chapter2-new.ppt

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1、0TheoryofElasticityIntroductionElasticityofSolidsFieldEquationsofElasticity-DifferentialFormulationPrismaticRodsPlaneProblems–TheoryandSolutionsPlaneProblems–ApplicationsVariationalFormulationofElasticityThree-dimensionalProblemsIndexElasticityofSolidsDefinitionofElasticityTwoPhysicalOriginsofElasti

2、cityTensorDescriptionofElasticityPhysicalFoundationofElasticSymmetry1Chapter2ReferencesJ.H.Weiner，Statisticalmechanicsofelasticity,Wiley,1981Green&Zerna，Theoreticalelasticity,1968Ashby&Jones，Engineeringmaterials2Chapter2DefinitionofElasticityDifferencebetweensolidsandfluidsMechanicsofSolids,TheNewEn

3、cyclopediaofBritannica,15thedition,Vol.23,pp.734-747,2002,“Amaterialiscalledsolidratherthanfluidifitcanalsosupportasubstantialshearingforceoverthetimescaleofsomenaturalprocessortechnologicalapplicationofinterest.”J.R.Rice3Chapter2.1DefinitionofElasticityElasticityWhereExplicitdependenceonXcanbeelimi

4、natedforhomogeneousmaterial4Chapter2.1DefinitionofElasticityRemarksStressisirrelevanttothestrainrate,aswellastothehistoryofdeformation.Nohysteresis:theoriginalconfigurationisrecoveredafterunload.infinitesimaldeformationhomogeneousmateriallinearelasticity6Chapter2.1DefinitionofElasticityHyperelastici

5、tyTwoassumptions:Theresponseoftheelasticbodyonlydependsonitscurrentstate.Thecurrentstateofanelasticbodycanbedescribedbyatensor.PathindependentconditionbygreatmathematicianGreen7Chapter2.1DefinitionofElasticityHyperelasticitylinearelastic:generalizedHooke’slaw:8Chapter2.1TwoPhysicalOriginsofElasticit

6、yEnergeticandEntropicStressesHelmholtzfreeenergy:Maxwellrelation:9Chapter2.2TwoPhysicalOriginsofElasticityEnergeticandEntropicStresses10Chapter2.2TwoPhysicalOriginsofElasticityCrystalsTheprimarybondingionic,covalentormetallicmeltat1000-5000KThesecondarybondingVanderWaalsandhydrogenbondsmeltat100-500

7、K11Chapter2.2TwoPhysicalOriginsofElasticityCrystals12Chapter2.2TwoPhysicalOriginsofElasticityCrystals13Stiffness：Maximuminter-atomicforceoccursatElasticityoflinearHooke’slawChapter2.2TwoPhysicalOrigin