Continuum Mechanics and Plasticity

ISBN-13: 9781584883630 / Angielski / Twarda / 2004 / 704 str.

Miguel J. Bagajewicz; Han-Chin Wu

Opis

Tremendous advances in computer technologies and methods have precipitated a great demand for refinements in the constitutive models of plasticity. Such refinements include the development of a model that would account for material anisotropy and produces results that compare well with experimental data. Key to developing such models-and to meeting many other challenges in the field- is a firm grasp of the principles of continuum mechanics and how they apply to the formulation of plasticity theory. Also critical is understanding the experimental aspects of plasticity and material anisotropy.
Integrating the traditionally separate subjects of continuum mechanics and plasticity, this book builds understanding in all of those areas. Part I provides systematic, comprehensive coverage of continuum mechanics, from a review of Carteisian tensors to the relevant conservation laws and constitutive equation. Part II offers an exhaustive presentation of the continuum theory of plasticity. This includes a unique treatment of the experimental aspects of plasticity, covers anisotropic plasticity, and incorporates recent research results related to the endochronic theory of plasticity obtained by the author and his colleagues.
By bringing all of these together in one book, Continuum Mechanics and Plasticity facilitates the learning of solid mechanics. Its readers will be well prepared for pursuing either research related to the mechanical behavior of engineering materials or developmental work in engineering analysis and design.

Spis treści

Part I Fundamentals of Continuum MechanicsCARTESIAN TENSORS Vectors The Transformation of Axes The Dyadic Product (The Tensor Product)Cartesian TensorsRotation of a TensorThe Isotropic TensorsVector and Tensor CalculusSTRESSForcesStress VectorThe Stress TensorEquations of EquilibriumSymmetry of the Stress TensorPrincipal StressesProperties of Eigenvalues and EigenvectorsNormal and Shear ComponentsMean and Deviatoric StressesOctahedral Shearing StressThe Stress InvariantsSpectral Decomposition of a Symmetric Tensor of Rank TwoPowers of a TensorCayley-Hamilton TheoremMOTION AND DEFORMATIONMaterial and Spatial DescriptionsDescription of DeformationDeformation of a NeighborhoodThe Deformation GradientThe Right Cauchy-Green Deformation TensorDeformation of Volume and Area of a Material ElementThe Left Cauchy-Green Deformation TensorThe Lagrangian and Eulerian Strain TensorsOther Strain MeasuresMaterial Rate of ChangeDual Vectors and Dual TensorsVelocity of a Particle Relative to a Neighboring ParticlePhysical Significance of the Rate of Deformation TensorPhysical Significance of the Spin TensorExpressions for D and W in Terms of FMaterial Derivative of Strain MeasuresMaterial Derivative of Area and Volume ElementsCONSERVATION LAWS AND CONSTITUTIVE EQUATIONBulk Material Rate of ChangeConservation LawsThe Constitutive Laws in the Material DescriptionObjective TensorsProperty of Deformation and Motion Tensors Under Reference Frame TransformationObjective RatesFinite ElasticityInfinitesimal Theory of ElasticityHypoelasticityPart II Continuum Theory of PlasticityFUNDAMENTALS OF CONTINUUM PLASTICITYSome Basic Mechanical TestsModeling the Stress-Strain CurveThe Effects of Hydrostatic PressureTorsion Test in the Large Strain RangeTHE FLOW THEORY OF PLASTICITYThe Concept of Yield CriterionThe Flow RuleThe Elastic-Perfectly Plastic MaterialStrain-HardeningThe Return-Mapping AlgorithmCombined Axial-Torsion of Strain-Hardening MaterialsFlow Theory in the Strain SpaceRemarksADVANCES IN PLASTICITYExperimenal Determination of YieldSurfacesThe Direction of the Plastic Strain IncrementMultisurface Models of Flow PlasticityThe Plastic Strain Trajectory ApproachFinite Plastic DeformationINTERNAL VARIABLE THEORY OF THERMO-MECHANICAL BEHAVIORS AND ENDOCHRONIC THEORY OF PLASTICITYConcepts and Terminologies of ThermodynamicsThermodynamics of Internal State VariablesThe Endochronic Theory of PlasticityTOPICS IN ENDOCHRONIC PLASTICITYAn Endochronic Theory of Anisotropic PlasticityEndochronic Plasticity in the Finite Strain RangeAn Endochronic Theory for Porous and Granular MaterialsAn Endochronic Formulation of a Plastically Deformed Damaged ContinuumANISOTROPIC PLASTICITY FOR SHEET METALSStandard Tests for Sheet MetalExperimental Yield Surface for Sheet MetalHill's Anisotropic Theory of PlasticityNonquadratic Yield FunctionsAnisotropic Plasticity Using Combined Isotropic-Kinematic HardeningDESCRIPTION OF ANISOTROPIC MATERIAL BEHAVIOR USING CURVILINEAR COORDINATESConvected Coordinate System and Convected Material ElementCurvilinear Coordinates and Base VectorsTensors and Special TensorsMultiplication of VectorsPhysical Components of a VectorDifferentiation of a Tensor with Respect to the Space CoordinatesStrain TensorStrain-Displacement RelationsStress Vector and Stress TensorPhysical Components of the Stress TensorOther Stress Tensors and the Cartesian Stress ComponentsStress Rate and Strain RateFurther Discussion of Stress RateA Theory of Plasticity for Anisotropic MetalsCOMBINED AXIAL-TORSION OF THIN-WALLED TUBESConvected Coordinates in the Combined Axial-Torsion of a Thin-Walled TubeThe Yield FunctionFlow Rule and Strain HardeningElastic Constitutive EquationsAlgorithm for ComputationNonlinear Kinematic HardeningDescription of Yield Surface with Various Preloading PathsA Stress Path of Tension-Unloading Followed by TorsionSummary and DiscussionAnswers and Hints to Selected ProblemsAuthor IndexSubject IndexEach chapter also includes an Introduction, References, and Problems

O autorze

Han-Chin Wu