"Continuum Damage Mechanics and Numerical Applications" presents a systematic development of the theory of Continuum Damage Mechanics and its numerical engineering applications using a unified form of the mathematical formulations in anisotropic and isotropic damage models. The theoretical framework is based on the thermodynamic theory of energy and material dissipation and is described by a set of fundamental formulations of constitutive equations of damaged materials, development equations of the damaged state, and evolution equations of micro-structures. According to concepts of damage-dissipation of the material state and effective evolution of material properties, all these advanced equations, which take nonsymmetrized effects of damage aspects into account, are developed and modified from the traditional general failure models so they are more easily applied and verified in a wide range of engineering practices by experimental testing. Dr. Wohua Zhang is a Professor at Engineering Mechanics Research Center in Zhejiang University of China. Dr. Yuanqiang Cai is a Professor at Department of Civil Engineering in Zhejiang University of China.

Recent developments in engineering and technology have brought about serious and enlarged demands for reliability, safety and economy in wide range of fields such as aeronautics, nuclear engineering, civil and structural engineering, automotive and production industry. This, in turn, has caused more interest in continuum damage mechanics and its engineering applications. This book aims to give a concise overview of the current state of damage mechanics, and then to show the fascinating possibility of this promising branch of mechanics, and to provide researchers, engineers and graduate students with an intelligible and self-contained textbook. The book consists of two parts and an appendix. Part I is concerned with the foundation of continuum damage mechanics. Basic concepts of material damage and the mechanical representation of damage state of various kinds are described in Chapters 1 and 2. In Chapters 3-5, irreversible thermodynamics, thermodynamic constitutive theory and its application to the modeling of the constitutive and the evolution equations of damaged materials are descried as a systematic basis for the subsequent development throughout the book. Part II describes the application of the fundamental theories developed in Part I to typical damage and fracture problems encountered in various fields of the current engineering. Important engineering aspects of elastic-plastic or ductile damage, their damage mechanics modeling and their further refinement are first discussed in Chapter 6. Chapters 7 and 8 are concerned with the modeling of fatigue, creep, creep-fatigue and their engineering application. Damage mechanics modeling of complicated crack closure behavior in elastic-brittle and composite materials are discussed in Chapters 9 and 10. In Chapter 11, applicability of the local approach to fracture by means of damage mechanics and finite element method, and the ensuing mathematical and numerical problems are briefly discussed. A proper understanding of the subject matter requires knowledge of tensor algebra and tensor calculus. At the end of this book, therefore, the foundations of tensor analysis are presented in the Appendix, especially for readers with insufficient mathematical background, but with keen interest in this exciting field of mechanics.

Modern engineering materials subjected to unfavorable mechanical and environmental conditions decrease in strength due to the accumulation of microstructural changes. For example, considering damage in metals we can mention creep damage, ductile plastic damage, embrittlement of steels and fatigue damage. To properly estimate the value of damage when designing reliable structures it is necessary to formulate the damage phenomenon in terms of mechanics. Then it is possible to analyse various engineering problems using analytical and computational techniques. During the last two decades the basic principles of continuum damage mechanics were formulated and some special problems were solved. Many scientific papers were published and several conferences on damage mechanics took place. Now continuum damage mechanics is rapidly developing branch of fracture mechanics. This book is probably the first one on the subject; it contains a sys tematic description of the basic aspects of damage mechanics and some of its applications. In general, a theoretical description of damage can be rather compli cated. The experiments in this field are difficult (especially under multiax ial stress and non-proportional loading). Therefore, experimental data, as a rule, are scarce. Determination of functions and constants, which play a role in the complex variants of the theory, from available experimental data is often practically impossible. ix L.M. Kachanov The problems of damage mechanics are mainly engineering ones. Therefore, the author tries to avoid superfluous mathematical formalism. Some more details of the book's subject can be found in the list of con tents.

later versions. In addition, the CD-ROM contains a complete solutions manual that includes detailed solutions to all the problems in the book. If the reader does not wish to consult these solutions, then a brief list of answers is provided in printed form at the end of the book. Iwouldliketothankmyfamilymembersfortheirhelpandcontinuedsupportwi- out which this book would not have been possible. I would also like to acknowledge the help of the editior at Springer-Verlag (Dr. Thomas Ditzinger) for his assistance in bringing this book out in its present form. Finally, I would like to thank my brother, Nicola, for preparing most of the line drawings in both editions. In this edition, I am providing two email addresses for my readers to contact me (pkattan@tedata. net. jo and pkattan@lsu. edu). The old email address that appeared in the ?rst edition was cancelled in 2004. December 2006 Peter I. Kattan PrefacetotheFirstEdition 3 This is a book for people who love ?nite elements and MATLAB . We will use the popular computer package MATLAB as a matrix calculator for doing ?nite element analysis. Problems will be solved mainly using MATLAB to carry out the tedious and lengthy matrix calculations in addition to some manual manipulations especially when applying the boundary conditions. In particular the steps of the ?nite element method are emphasized in this book. The reader will not ?nd ready-made MATLAB programsforuseasblackboxes. Insteadstep-by-stepsolutionsof?niteelementpr- lems are examined in detail using MATLAB.

Reflecting his major contributions to the field, Jean Lemaitre’s "Engineering Damage Mechanics" presents simplified and advanced methods organized within a unified framework for designers of any mechanical component. Explains how to apply continuous damage mechanics to failures of mechanical and civil engineering components in ductile, creep, fatigue and brittle conditions. Incorporates many basic examples, while emphasizing key practical considerations such as material parameter identification, and provides perspective on the advantage and disadvantages of various approaches.

This volume consists of a collection of chapters by recognized experts to provide a comprehensive fundamental theoretical continuum treatment of constitutive laws used for modelling the mechanical and coupled-field properties of various types of solid materials. It covers the main types of solid material behaviour, including isotropic and anisotropic nonlinear elasticity, implicit theories, viscoelasticity, plasticity, electro- and magneto-mechanical interactions, growth, damage, thermomechanics, poroelasticity, composites and homogenization. The volume provides a general framework for research in a wide range of applications involving the deformation of solid materials. It will be of considerable benefit to both established and early career researchers concerned with fundamental theory in solid mechanics and its applications by collecting diverse material in a single volume. The readership ranges from beginning graduate students to senior researchers in academia and industry.

An extensive and comprehensive survey of one- and three-dimensional damage models for elastic and inelastic solids. The book not only provides a rich current source of knowledge, but also describes examples of practical applications, numerical procedures, and computer codes. The style throughout is systematic, clear, and concise, and supported by illustrative diagrams. The state of the art is given by some 200 references.