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1、INTERNATIONALJOURNALFORNUMERICALMETHODSINENGINEERINGInt.J.Numer.Meth.Engng2015;101:127147Publishedonline1October2014inWileyOnlineLibrary(wileyonlinelibrary.com).DOI:10.1002/nme.4792AxisymmetricformofthegeneralizedinterpolationmaterialpointmethodJohnA.Nairn1,*,andJamesE.Guilkey21WoodScienceandEng
2、ineering,OregonStateUniversity,Corvallis,OR,USA2SchlumbergerTechnologyCorporation,Rasharon,TX,USASUMMARYThispaperreformulatestheaxisymmetricformofthematerialpointmethod(MPM)usinggeneralizedinterpolationmaterialpoint(GIMP)methods.Thereformulationledtoaneedfornewshapefunctionsandgradientsspecificfo
3、raxisymmetrythatwerenotavailablebefore.ThenewshapefunctionsdiffermostfromplanarshapefunctionsneartheoriginwhererD0.AsecondpurposeforthispaperwastoevaluatetheconsequencesofaxisymmetryonavarietyMPMextensionsthathavebeendevelopedsincetheoriginalworkonaxisymmetricMPM.Theseextensionsincludedconvected
4、particledomainintegration(CPDI),tractionboundaryconditions,explicitcracks,multimaterialmodeMPMforcontact,thermalconduction,andsolventdiffusion.Someexamplesshowthattheaxisymmetricshapefunctionsworkwellandareespeciallycrucialneartheorigin.Onereal-worldexampleisgivenformodelingacylinder-penetration
5、problem.Finally,achecklistforsoftwaredevelopmentdescribesalltasksneededtoconvert2Dplanaror3DcodestoincludeanoptionforaxisymmetricMPM.Copyright©2014JohnWiley&Sons,Ltd.Received10January2013;Revised20December2013;Accepted18August2014KEYWORDS:materialpointmethod;axisymmetry;penetration;MPM;GIMP;CPDI
6、1.INTRODUCTIONThematerialpointmethod(MPM)[1,2]isenjoyingincreasingpopularityasacompu-tationaltoolforsolidmechanicsinvestigations,particularlyforsimulationsinvolvinglargedeformations[3],contact[46],andfracture[79].Inaddition,itsutilityfortreatinghistory-dependentmaterialpropertieshasledtoMPMbeing
7、implementedinthehistoricallyEulerianCTHsoftwarefromSandiaNationalLaboratory[10].ExtensionstotheoriginalMPMformu-lationsdescribedbySulskyetal.[1,2]includetheGeneralizedInterpolationMaterialPoint(GIMP)Method[11]andmorerecently
