清华弹性力学课件_elasticity of solids

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

2、tionofElasticityTwoPhysicalOriginsofElasticityTensorDescriptionofElasticityPhysicalFoundationofElasticSymmetry1Chapter2ReferencesJ.H.Weiner，Statisticalmechanicsofelasticity,Wiley,1981Green&Zerna，Theoreticalelasticity,1968Ashby&Jones，Engineeringmaterials2Chap

3、ter2DefinitionofElasticityDifferencebetweensolidsandfluidsMechanicsofSolids,TheNewEncyclopediaofBritannica,15thedition,Vol.23,pp.734-747,2002,“Amaterialiscalledsolidratherthanfluidifitcanalsosupportasubstantialshearingforceoverthetimescaleofsomenaturalproces

4、sortechnologicalapplicationofinterest.”J.R.Rice3Chapter2.1DefinitionofElasticityElasticityWhereExplicitdependenceonXcanbeeliminatedforhomogeneousmaterial4Chapter2.1DefinitionofElasticityRemarksStressisirrelevanttothestrainrate,aswellastothehistoryofdeformati

5、on.Nohysteresis:theoriginalconfigurationisrecoveredafterunload.infinitesimaldeformationhomogeneousmateriallinearelasticity6Chapter2.1DefinitionofElasticityHyperelasticityTwoassumptions:Theresponseoftheelasticbodyonlydependsonitscurrentstate.Thecurrentstateof

6、anelasticbodycanbedescribedbyatensor.PathindependentconditionbygreatmathematicianGreen7Chapter2.1DefinitionofElasticityHyperelasticitylinearelastic:generalizedHooke’slaw:8Chapter2.1TwoPhysicalOriginsofElasticityEnergeticandEntropicStressesHelmholtzfreeenergy

7、:Maxwellrelation:9Chapter2.2TwoPhysicalOriginsofElasticityEnergeticandEntropicStresses10Chapter2.2TwoPhysicalOriginsofElasticityCrystalsTheprimarybondingionic,covalentormetallicmeltat1000-5000KThesecondarybondingVanderWaalsandhydrogenbondsmeltat100-500K11Cha

8、pter2.2TwoPhysicalOriginsofElasticityCrystals12Chapter2.2TwoPhysicalOriginsofElasticityCrystals13Stiffness：Maximuminter-atomicforceoccursatElasticityoflinearHooke’slawChapter2.2TwoPhysicalOrigin