Continuum Mechanics and Plasticity: 1st Edition (Hardback) book cover

Continuum Mechanics and Plasticity

1st Edition

By Han-Chin Wu

Chapman and Hall/CRC

704 pages | 258 B/W Illus.

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pub: 2004-12-20
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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

About the Series

Modern Mechanics and Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
SCI040000
SCIENCE / Mathematical Physics
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical
TEC021000
TECHNOLOGY & ENGINEERING / Material Science