Rice，mathematical analysis in the mechanics of fracture

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1、J.RRice,"MathematicalAnalysisintheMechanicsofFracture",Chapter3ofFracture:AnAdvancedTreatise(Vol.2,MathematicalFundamentals)(ed.H.Liebowitz),AcademicPress,N.Y.,1968,pp.191-311.CHAPTER3MATHEMATICALANALYSISINTHEMECHANICSOFFRACTUREJamesR.RiceI.Introduction19

2、2II.PreliminariesandRelevantConceptsfromtheMechanicsofSolids193A.StressandStrainFields194B.Elasticity195C.Two-DimensionalLinearElasticDeformationFields196D.ContinuumPlasticity200E.EnergyVariationsandAssociatedMethods205III.LinearElasticityintheAnalysisofD

3、eformationandFracture213A.LinearElasticCrackTipStressFields214B.SomeElasticCrackProblems218C.ApproximateMethodsforElasticStressAnalysisofCracks223D.EnergyVariationsinElasticCrackProblems229E.ElasticBrittleFracture232F.DynamicSingularitiesforRunningCracks2

4、35G.StressConcentrationsandEnergyVariationsforNotches238IV.PlasticityintheAnalysisofDeformationandFracture243A.Small-ScaleYieldingnearCracksandNotches.243B.CracksinElastic-PlasticAntiplaneStrainFields246C.CracksinElastic-PlasticTensileFields262D.Elastic-P

5、lasticAnalysisofExtendingCracksandFractureInstability277E.Elastic-Plastic$trainConcentrationsatSmooth-EndedNotches288F.LimitAnalysisofNotchedBodies296G.FractureMechanismsinDuctileMaterials297V.RecommendedResearch301VI.Summary304Symbols306References308Abst

6、ract:Thischaptersurveysmathematicalmethodsandprincipalresultsinthemechanicsoffracture.Primaryemphasisisplacedontheanalysisofcrackextensionastreatedthroughmethodsofconti~uummechanics.SectionIIbegins191192JAMESR.RICEwithrelevantconceptsandbasicequationsfrom

7、themechanicsofsolids,includingasurveyofelasticityandplasticity,andofassociatedmathematicalmethodsforboundaryvalueproblems,suchasanalyticfunctiontheory.Energycomparisonmethodsandtherelatedpath-independentenergyintegralareintroducedinthissection;thesenovelm

8、ethodsofanalysisprovetobewidelyapplicableforsubse•quentlytreatednotchandcrackproblems.SectionIIIdealswiththeapplicationoflinearelasticitytofracture.Severaltwo-dimensionalcrack,problemsaresolvedandapproximatemethodsa