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1、ComputerMethodsinAppliedMechanicsandEngineering90(1991)781-804North-HollandAdaptivemeshrefinementinstrainlocalizationproblemsM.OrtizandJ.J.t)uigley,IVDivisionofEngineering,BrownUniversity,Providence,RI,USAReceived3(IAugust1990Revisedmanuscriptreceived20February1991Anadap
2、tivemeshingmethodtailoredtoproblemsofstrainlocalizationisgiven.Theadaptionstrategyconsistsofequi-distributingthevariationofthevelocityfieldovertheelementsofthemesh.Aheuristicjustificationfortheuseofvariationsasindicatorsisadvanced,andpossibleconnectionswithinterpolatione
3、rrorboundsarediscussed.MeshesareconstructedbyDelaunaytriangulatiorItisshownhowtheHu-Washizuprincipledeterminesaconsistenttransferoperatorforthestatevariables.Examplesofapplicationaregivenwhichdemonstratetheversatilityofthemethod.1.IntroductionProblemsofstrainlocalization
4、ofteninvolvetwoormorewell-differentiatedlengthscales:aglobalscalecommensuratewiththemacroscopicfeaturesofthesolid;andalocalormicroscopicscaleoftheorderoftheshearbandthickness.Inmanycasesofinterest,themicro-scalesteadilycollapsesintime.Dependingonthelevelofmodeling,thispr
5、ocessofcollapsecanbeself-limitingoritcancontinueadinfinitum.Examplesoftheformertypeofbehaviorarefoundinsolidswithanintrinsiccharacteristiclength,suchasnon-localandpolarcontinua,thermallyconductingplasticsolidswiththermalsoftening,solidswithcohesiveinterfaces,andothers.By
6、wayofcontrast,rate-dependentsolidslackinganinternallengthexhibitshearbandsforwhichthecollapseofthemicroscalemaynotbeself-limiting.Ineithercase,itmaybeofinteresttoresolvethesolutionatboththemacroandmicroscalesconcurrently.Becausethetime-dependentlocation,shapeandstructure
7、oftheshearbandaregenerallynotknownbeforehand,methodsofsolutionincorporatingsomeformofmeshadaptivitynaturallysuggestthemselves.Whereasadaptivemethodsforlinearelasticityandcertainclassesofnonlinearproblemshavebeendevelopedtoanadvancedstate(see,e.g.,[1]),thereiscomparativel
8、ymuchlessexperienceonthedesignandapplicationofmeshadaptiontechniquestoproblemsinvolvinghistorydependent
