Damage Mechanics
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Summary
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.
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
Editorial 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
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