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1、ManuscriptforpublicationasChapter2ofthebookMechanicsandMaterials:FundamentalsandLinkages(eds.M.A.Meyers,R.W.Armstrong,andH.Kirchner),Wiley,publicationexpected1998.FoundationsofSolidMechanicsJamesR.RiceDivisionofEngineeringandAppliedSciencesandDepartmentofEarthandPlanetarySciencesHa
2、rvardUniversityJanuary,19981.IntroductionThischapterisdevotedtoareviewoffoundationsofsolidmechanics.Itisbasedonaneditedtranscriptoftwolecturesbytheauthoronthatsubjectata1993summerschooloftheNSFInstituteforMechanicsandMaterials.Inuniversitycourses,itusuallytakesahealthypartoftheseme
3、stertogooverthematerial.So,itishopedthatthestudentwillappreciatethatthisisindeedareview.Itisassumedthatthematerialhastosomeextentbeenencounteredbefore,anditishopedthatthisquickreviewwillhelpthereaderputthingstogetherinhisorherownmind.Pleaseseethebibliographyforreferencesonthehistor
4、yofthesubject,andforfurtherreadings.Figure1showsanorthogonalCartesianreferenceframe,whichweconsidertobeaNewtonianframe.Coordinatesinspacearedenoted1,2,3;thee'sareunitvectorsalongthesecoordinatedirections.Thevectorx,whichdenotesapositioninspace,hascomponentsx1,x2,x3.visthevelocityve
5、ctorforthisposition.1Wefocusonanarbitrarilychosenregionofsomebody.ThatregionhasvolumeV;itssurfaceisdenotedbyS.WeseeinFig.1anelementofsurface,dS,aunitnormaltothesurface,n,andanelementofvolume,dV.Thequantitieswhicharegoingtoentertheequationsofmotionare,ofcourse,thelinearandangularmom
6、entum.Thesearetakenasintegralsovertheregionofmassdensitytimesvelocityintegratedovervolume,andfortheangularmomentum,thecrossproductofmassdensitytimesvelocityintegratedovervolume:Linearmomentum≡P=∫ρvdV(1)VAngularmomentum(relativetothecoordinateorigin)≡H=∫ρx×vdV(2)VThestudentmayreason
7、ablyask:"Inmicroscopicterms,whatdothesequantitiesmean?"Ofcourse,massdensityisanaverageofmassperunitvolume,andweassumeinatheoryofthetypetobediscussedthatitistakenoverspatialandtemporalscalesthatarelargeenoughtobeindependentofanyfluctuationsatthemicroscopiclevel.Ifweask"Whatdoesveloc
8、itymean?",especiallywhenwe
