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Continuum Mechanics and Plasticity




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ISBN 9781584883630
Published December 20, 2004 by Chapman and Hall/CRC
704 Pages 258 B/W Illustrations

 
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Book Description

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.

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

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