A new branch of science usually develops thus. Somebody publishes the basic ideas. Hesitatingly at first, then little by little, other original contributions appear, until a certain threshold is reached. Then, overview articles are printed, conferences are held, and a first mention is made in textbooks, until specialized monographs are written. Continuum darnage mechanics has reached that status now. To analyze or, if possible, to predict the failure of machine parts or other structures is one of the main goals of engineering science. Consequently fracture mechanics became one of its leading branches. It was based on the analysis of existing cracks. However, especially under conditions of cyclic loading, this might be too late to prevent a disaster. Therefore, the question regarding the precursory state, that is, the evolution of intemal darnage before macrocracks become visible, was then posed. One of the successful approaches to the problern was Weibull's theory which examined, in a statistical manner, the "weakest link" in the material volume under consideration. Unfortunately it proved too difficult mathematically to be applied to complicated parts or structures. Therefore it was highly appreciated by the scientific of material community when L. M. Kachanov published in 1958 a simple model darnage which subsequently could be extended to brittle elastic, plastic or viscous materials under all conditions of uniaxial or multiaxial, simple or cyclic loadings, so that it may be considered nearly universal.

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

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.

The principal objective of this book is to relate the random distributions of defects and material strength on the microscopic scale with the deformation and residual strength of materials on the macroscopic scale. To reach this goal the authors considered experimental, analytical and computational models on atomic, microscopic and macroscopic scales.

This book provides the first truly comprehensive study of damage mechanics. All concepts are carefully identified and defined in micro- and macroscopic scales. In terms of the methods and observation scales, the main part of the book is divided into three chapters. These chapters consider the stochastic models applied to atomistic scale, micromechanical models (for arbitary concentrations of defects) on microscopic scale and continuum models on the macroscopic scale. It is intended for people who are doing or planning to do research in the mechanics and material science aspects of brittle deformation of solids with heterogeneous microstructure.

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.

When asked to start teaching a course on engineering fracture mechanics, I realized that a concise textbook, giving a general oversight of the field, did not exist. The explanation is undoubtedly that the subject is still in a stage of early development, and that the methodologies have still a very limited applicability. It is not possible to give rules for general application of fracture mechanics concepts. Yet our comprehension of cracking and fracture beha viour of materials and structures is steadily increasing. Further developments may be expected in the not too distant future, enabling useful prediction of fracture safety and fracture characteristics on the basis of advanced fracture mechanics procedures. The user of such advanced procedures m\lst have a general understanding of the elementary concepts, which are provided by this volume. Emphasis was placed on the practical application of fracture mechanics, but it was aimed to treat the subject in a way that may interest both metallurgists and engineers. For the latter, some general knowledge of fracture mechanisms and fracture criteria is indispensable for an apprecia tion of the limita tions of fracture mechanics. Therefore a general discussion is provided on fracture mechanisms, fracture criteria, and other metal lurgical aspects, without going into much detail. Numerous references are provided to enable a more detailed study of these subjects which are still in a stage of speculative treatment.

This book is about the use of fracture mechanics for the solution of practical problems; academic rigor is not at issue and dealt with only in as far as it improves insight and understanding; it often concerns secondary errors in engineering. Knowledge of (ignorance of) such basic input as loads and stresses in practical cases may cause errors far overshadowing those introduced by shortcomings of fracture mechanics and necessary approximations; this is amply demonstrated in the text. I have presented more than three dozen 40-hour courses on fracture mechanics and damage tolerance analysis, so that I have probably more experience in teaching the subject than anyone else. I learned more than the students, and became cognizant of difficulties and of the real concerns in applications. In particular I found, how a subject should be explained to appeal to the practicing engineer to demonstrate that his practical problem can indeed be solved with engineering methods. This experience is reflected in the presenta tions in this book. Sufficient background is provided for an understanding of the issues, but pragamatism prevails. Mathematics cannot be avoided, but they are presented in a way that appeals to insight and intuition, in lieu of formal derivations which would show but the mathematical skill of the writer.

This publication is aimed at students, teachers, and researchers of Continuum Mechanics and focused extensively on stating and developing Initial Boundary Value equations used to solve physical problems. With respect to notation, the tensorial, indicial and Voigt notations have been used indiscriminately. The book is divided into twelve chapters with the following topics: Tensors, Continuum Kinematics, Stress, The Objectivity of Tensors, The Fundamental Equations of Continuum Mechanics, An Introduction to Constitutive Equations, Linear Elasticity, Hyperelasticity, Plasticity (small and large deformations), Thermoelasticity (small and large deformations), Damage Mechanics (small and large deformations), and An Introduction to Fluids. Moreover, the text is supplemented with over 280 figures, over 100 solved problems, and 130 references.

In mechanical engineering and structural analysis there is a significant gap between the material models currently used by engineers for industry applications and those already available in research laboratories. This is especially apparent with the huge progress of computational possibilities and the corresponding dissemination of numerical tools in engineering practice, which essentially deliver linear solutions. Future improvements of design and life assessment methods necessarily involve non-linear solutions for inelastic responses, in plasticity or viscoplasticity, as well as damage and fracture analyses. The dissemination of knowledge can be improved by software developments, data base completion and generalization, but also by information and training. With such a perspective Non-Linear Mechanics of Materials proposes a knowledge actualization, in order to better understand and use recent material constitutive and damage modeling methods in the context of structural analysis or multiscale material microstructure computations.