Damage Mechanics: 1st Edition (Hardback) book cover

Damage Mechanics

1st Edition

By George Z. Voyiadjis, Peter I. Kattan

CRC Press

280 pages | 39 B/W Illus.

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pub: 2005-06-23
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Description

Before a structure or component can be completed, before any analytical model can be constructed, and even before the design can be formulated, you must have a fundamental understanding of damage behavior in order to produce a safe and effective design. Damage Mechanics presents the underlying principles of continuum damage mechanics along with the latest research. The authors consider both isotropic and anisotropic theories as well as elastic and elasto-plastic damage analyses using a self-contained, easily understood approach.

Beginning with the requisite mathematics, Damage Mechanics guides you from the very basic concepts to advanced mathematical and mechanical models. The first chapter offers a brief MAPLE® tutorial and supplies all of the MAPLE commands needed to solve the various problems throughout the chapter. The authors then discuss the basics of elasticity theory within the continuum mechanics framework, the simple case of isotropic damage, effective stress, damage evolution, kinematic description of damage, and the general case of anisotropic damage. The remainder of the book includes a review of plasticity theory, formulation of a coupled elasto-plastic damage theory developed by the authors, and the kinematics of damage for finite-strain elasto-plastic solids.

From fundamental concepts to the latest advances, this book contains everything that you need to study the damage mechanics of metals and homogeneous materials.

Reviews

"In total, the advantage of this textbook is its self-sufficiency. The book includes numerous examples and problems, and may be very useful to undergraduate and postgraduate students studying damage mechanics, fracture mechanics and also the problems of elasticity and plasticity."

-I.A. Parinov, Zentralblatt MATH, Vol. 1090, No. 16, 2006

Table of Contents

PREFACE

MATHEMATICAL PRELIMINARIES

MAPLE Tutorial

Vectors

Matrices

Indicial Notation

Transformation of Vectors

Cartesian Tensors

Eigenvalues and Eigenvectors of Tensors

Tensor Calculus

MAPLE Tensor Commands

ELASTICITY THEORY

Motion of a Continuum

Deformation and Strain

Stress

Linear Elastic Relation

ISOTROPIC DAMAGE MECHANICS

Introduction

Damage Variables

Effective Stress

Damage Evolution

KINEMATIC DESCRIPTION OF DAMAGE

Introduction

Theoretical Preliminaries

Description of Damage State

Fourth-Order Anisotropic Damage Effect Tensor

Kinematic Description of Elastic-Damage Deformation

Constitutive Equation of Elastic-Damage Behavior

Conclusion

ANISOTROPIC DAMAGE MECHANICS

Introduction

Anisotropic Damage Criterion

Damage Tensor

Damage Evolution

Constitutive Model

Uniaxial Tension Analysis

Finite Element Implementation

Center-Cracked Thin Plate Under In-Plane Tensile Forces

Conclusion

PLASTICITY THEORY

Introduction

Theoretical Formulation

Monotonic and Cyclic Tension Loadings on 316 Stainless Steel

Modification of the Kinematic Hardening Model for Non-Proportional Loading

Model Predictions and Comparisons with Experimental Data for Non-Proportional Loadings

Ratchetting

Conclusions

COUPLED DAMAGE PLASTICITY

Stress Transformation Between Damaged and Undamaged States

Strain Rate Transformation Between Damaged and Undamaged States

Constitutive Model

Application to Void Growth: Gurson's Model

Effective Spin Tensor

KINEMATICS OF DAMAGE FOR FINITE-STRAIN ELASTO-PLASTIC SOLIDS

Theoretical Preliminaries

Description of Damage State

Fourth-Order Anisotropic Damage Effect Tensor

The Kinematics of Damage for Elasto-Plastic Behavior with Finite Strains

Irreversible Thermodynamics

Constitutive Equation for Finite Elasto-Plastic Deformation with Damage Behavior

REFERENCES

INDEX

About the Series

Mechanical Engineering

A Series of Textbooks and Reference Books

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
SCI041000
SCIENCE / Mechanics / General
TEC009020
TECHNOLOGY & ENGINEERING / Civil / General
TEC016000
TECHNOLOGY & ENGINEERING / Industrial Design / General