaqusAnalysisUser'sManual）.

Elementswithhourglassingmodes

Ifthiscapabilityisusedtodescribethematerialofelementswithhourglassingmodes,youmustdefinethehourglassstiffnessfactorforhourglasscontrolbasedonthetotalstiffnessapproachaspartoftheelementsectiondefinition.Thehourglassstiffnessfactorisnotrequiredforenhancedhourglasscontrol,butyoucandefineascalingfactorforthestiffnessassociatedwiththedrilldegreeoffreedom（rotationaboutthesurfacenormal）.See“Sectioncontrols,”Section26.1.4oftheAbaqus

AnalysisUser'sManual,forinformationonspecifyingthestiffness

factor.

Pipe-soilinteractionelements

Theconstitutivebehaviorofthepipe-soilinteractionelements（see“Pipe-soilinteractionelements,”Section31.12.1oftheAbaqusAnalysis

User'sManual）isdefinedbytheforceperunitlengthcausedbyrelativedisplacementbetweentwoedgesoftheelement.Therelative-displacementsareavailableas“strains”（STRANandDSTRAN）.ThecorrespondingforcesperunitlengthmustbedefinedintheSTRESSarray.TheJacobianmatrixdefinesthevariationofforceperunitlengthwithrespecttorelativedisplacement.

Fortwo-dimensionalelementstwoin-planecomponentsof“stress”and

“strain”exist（NTENS=NDI=2,andNSHR=0）.Forthree-dimensional

elementsthreecomponentsof“stress”and“strain”exist（NTENS=NDI=3,

andNSHR=0）.

Largevolumechangeswithgeometricnonlinearity

Ifthematerialmodelallowslargevolumechangesandgeometricnonlinearityisconsidered,theexactdefinitionoftheconsistentJacobianshouldbeusedtoensurerapidconvergence.Theseconditionsaremostcommonlyencounteredwhenconsideringeitherlargeelasticstrainsorpressure-dependentplasticity.Intheformercase,total-form

utiveequationsrelatingtheCauchystresstothedeformationconstit

gradientarecommonlyused;inthelattercase,rate-formconstitutivelawsaregenerallyused.

Fortotal-formconstitutivelaws,theexactconsistentJacobianis

definedthroughthevariationinKirchhoffstress:

Here,Jisthedeterminantofthedeformationgradient,istheCauchy

stress,isthevirtualrateofdeformation,andisthevirtualspin

tensor,definedas

and

Forrate-formconstitutivelaws,theexactconsistentJacobianisgivenby

Usewithincompressibleelasticmaterials

Foruser-definedincompressibleelasticmaterials,usersubroutineUHYPER

shouldbeusedratherthanusersubroutineUMAT.InUMATincompressible

materialsmustbemodeledviaapenaltymethod;thatis,youmustensurethatafinitebulkmodulusisused.Thebulkmodulusshouldbelargeenoughtomodelincompressibilitysufficientlybutsmallenoughtoavoidlossofprecision.Asageneralguideline,thebulkmodulusshouldbeabout–timestheshearmodulus.Thetangentbulkmoduluscanbe

calculatedfrom

IfahybridelementisusedwithusersubroutineUMAT,Abaqus/Standardwill

replacethepressurestresscalculatedfromyourdefinitionofSTRESSwiththatderivedfromtheLagrangemultiplierandwillmodifytheJacobianappropriately.

Forincompressiblepressure-sensitivematerialstheelementchoiceis

UMAT.Inparticular,particularlyimportantwhenusingusersubroutine

first-orderwedgeelementsshouldbeavoided.FortheseelementsthetechniqueisnotusedtoalterthedeformationgradientthatispassedintousersubroutineUMAT,whichincreasestheriskofvolumetriclocking.IncrementsforwhichonlytheJacobiancanbedefined

Abaqus/StandardpasseszerostrainincrementsintousersubroutineUMAT

tostartthefirstincrementofallthestepsandallincrementsofstepsforwhichyouhavesuppressedextrapolation（see“Procedures:

overview,”

Section6.1.1oftheAbaqusAnalysisUser'sManual）.Inthiscaseyoucan

defineonlytheJacobian（DDSDDE）.

Utilityroutines

SeveralutilityroutinesmayhelpincodingusersubroutineUMAT.Their

functionsincludedeterminingstressinvariantsforastresstensorandcalculatingprincipalvaluesanddirectionsforstressorstraintensors.Theseutilityroutinesarediscussedindetailin“Obtainingstress

invariants,principalstress/strainvaluesanddirections,androtatingtensorsinanAbaqus/Standardanalysis,”Section2.1.11.

Usersubroutineinterface

SUBROUTINEUMAT（STRESS,STATEV,DDSDDE,SSE,SPD,SCD,

1RPL,DDSDDT,DRPLDE,DRPLDT,

2STRAN,DSTRA