Continuum Damage Mechanics And The Finite Element Method

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.

The major goal of this book is to present the implementation of some damage models with finite elements. The damage models are based on the principles of continuum damage mechanics and the effective stress concept. Several books have appeared recently on damage mechanics but are mostly theoretical in nature. Alternatively, this book provides a complete finite element program that includes the effects of damage. The book consists of two parts. Part I includes two chapters mainly review ing topics from finite element analysis and continuum damage mechanics. The reader is cautioned that the material contained in this part is introductor- other references must be consulted for the theoretical aspects of these topics. For a complete theoretical treatment of the subject, the reader is referred to the book Advances in Damage Mechanics: Metals and Metal Matrix Composites by Voyiadjis and Kattan, published in 1999. In Part II the finite element program DNA is introduced in three chapters. DNA stands for "Da mage Nonlinear Analysis". The program can be used for the analysis of elasto plastic material behavior including the effects of damage within the frame work of damage mechanics. Two versions of DNA are presented - one for small strain analysis and one for finite strain analysis. The program makes extensive calls to a library of tensor operations developed by the authors. The tensor library is extensively outlined in the last chapter of the book.

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.

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

Created in 1975, LMT-Cachan is a joint laboratory École Normale Superieure de Cachan, Pierre & Marie Curie (Paris 6) University and the French Research Council CNRS (Department of Engineering Sciences). The Year 2000 marked the 25th anniversary of LMT. On this occasion, a series of lectures was organized in Cachan in September-October, 2000. This publication contains peer-reviewed proceedings of these lectures and is aimed to present engineers and scientists with an overview of the latest developments in the field of damage mechanics. The formulation of damage models and their identification procedures were discussed for a variety of materials.

This textbook offers readers an introduction to fracture mechanics, equipping them to grasp the basic ideas of the presented approaches to modeling in applied mechanics In the first part, the book reviews and expands on the classical theory of elastic and elasto-plastic material behavior. A solid understanding of these two topics is the essential prerequisite to advancing to damage and fracture mechanics. Thus, the second part of this course provides an introduction to the treatment of damage and fractures in the context of applied mechanics Wherever possible, the one-dimensional case is first introduced and then generalized in a following step. This departs somewhat from the more classical approach, where first the most general case is derived and then simplified to special cases. In general, the required mathematics background is kept to a minimum Tutorials are included at the end of each chapter, presenting the major steps for the solution and offering valuable tips and tricks. The supplementary problems featured in the book

"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.

A unified treatment of nonlinear continuum analysis and finite element techniques.

Contains papers from the May 1996 Symposium on Applications of Continuum Damage Mechanics (CDM) to Fatigue and Fracture. Papers in Section I deal with various aspects of modeling damage in composite materials, such as high temperature environmental degradation, fatigue, and viscous damage in metal a