内容简介

本书紧密结合工程实际，从变量描述、力学方程建立、线性化求解以及结果应用等几个方面阐述塑性变形过程，系统总结了线性屈服准则的开发及其应用的研究进展，力求做到物理概念明确、推导严谨缜密、预测公式简明实用，使读者对材料的变形特性、塑性加工过程及其结构件的塑性行为有深刻的理解。本书的前两章为基础部分，主要参考了王仲仁、俞茂宏、赵德文、刘相华等人的著作；后五章为线性屈服准则的开发与应用部分，主要选自本人近年来在国内外发表的学术论文。其中收录的内容多数为原始创新成果，曾得到国内外同行的高度赞誉。

目录

1.FundamentalTheoryofStressandStrain1.1SummationConvention1.1.1FreeSubscript1.1.2DumbSubscript1.1.3Differential-formsummationconvection1.2StressAnalysis1.2.1ConceptofStress1.2.2StressStateandItsDescription1.2.3Stresstensoranddeviatoricstresstensor1.3StrainAnalysis1.3.1EngineeringStrainandTrueStrain1.3.2GeometricEquation1.3.3StrainTensorandItsDecompositionReferences2.MechanicalEquationandBoundaryCondition2.1EquilibriumDifferentialEquation2.2DeformationCompatibilityEquation2.3ClassicalYieldCriteria
2.3.1ConceptofYieldCriterion2.3.2TrescaYieldCriterion2.3.3MisesYieldCriterion2.3.4GeometricalIllustrationofYieldCriteria2.3.5TwinShearStressYieldCriterion2.3.6Unifiedyieldcriterion2.4ConstitutiveEquation2.4.1IncrementalTheory2.4.2TotalStrainTheory2.4.3EquivalentStressandEquivalentStrain2.5ModelsofDeformationMaterials2.5.1Modeloflinearlyelasticbody2.5.2Modelofelastic-perfectlyplasticbody2.5.3Modelofelastic-plasticstrengtheningbody2.5.4Rigid-plasticModel2.5.5ComplexDeformationModel2.6DeformationResistanceModel
2.7BasicConditionofPlasticDeformation2.7.1Volume-constancyCondition2.7.2StressBoundaryCondition2.7.3FrictionBoundaryConditionReferencesAnalyticalPrincipleofPlasticMechanics3.1ThermodynamicBasisofEnergyTheory3.1.1VariationofKineticEnergy()3.1.2VariationofExternalWork(
)3.1.3Variationofinternalenergy()3.2AdmissibleMechanicalFields3.2.1Staticallyadmissiblestressfield3.2.2Kinematicallyadmissiblevelocity3.3VirtualWorkPrinciple3.4TheMinimumPotentialEnergyPrinciple3.5TheMaximumPlasticWorkPrinciple3.6Rigid-plasticVariationalPrinciple
3.6.1Thefirstvariationalprinciple3.6.2Thesecondvariationalprinciple3.7LimitEquilibriumTheory3.7.1Thelowerboundtheorem3.7.2TheupperboundtheoremReferences4.AnalyticalMethodsofPlasticMechanics4.1SlabMethod4.1.1BasicAssumption4.1.2MainAnalysisSteps4.1.3AnCitedExample-CompressionThin-pieceonRoughAnvilSurface
4.1.4EvaluationoftheslabMethod4.2MeanEnergyMethod4.3SlipLineMethod4.3.1BasicAssumption4.3.2BasicConceptandEquation4.3.3GeneralSolutionProcedureofSliplinefield4.3.4Anexample—indentationofansemi-infinitebodybyflatpunch4.3.5EvaluationoftheSlipLineMethod4.4AnalyticalMethodandBasicEquationofUpperBoundMethod4.4.1AnalyticalMethodofTriangleVelocityField4.4.2AnalyticalMethodofContinuousVelocityField4.4.3AnalyticalExamplesoftheUpperBoundMethod4.5LowerBoundMethodandItsExample4.6EvaluationofTheseTwoLimitAnalysisMethod
4.7VariationalMethodandItsexample4.7.1BasicAnalyticalProcedures4.7.2AnExample—UpsettingofAnEquilateralPolygonCylinder4.7.3EvaluationofVariationalMethod4.8Linearizationsolutionmethodofyieldcriterion4.8.1Developmentofalinearyieldcriterion4.8.2Twolinearizationsolutionmethods
References5.Developmentoflinearlyapproximatedyieldcriteriabasedongeometricalparameters5.1Equalperimeteryieldcriterion5.1.1Mathematicalexpression5.1.2Yieldloci5.1.3GeometricallocationofintersectionpointH5.1.4ComparisonwithMisescriterion5.1.5Specificplasticworkrate
5.1.6Experimentalvalidation5.2EqualAreayieldcriterion5.2.1YieldequationofEAyieldcriterion5.2.2Specificplasticworkrate5.2.3Precisionanalysis5.2.4Calculationexample5.3Geometricalapproximationyieldcriterion5.3.1Mathematicalexpressionandyieldlocus5.3.2Specificplasticwork
5.3.3Experimentalvalidation5.4Geometricalmidlineyieldcriterion5.4.1Derivationofgeometricalmidlineyieldcriterion5.4.2Yieldlocus5.4.3Specificplasticworkrate5.4.4Accuracyanalysis5.5AAyieldcriterion5.5.1YieldEquation5.5.2Yieldloci5.5.3SpecificplasticworkrateReferences6.Developmentoflinearlyapproximatedyieldcriteriabasedonmathematicalaveragemethods6.1Meanyieldcriterion6.1.1Mathematicalexpression6.1.2Yieldlocus6.1.3Specificplasticworkrate6.1.4Calculationexample6.2Weightedaverageyieldcriterion6.2.1MathematicalexpressionofWAyieldcriterion
6.2.2Yieldlocus6.2.3Specificplasticworkrate6.2.4Yieldvalidation6.3Derivationofmeaninfluencefactoryieldcriterion6.3.1Mathematicalexpression6.3.2YieldlocusoftheMIFyieldcriterion6.3.3Plasticworkrateperunitvolume6.3.4Experimentalverification6.4Arithmeticmeanyieldcriterion
6.4.1Formuladerivation6.4.2Yieldlocus6.4.3Specificplasticworkrate6.4.4ExperimentalvalidationReferences7.TheLinearizationSolutionMethodsandTheirApplicationsontheLimitAnalysisofPipelineandSheet7.1FailureanalysisofstraightpipelinewithWAyieldcriterion7.1.1Modelingofburstpressure
7.1.2Experimentalvalidationandparameteranalysis7.2LimitanalysisofpipeelbowwithGMyieldcriterion7.2.1Stressfieldforpipeelbow7.2.2Plasticcollapseload7.2.3Resultsanddiscussion7.3ModelingofburstpressureforpipeelbowwithUYCcriterion7.3.1Unifiedyieldcriterion7.3.2Stressfieldforpipeelbow7.3.3Stress-strainlaw7.3.4ExperimentalrelationshipofnandYTratio7.3.5Estimatingnfromyieldortensilestress7.3.6UYC-basedsolution7.3.7Specialcaseanddiscussion7.3.8Comparisonwithnumericalresults7.3.9Experimentalvalidation7.4AnalysisoflimitloadofcircularplatebyMIFyieldcriterion
7.4.1Basicequation7.4.2Calculationofthelimitload7.4.3Analysisandfiniteelementnumericalverification7.5ApplicationofGAcriteriontolimitanalysisofacircularplate7.5.1Kinematicallyadmissiblestrainfield7.5.2PlasticworkfunctionalandlimitloadbasedonGAcriterion7.5.3ComparisonanddiscussionwithtraditionalresultsReferences8.ApplicationoftheReplaceMethodofSpecificPlasticWorkRateon2DMetalForming8.1AnalysisofbroadsiderollingforceforheavyplatebyMYcriterion8.1.1Velocityfieldforbroadsiderolling8.1.2Internalstrainenergyrate
8.1.3Frictionenergyrate8.1.4Shearenergyrate8.1.5Thetotalpoweranditsminimization8.1.6Experimentalvalidationanddiscussion8.2AnalysisofrollingplatewithEAyieldcriteroin8.2.1Kinematicallyadmissiblevelocityfield8.2.2Formingpowerfunctional8.2.3Totalpowerandminimization
8.2.4Applicationexample8.3AnalysisofdefectclosurebehaviorinheavyplatewithMYcriterion8.3.1Kinematicallyadmissiblevelocityfield8.3.2Internaldeformationenergyrate8.3.3Shearenergyrate8.3.4Frictionenergyrate8.3.5Thetotalenergyrateanditsminimization8.3.6Defectclosurecriterion
8.3.7Discussionandvalidation8.4AnalysisoftwinparabolicdrawingbyMY8.4.1Velocityfieldinthedeformationzone8.4.2Internalstrainenergyrate8.4.3Shearenergyrate8.4.4Frictionenergyrate8.4.5Externallysupplieddrawingstress8.4.6Optimaldiesemi-angle8.4.7ComparisonwithFEAandtraditionalresults
8.4.8Discussions8.5ApplicationofAAyieldcriteriontostripforging8.5.1ProcedureanalysisbyAAyieldcriterion8.5.2Comparisonofvariouscriteria8.6ForgingAnalysisofahollowroundworkpiecewithTSSyieldcriterion8.6.1Velocityfield8.6.2Theenergyratefunctional8.6.3Calculationprocedure
References9.Analysisof3DMetalFormingbytheReplaceMethodofSpecificplasticworkrate9.1AnalysisofrollingforceforheavyplatebyMYcriterion9.1.1Globalweightedvelocityfield9.1.2Totalenergyrate9.1.3ResultsandDiscussions9.2ModelingofplaterollingforcebyEPyieldcriterion
9.2.1Rollingenergyrate9.3Analysisofthree-dimensionalforgingbyWAyieldcriterion9.3.1Mathematicaldescriptionof3Dforging9.3.2Forgingenergyrate9.3.3ExperimentanddiscussionReferences