IntroductiontoConstitutiveTheoriesIntroductionto本构理论

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1、IntroductiontoConstitutiveTheoriesNicholasZabarasMaterialsProcessDesignandControlLaboratorySibleySchoolofMechanicalandAerospaceEngineering101FrankH.T.RhodesHallCornellUniversityIthaca,NY14853-3801Email:nzabaras@gmail.comURL:http://mpdc.mae.cornell.edu/

2、November7,2013Following:Chapters34-46,MortonE.Gurtin,EliotFried,LallitAnand,TheMechanicsandThermodynamicsofContinua(2010)(freeonlineversionavailableforCornellstudents)FoundationsofSolidMechanics,Fall2013(N.Zabaras)1ConstitutiveEquationsThebalancelawsf

3、ormass,momentum,andenergyandtheimbalancelawforentropyarefundamentalprinciplespresumedtoholdforallbodies(solid,liquid,orgas).Incontrast,theconstitutionofaclassofbodiescomposedofaparticularmaterialisspecifiedbyconstitutiveequations.Constitutiveequa

4、tionslimittheclassofprocessesthatbodiescomprisedofagivenmaterialmayundergo.FoundationsofSolidMechanics,Fall2013(N.Zabaras)2GeneralConsiderationsTruesdell&Noll(1965):Thegeneralphysicallawsinthemselvesdonotsufficetodeterminethedeformationormotionofabody

5、subjecttogivenloading.Beforeadeterminateproblemcanbeformulated,itisnecessarytospecifythematerialofwhichthebodyismade.Suchspecificationisstatedbyconstitutiveequations,whichrelatethestresstensor...tothemotion.E.g.,theclassicaltheoryofelasticityrestsupo

6、ntheassumptionthatthestresstensoratapointdependslinearlyonthechangesinlengthandmutualanglesufferedbyelementsatthatpoint...Theclassicaltheoryofviscousfluidsisbasedontheassumptionthatthestresstensordependslinearlyontheinstantaneousratesofchangeoflengtha

7、ndmutualangle.FoundationsofSolidMechanics,Fall2013(N.Zabaras)3GeneralConsiderationsTruesdell&Noll(1965):Theclassicaltheoryofelasticityandthatofviscousfluidsrepresentinidealformanaspect,andadifferentone,ofthemechanicalbehaviorofnearlyallnaturalmaterial

8、s,and...Eachdoespredictwithconsiderable...accuracytheobservedresponseofmanydifferentnaturalmaterialsincertainrestrictedsituations.FoundationsofSolidMechanics,Fall2013(N.Zabaras)4ConstitutiveResponseFunctionsAconstitutiveequationgivest