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1、InternationalJournalofSolidsandStructures48(2011)3001–3010ContentslistsavailableatScienceDirectInternationalJournalofSolidsandStructuresjournalhomepage:www.elsevier.com/locate/ijsolstrAC2continuousapproximationtotheMohr–CoulombyieldsurfaceA.J.Abbo⇑,A.V.Lyamin
2、,S.W.Sloan,J.P.HambletonCentreforGeotechnicalandMaterialsModelling,UniversityofNewcastle,Callaghan,NSW2308,AustraliaarticleinfoabstractArticlehistory:Inspiteofthedevelopmentofmoresophisticatedconstitutivemodelsforsoil,theMohr–CoulombyieldReceived27January2011
3、criterionremainsapopularchoiceforgeotechnicalanalysisduetoitssimplicityandeaseofusebyprac-Receivedinrevisedform14June2011tisingengineers.Theimplementationofthecriterioninfiniteelementprograms,however,presentssomeAvailableonline1July2011numericaldifficultiesduet
4、othegradientdiscontinuitieswhichoccuratboththeedgesandthetipofthehexagonalyieldsurfacepyramid.Furthermore,someimplicittechniquesutilisingconsistenttangentKeywords:stiffnessformulationsareunabletoachievefullquadraticconvergenceastheyieldcriteriaisnotC2con-Mohr
5、–Coulombtinuous.ThispaperextendsthepreviousworkofAbboandSloan(1995)throughtheintroductionofC2ElastoplasticitycontinuousroundingoftheMohr–Coulombyieldsurfaceintheoctahedralplane.Thisapproximation,ConsistenttangentFiniteelementwhencombinedwiththehyperbolicappro
6、ximationinthemeridionalplane(AbboandSloan,1995),describesayieldsurfacethatisC2continuousatallstressstates.ThenewsmoothyieldsurfacecanbemadetoapproximatetheMohr–Coulombyieldfunctionascloselyasrequiredbyadjustingonlytwoparameters,andissuitableforconsistenttange
7、ntstiffnessformulations.CrownCopyrightÓ2011PublishedbyElsevierLtd.Allrightsreserved.1.Introductionyieldsurfacesandimplementtheconstitutivelawasamulti-sur-faceyieldfunctionusingtheformulationofKoiter(1953)(e.g.TheMohr–Coulombyieldcriterionprovidesarelativelysi
8、mpleRistinmaaandTryding,1993;Clausenetal.,2006).Theapproachmodelforsimulatingtheplasticbehaviourofsoil.Othermoreusedinthispaperistoderiveasmoothapproximationtotheyieldsophisticatedconstit
