1st Edition

The Mechanical and Thermodynamical Theory of Plasticity

ISBN 9780849372308
Published April 26, 2012 by CRC Press
784 Pages 231 B/W Illustrations

USD $175.00

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Book Description

Born out of 15 years of courses and lectures on continuum mechanics, nonlinear mechanics, continuum thermodynamics, viscoelasticity, plasticity, crystal plasticity, and thermodynamic plasticity, The Mechanical and Thermodynamical Theory of Plasticity represents one of the most extensive and in-depth treatises on the mechanical and thermodynamical aspects of plastic and visicoplastic flow. Suitable for student readers and experts alike, it offers a clear and comprehensive presentation of multi-dimensional continuum thermodynamics to both aid in initial understanding and introduce and explore advanced topics.

Covering a wide range of foundational subjects and presenting unique insights into the unification of disparate theories and practices, this book offers an extensive number of problems, figures, and examples to help the reader grasp the subject from many levels. Starting from one-dimensional axial motion in bars, the book builds a clear understanding of mechanics and continuum thermodynamics during plastic flow. This approach makes it accessible and applicable for a varied audience, including students and experts from engineering mechanics, mechanical engineering, civil engineering, and materials science.

Table of Contents

Plasticity In The 1-D Bar
Introduction to Plastic Response
The Bar and The Continuum Assumption
Motion and Temperature of Points on a Bar
Stretch Ratio, Strain, Velocity Gradient, Temperature Gradient
Superposition of Deformations
Elastic, Plastic, and Thermal Strains
Examples of Constitutive Models
Mechanical Theory of Rate-Independent Plasticity
Mechanical Models for Plasticity
Temperature-Dependent Plasticity
An Infinitesimal Theory of Thermoplasticity
Rate-Dependent Models for Plasticity
Load Control as Opposed to Strain Control
Numerical Integration of Constitutive Equations
The Balance Laws
Thermodynamic Restrictions on Constitutive Equations
Heat Generation and Flow
Equilibrium and Quasi-Equilibrium Problems
Dynamic Loading Problems: Numerical Solution
Dealing with Discontinuities: Jump Conditions
Plastic Drawing of Bars
Elastic and Plastic (Shock) Waves in a Bar
General Comment on Selection of Moduli
Notation and Summary

Vectors and Tensors
Matrix algebra
Tensor calculus

Describing Motion, Deformation and Temperature
Position, Velocity, Acceleration And Temperature
Configurations of Material Bodies
Streamlines and Pathlines
Deformation Gradient and Temperature Gradient
Stretch and Strain Tensors
Velocity Gradient
Relative Deformation
Triaxial Extension, Simple Shear, Bending and Torsion
Small Deformations

Elastic, Plastic And Thermal Deformation
Elastic and Plastic Deformation Gradients
Elastic and Plastic Strains
Elastic and Plastic Velocity Gradients
Infinitesimal Elastic and Plastic Deformations
Large Rigid Body Rotations
Thermal Deformation and Thermal Strain

Traction, Stress and Heat Flux
The Traction Vector
The Relation between Tractions on Different Surfaces
The Stress Tensor
Isotropic Invariants and the Deviatoric Stress
Examples of Elementary States of Stress
True Stress as Opposed to Engineering Stress
The Piola-Kirchhoff, Rotated and Convected Stresses
Heat Flux

Balance Laws and Jump Conditions
Transport Relations
Conservation of Mass
Balance of Linear Momentum
Balance of Angular Momentum
Balance of Work snd Energy
Entropy and the Entropy Production Inequality
Heat Flow and Thermodynamic Processes
Infinitesimal Deformations
The Generalized Balance Law
Jump Conditions
Perturbing a Motion
Initial and Boundary Conditions

Infinitesimal Plasticity
A Mechanical Analog for Plasticity
Elastic Perfectly-Plastic Response
Common Assumptions
Von Mises Yield Function with Combined Isotropic and Kinematic Hardening
Free-Energy of Quadratic Form
Scalar Stress and Hardening Functions
Multiple Elements in Parallel
Multiple Elements in Series
Rate-Dependent Plasticity
Deformation Plasticity

Solutions for Infinitesimal Plasticity
Homogeneous Deformations
Torsion-Extension of a Thin Circular Cylindrical Tube
Compression in Plane Strain
Torsion of Circular Members
Torsion of Prismatic Sections
Non-Uniform Loading of Bars
Cylindrical and Spherical Symmetry
Two-Dimensional Problems
Heat and Its Generation

First-Gradient Thermo-Mechanical Materials
First-Gradient Theories
Superposition of Pure Translations
Superposition of Rigid Body Rotations
Material Symmetry
First-Gradient State Variable Models
Higher Gradient and Non-Local Models

Elastic And Thermoelastic Solids
The Thermoelastic Solid
The Influence of Pure Rigid-Body Translation on the Constitutive Response
The Influence of Pure Rigid-Body Rotation on the Constitutive Response
Material Symmetry
Change of Reference Configuration
A Thermodynamically Consistent Model
Models Based on Fe And FӨ
Specific Free-Energy of Quadratic Form in Strain
Heat Generation and Heat Capacity
Material Constraints
Multiple Material Constraints
Superposition of Deformations

Finite Deformation Mechanical Theory of Plasticity
General Mechanical Theory of Plasticity
Rigid Body Motions
Material Symmetry
Stress Depending Only on Elastic Deformation Gradient
Stress Depending on both Elastic Deformation and Plastic Strain
General Comments
Deformation Plasticity

Thermoplastic Solids
A Simple Thermo-Mechanical Analog
Thermodynamic Constraint
Isotropic Examples with J2 Type Yield Functions
Superposition of Rigid Body Motions
Material Symmetry
An Initially Isotropic Material
Models Depending on Cp
Heat Generation and Heat Flow
Specific Free-Energy of Quadratic Form in Strain
Plasticity Models Based on Green Strains
Heat Flux Vector
Material Constraints
Models Based on F = Fefөfp

Viscoelastic Solids
One-Dimensional Linear Viscoelasticity
One-Dimensional Nonlinear Viscoelasticity
Three-Dimensional Linear Viscoelasticity
A One-Element Thermo-Viscoelastic Model
Multi-Element Thermodynamic Viscoelastic Model
Initially Isotropic Models: Free-Energy and Thermodynamic Stresses
Quasi-Linear Viscoelastic Model
Material Constraints
Models Based on F = Fefөfve

Rate-Dependent Plasticity
Infinitesimal Mechanical and Thermo-Mechanical Models with Viscoplastic Flow
Nonlinear Thermoelastic-Viscoplastic Model
Single-Element Viscoelastic-Viscoplastic
Full Viscoelastic-Viscoplastic Model
Material Constraints
Models Based on F = Fefөfvp

Crystal plasticity
Crystal Structures and Slip Systems
Elastic Crystal Distortion
Kinematics of Single-Crystal Deformation
Resolved Shear Stress and Overstress
Yield Function
Thermo-Mechanical Models
Rate-Dependent Models

A Representation of functions
Transversely Isotropic

B Representation for fourth order constants
Transversely Isotropic
Crystal Classes

C Basic Equations
Basic Equations
Curvilinear Coordinates
Rectangular Coordinates
Cylindrical Coordinates
Spherical Coordinates


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"an excellent text for a graduate-level course in plasticity…the approach and selection of topics are appropriate for the audience. ... Professor Negahban has done an excellent job in presenting a unified approach to include thermal effects in the theory of finite deformation of plastic solids. The simple thermo-mechanical analog presented at the beginning of the chapter is also very instructive to the reader. {presented figures are] particularly helpful in understanding the mechanisms in a simple (one-dimensional) setting … The learning features included in this chapter are excellent (the figures are clear and illustrative). The table of contents is well-balanced and very clear…The in-depth and unified approach to many topics discussed in the text (e.g., thermoplasticity under finite deformation) is of particular interest..."
Ken Zuo, University of Alabama in Huntsville, USA

"… takes a modern, in depth approach to the subject of thermoplasticity. The chapters are written to be somewhat self-contained. …. can be adapted to satisfy a variety of courses and subjects. The author has done an admirable job of pointing out how the text would satisfy these competing requirements."
Ronald E. Smelser, The University of North Carolina at Charlotte, USA