1st Edition

Continuum Mechanics and Plasticity

By Han-Chin Wu Copyright 2004
    704 Pages 258 B/W Illustrations
    by Chapman & Hall

    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.

    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

    Biography

    Han-Chin Wu