Continuum Mechanics and Plasticity

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

Table of Contents:
Part I Fundamentals of Continuum Mechanics CARTESIAN TENSORS Vectors The Transformation of Axes The Dyadic Product (The Tensor Product) Cartesian Tensors Rotation of a Tensor The Isotropic Tensors Vector and Tensor Calculus STRESS Forces Stress Vector The Stress Tensor Equations of Equilibrium Symmetry of the Stress Tensor Principal Stresses Properties of Eigenvalues and Eigenvectors Normal and Shear Components Mean and Deviatoric Stresses Octahedral Shearing Stress The Stress Invariants Spectral Decomposition of a Symmetric Tensor of Rank Two Powers of a Tensor Cayley-Hamilton Theorem MOTION AND DEFORMATION Material and Spatial Descriptions Description of Deformation Deformation of a Neighborhood The Deformation Gradient The Right Cauchy-Green Deformation Tensor Deformation of Volume and Area of a Material Element The Left Cauchy-Green Deformation Tensor The Lagrangian and Eulerian Strain Tensors Other Strain Measures Material Rate of Change Dual Vectors and Dual Tensors Velocity of a Particle Relative to a Neighboring Particle Physical Significance of the Rate of Deformation Tensor Physical Significance of the Spin Tensor Expressions for D and W in Terms of F Material Derivative of Strain Measures Material Derivative of Area and Volume Elements CONSERVATION LAWS AND CONSTITUTIVE EQUATION Bulk Material Rate of Change Conservation Laws The Constitutive Laws in the Material Description Objective Tensors Property of Deformation and Motion Tensors Under Reference Frame Transformation Objective Rates Finite Elasticity Infinitesimal Theory of Elasticity Hypoelasticity Part II Continuum Theory of Plasticity FUNDAMENTALS OF CONTINUUM PLASTICITY Some Basic Mechanical Tests Modeling the Stress-Strain Curve The Effects of Hydrostatic Pressure Torsion Test in the Large Strain Range THE FLOW THEORY OF PLASTICITY The Concept of Yield Criterion The Flow Rule The Elastic-Perfectly Plastic Material Strain-Hardening The Return-Mapping Algorithm Combined Axial-Torsion of Strain-Hardening Materials Flow Theory in the Strain Space Remarks ADVANCES IN PLASTICITY Experimenal Determination of YieldSurfaces The Direction of the Plastic Strain Increment Multisurface Models of Flow Plasticity The Plastic Strain Trajectory Approach Finite Plastic Deformation INTERNAL VARIABLE THEORY OF THERMO-MECHANICAL BEHAVIORS AND ENDOCHRONIC THEORY OF PLASTICITY Concepts and Terminologies of Thermodynamics Thermodynamics of Internal State Variables The Endochronic Theory of Plasticity TOPICS IN ENDOCHRONIC PLASTICITY An Endochronic Theory of Anisotropic Plasticity Endochronic Plasticity in the Finite Strain Range An Endochronic Theory for Porous and Granular Materials An Endochronic Formulation of a Plastically Deformed Damaged Continuum ANISOTROPIC PLASTICITY FOR SHEET METALS Standard Tests for Sheet Metal Experimental Yield Surface for Sheet Metal Hill's Anisotropic Theory of Plasticity Nonquadratic Yield Functions Anisotropic Plasticity Using Combined Isotropic-Kinematic Hardening DESCRIPTION OF ANISOTROPIC MATERIAL BEHAVIOR USING CURVILINEAR COORDINATES Convected Coordinate System and Convected Material Element Curvilinear Coordinates and Base Vectors Tensors and Special Tensors Multiplication of Vectors Physical Components of a Vector Differentiation of a Tensor with Respect to the Space Coordinates Strain Tensor Strain-Displacement Relations Stress Vector and Stress Tensor Physical Components of the Stress Tensor Other Stress Tensors and the Cartesian Stress Components Stress Rate and Strain Rate Further Discussion of Stress Rate A Theory of Plasticity for Anisotropic Metals COMBINED AXIAL-TORSION OF THIN-WALLED TUBES Convected Coordinates in the Combined Axial-Torsion of a Thin-Walled Tube The Yield Function Flow Rule and Strain Hardening Elastic Constitutive Equations Algorithm for Computation Nonlinear Kinematic Hardening Description of Yield Surface with Various Preloading Paths A Stress Path of Tension-Unloading Followed by Torsion Summary and Discussion Answers and Hints to Selected Problems Author Index Subject Index Each chapter also includes an Introduction, References, and Problems