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1、THEORETICAL&APPLIEDMECHANICSLETTERS2,021003(2012)CouplingbetweenfiniteelementmethodandmaterialpointmethodforproblemswithextremedeformationYanpingLian,XiongZhang,a)andYanLiuAML,SchoolofAerospace,TsinghuaUniversity,Beijing100084,China(Received31December2011;accepted10
2、January2012;publishedonline10March2012)AbstractAsaLagrangianmeshlessmethod,thematerialpointmethod(MPM)issuitablefordynamicproblemswithextremedeformation,butitseciencyandaccuracyarenotasgoodasthatofthe niteelementmethod(FEM)forsmalldeformationproblems.Therefore,ana
3、lgorithmforthecouplingofFEMandMPMisproposedtotakeadvantagesofbothmethods.Furthermore,aconversionschemeofelementstoparticlesisdeveloped.Hence,thematerialdomainis rstlydiscretizedby niteelements,andthenthedistortedelementsareautomaticallyconvertedintoMPMparticlestoav
4、oidelemententanglement.Theinteractionbetween niteelementsandMPMparticlesisimplementedbasedonthebackgroundgridinMPMframework.NumericalresultsareingoodagreementwithexperimentaldataandtheeciencyofthismethodishigherthanthatofbothFEMandMPM.c2012TheChineseSocietyofTheor
5、eticalandAppliedMechanics.[doi:10.1063/2.1202103]Keywordsmaterialpointmethod,couplingmethod,conversionscheme,penetration,landslideNumericalsimulationofproblemsinvolvingextrememain.Ineachtimestep,theparticlesareattachedtodeformation,suchasexplosion,impactandlandslid
6、e,isthebackgroundgridsothegridservesasa niteel-abigchallengeforLagrangian niteelementmethodementdiscretizationtothematerialdomain.Unlike(FEM)duetothemeshdistortionwhichwilldecreaseothermeshlessmethods,thetrialfunctionsofMPMareitseciencyandaccuracysigni cantly.Inco
7、ntrastthesameasthoseofFEM.SoMPMshowssomead-toLagrangianmethods,EulerianmethodsuseEule-vantagesoverothermeshlessmethodsineciencyandrianmeshwithoutmeshdistortionbutareaccompaniedtensionstability10.However,theeciencyofMPMisbythedicultiesfortherepresentationofthebou
8、nd-notasgoodasthatofFEMduetothemappingsbe-aryofmaterialandtrackingthedeformationhistorytweenbackgroundgridandparticles,andtheaccuracyofmaterial.A
