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外文原版-multiscale_modeling_digimat_to_ansys.pdf

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外文原版-multiscale_modeling_digimat_to_ansys.pdf

1|PageCopyright©eXstreamengineering,2009MultiScaleModelingofCompositeMaterialsandStructureswithDIGIMATtoANSYSDocumentVersion1.0,February2009Copyright,eXstreamengineering,2009infoeXstream.comwww.eXstream.comMaterialsEngineeringPlastics,ReinforcedPlastics.eXstreamTechnologyDIGIMAT,DigimatMF,DigimatFE,DigimattoANSYS,MAP.ComplementaryCAETechnologyMoldflow,Moldex3D,SigmaSoft,ANSYS.IndustryMaterialSuppliers,Automotive,Aerospace,ConsumerIndustrialProducts.TABLEOFCONTENTEXECUTIVESUMMARY...................................................................................................................................2MaterialMultiScaleModelinganintroduction.....................................................................................2FEHomogenizationanapplicationtonanocomposites..........................................................................5ModelingFillerClustering,atypicalnanoeffect..................................................................................5ResultComparison...............................................................................................................................7FE/MFHCoupledComputationanapplicationtoanindustrialpart.....................................................9ProblemDescription...............................................................................................................................9MaterialModeling...............................................................................................................................10SimulationResults.................................................................................................................................11Bibliography........................................................................................................................................12LegalNotice.eX,eXdigimatandeXstreamengineeringareregisteredtrademarksofeXstreamengineeringSA.Theotherproductandcompanynamesandlogosaretrademarksorregisteredtrademarksoftheirrespectiveowners.2|PageCopyright©eXstreamengineering,2009EXECUTIVESUMMARYInthispaper,webrieflyintroducetwomultiscalemodelingapproaches,namelytheMeanFieldMFHandFiniteElementHomogenizationFEHmethods.Thesepowerfultechniquesrelatethemicroscopicandmacroscopicstressandstrainfieldswhenmodelingmaterialbehaviorsandhencecancapturetheinfluenceofthematerialmicrostructurei.e.fiberorientation,fibercontent,fiberlength,etc.onitsmacroscopicresponse.Toillustratethesetechniques,wealsopresentianapplicationoffiniteelementhomogenizationtoananostructureandiithestudyofaninjectedglassfiberreinforcedplasticneonlightclaspusingfiniteelementcomputationsatthemacroscalecoupledwithMFhomogenizationatthemicroscale.MaterialMultiScaleModelinganintroductionAsamotivatingexample,letusconsideraplasticpartmadeupofathermoplasticpolymerreinforcedwithshortglassfibers.Astypicaloftheinjectionmoldingmanufacturingprocess,thefiberdistributioninsidethefinalproductwillvarywidelyintermsoforientationandlength,seeFigure1.Thecompositematerialwillbebothanisotropicandheterogeneous,whichmakesitextremelydifficulttoperformareliablesimulationoftheproductusingaclassicalapproachbasedonmacroscopicconstitutivemodels.However,apredictivesimulationispossibleviaamultiscaleapproach,whichcanbedescribedinarathergeneralsettingasfollows.Figure1Fiberorientationdistributioninaninjectedglassfiberreinforcedplasticclutchpedal.CourtesyofRhodiaTrelleborg.Letusstudyaheterogeneoussolidbodywhosemicrostructureconsistsofamatrixmaterialandmultiplephasesofsocalledinclusions,whichcanbeshortfibers,platelets,particles,microcavitiesormicrocracks.OurobjectiveistopredicttheresponseofthebodyundergivenloadsandboundaryconditionsBCs,basedonitsmicrostructure.Wecandistinguishtwoscales,themicroscopicandmacroscopiclevels,respectively.Theformercorrespondstothescaleoftheheterogeneities,whileatthemacroscale,thesolidcanbeseenaslocallyhomogeneousseeFigure2.Inpractice,itwouldbecomputationallyimpossibletosolvethemechanicalproblematthefinemicroscale.Therefore,weconsiderthemacroscaleandassumethateachmaterialpointisthecenterofarepresentativevolumeelementRVE,whichcontainstheunderlyingheterogeneousmicrostructure.Classicalsolidmechanicsanalysisiscarriedoutatthemacroscale,exceptthatateachcomputationpoint,strainorstressvaluesaretransmittedasBCstotheunderlyingRVE.Inotherwords,anumericalzoomisrealizedateachmacropoint.TheRVEproblemsaresolvedandeachofthemreturnsstressandstiffnessvalues,whichareusedatthemacroscale.3|PageCopyright©eXstreamengineering,2009Figure2Illustrationofthemultiscalematerialmodelingapproach,afterNematNasserandHori1.NowtheonlydifficultyinthistwoscalesandmoregenerallymultiscaleapproachistosolvetheRVEproblems.ItcanbeshownthatforaRVEunderclassicalBCs,themacrostrainsandstressesareequaltothevolumeaveragesovertheRVEoftheunknownmicrostrainandstressfieldsinsidetheRVE.Inlinearelasticity,relatingthosetwomeanvaluesgivestheeffectiveoroverallstiffnessofthecompositeatthemacroscale.InordertosolvetheRVEproblem,onecanusethewellknownfiniteelementFEmethod,seeFigures7to10.Thismethodofferstheadvantagesofbeingverygeneralandextremelyaccurate.However,ithastwomajordrawbackswhichareseriousmeshingdifficultiesforrealisticmicrostructuresandalargeCPUtimefornonlinearproblems,suchasforinelasticmaterialbehaviour.AnothercompletelydifferentmethodismeanfieldhomogenizationMFH,whichisbasedonassumedrelationsbetweenvolumeaveragesofstressorstrainfieldsineachphaseofaRVEseeFigure3.ComparedtothedirectFEmethod,andactuallytoallotherexistingscaletransitionmethods,MFHisboththeeasiesttouseandthefastestintermsofCPUtime.However,twoshortcomingsofMFHarethatitisunabletogivedetailedstrainandstressfieldsineachphaseanditisrestrictedtoellipsoidalinclusionshapes.Figure3Meanfieldhomogenizationprocessilocalstrainsarecomputedbasedonthemacrostrains,iilocalstressesarecomputedbasedonthelocalstrainsandaccordingtoeachphaseconstitutivemodel,andiiimacrostressesarecomputedbyaveragingthelocalstresses.4|PageCopyright©eXstreamengineering,2009AtypicalexampleofMFHistheMoriTanakamodel2whichissuccessfullyapplicabletotwophasecompositeswithidenticalandalignedellipsoidalinclusions.ThemodelassumesthateachinclusionoftheRVEbehavesasifitwerealoneinaninfinitebodymadeoftherealmatrixmaterial.TheBCsinthesingleinclusionproblemcorrespondtothevolumeaverageofthestrainfieldinthematrixphaseoftherealRVE.ThesingleinclusionproblemwassolvedanalyticallybyJ.D.Eshelby3inalandmarkpaper,whichisthecornerstoneofMFHmodels.Figure4SchematicoftheMoriTanakahomogenizationprocedure.MoriTanakaandotherMFHmodelsweregeneralizedtoothercases,suchasthermoelasticcoupling,twophasecompositeswithmisalignedfibersusingamultistepapproachormultiphasecompositesusingamultilevelmethod.ThepredictionshavebeenextensivelyverifiedagainstdirectFEsimulationofRVEsorvalidatedagainstexperimentalresults.Asageneralconclusion,itwasfoundthatinlinearthermoelasticity,MFHcangiveextremelyaccuratepredictionsofeffectiveproperties,althoughfordistributedorientations,progressinclosureapproximationwillbewelcomed.NotealsothatMFHcanbeusedforUD,andforeachyarninwovencomposites.AnimportantandstillongoingeffortbothintheoreticalmodelingandincomputationalmethodsisthegeneralizationofMFHtothematerialorgeometricnonlinearrealms.Suchextensioninvolvessomemajordifficulties.Thefirstoneislinearization,whereconstitutiveequationsatmicroscaleneedtobelinearizedontolinearelasticorthermoelasticlikeformat.Thesecondissueisthedefinitionofsocalledcomparisonmaterialswhicharefictitiousmaterialsdesignedtopossessuniforminstantaneousstiffnessoperatorsineachphase.Thenextproblemtobesolvedisfirstordervssecondorderhomogenization.Infirstorderhomogenizationcomparisonmaterialsarecomputedwithrealconstitutivemodelsbutvolumeaveragesofstrainorstressfieldsperphase.Inasecondorderformulation,richerstatisticalinformation,namelythevarianceofstrainorstressfieldsperphaseisalsotakenintoaccount.Finally,averytechnicaldifficultyconcernsthecomputationofEshelbysorHillstensorsandisrelatedtotheanisotropyofthecomparisoninstantaneousstiffnessoperator.Withinacoupledmultiscaleanalysis,FEmethodisusedatmacroscale,whileateachGaussintegrationpoint,MFHcomputationiscarriedout,eitherinthelinearornonlinearregime.Thisisthemostfeasibleapproachinpractice.SeeFigure5.EachinclusionRVEhomogenization

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