Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity, 1st Edition (Hardback) book cover

Continuum Mechanics

Elasticity, Plasticity, Viscoelasticity, 1st Edition

By Ellis H. Dill

CRC Press

368 pages | 67 B/W Illus.

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pub: 2006-11-10
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Description

Most books on continuum mechanics focus on elasticity and fluid mechanics. But whether student or practicing professional, modern engineers need a more thorough treatment to understand the behavior of the complex materials and systems in use today. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity offers a complete tour of the subject that includes not only elasticity and fluid mechanics but also covers plasticity, viscoelasticity, and the continuum model for fatigue and fracture mechanics.

In addition to a broader scope, this book also supplies a review of the necessary mathematical tools and results for a self-contained treatment. The author provides finite element formulations of the equations encountered throughout the chapters and uses an approach with just the right amount of mathematical rigor without being too theoretical for practical use. Working systematically from the continuum model for the thermomechanics of materials, coverage moves through linear and nonlinear elasticity using both tensor and matrix notation, plasticity, viscoelasticity, and concludes by introducing the fundamentals of fracture mechanics and fatigue of metals. Requisite mathematical tools appear in the final chapter for easy reference.

Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity builds a strong understanding of the principles, equations, and finite element formulations needed to solve real engineering problems.

Table of Contents

FUNDAMENTALS OF CONTINUUM MECHANICS

Material Models

Classical Space-Time

Material Bodies

Strain

Rate of Strain

Curvilinear Coordinate Systems

Conservation of Mass

Balance of Momentum

Balance of Energy

Constitutive Equations

Thermodynamic Dissipation

Objectivity: Invariance for Rigid Motions

Coleman-Mizel Model

Fluid Mechanics

Problems for Chapter 1

Bibliography

NONLINEAR ELASTICITY

Thermoelasticity

Material Symmetries

Isotropic Materials

Incompressible Materials

Conjugate Measures of Stress and Strain

Some Symmetry Groups

Rate Formulations for Elastic Materials

Energy Principles

Geometry of Small Deformations

Linear Elasticity

Special Constitutive Models for Isotropic Materials

Mechanical Restrictions on the Constitutive Relations

Problems for Chapter 2

Bibliography

LINEAR ELASTICITY

Basic Equations

Plane Strain

Plane Stress

Properties of Solutions

Potential Energy

Special Matrix Notation

The Finite Element Method of Solution

General Equations for an Assembly of Elements

Finite Element Analysis for Large Deformations

Problems for Chapter 3

Bibliography

PLASTICITY

Classical Theory of Plasticity

Work Principle

von Mises-Type Yield Criterion

Hill Yield Criterion for Orthotropic Materials

Isotropic Hardening

Kinematic Hardening

Combined Hardening laws

General Equations of Plasticity

Strain Formulation of Plasticity

Finite Element Analysis

Large Deformations

Thermodynamics of Elastic-Plastic Materials

Problems for Chapter 4

Bibliography

VISCOELASTICITY

Linear Viscoelasticity

Effect of Temperature

Nonlinear Viscoelasticity

Thermodynamics of Materials with Fading Memory

Problems for Chapter 5

Bibliography

FRACTURE AND FATIGUE

Fracture Criterion

Plane Crack through a Sheet

Fracture Modes

Calculation of the Stress Intensity Factor

Crack Growth

Problems for Chapter 6

Bibliography

MATHEMATICAL TOOLS FOR CONTINUUM MECHANICS

Sets of Real Numbers

Matrices

Vector Analysis

Tensors

Isotropic Functions

Abstract Derivatives

Some Basic Mathematical Definitions and Theorems

Problems for Chapter 7

Bibliography

INDEX

Subject Categories

BISAC Subject Codes/Headings:
SCI041000
SCIENCE / Mechanics / General
TEC009020
TECHNOLOGY & ENGINEERING / Civil / General
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical