The Mechanical and Thermodynamical Theory of Plasticity: 1st Edition (Hardback) book cover

The Mechanical and Thermodynamical Theory of Plasticity

1st Edition

By Mehrdad Negahban

CRC Press

784 pages | 231 B/W Illus.

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pub: 2012-04-26
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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.


"an excellent text for a graduate-level course in plasticity…the approach and selection of topics areappropriate 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

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


Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Mechanics / General