This book focuses on the theoretical aspects of small strain theory of elastoplasticity with hardening assumptions. It provides a comprehensive and unified treatment of the mathematical theory and numerical analysis. It is divided into three parts, with the first part providing a detailed introduction to plasticity, the second part covering the mathematical analysis of the elasticity problem, and the third part devoted to error analysis of various semi-discrete and fully discrete approximations for variational formulations of the elastoplasticity. This revised and expanded edition includes material on single-crystal and strain-gradient plasticity. In addition, the entire book has been revised to make it more accessible to readers who are actively involved in computations but less so in numerical analysis. Reviews of earlier edition: "The authors have written an excellent book which can be recommended for specialists in plasticity who wish to know more about the mathematical theory, as well as those with a background in the mathematical sciences who seek a self-contained account of the mechanics and mathematics of plasticity theory." (ZAMM, 2002) "In summary, the book represents an impressive comprehensive overview of the mathematical approach to the theory and numerics of plasticity. Scientists as well as lecturers and graduate students will find the book very useful as a reference for research or for preparing courses in this field." (Technische Mechanik) "The book is professionally written and will be a useful reference to researchers and students interested in mathematical and numerical problems of plasticity. It represents a major contribution in the area of continuum mechanics and numerical analysis." (Math Reviews)

Inelastic media constitute a rich source of interesting and important problems in theoretical, experimental and computationalmechanics. Signi?cantinsightshavebeengainedthroughstudiesofthemathematicalchar- teristics of new models. New constitutive theories have lead to variational and other formulations that are generally more complex, often highly nonlinear, and requ- ing new tools for their successful resolution. Likewise, there have been signi?cant advances of a computational nature, coupled to the development of new algorithms for solving such problems in discrete form. It is clear, therefore, that research in the broad area of inelastic media offers c- temporary investigators a range of challenges which are most fruitfully addressed througha combinationof theoretical, experimentaland computationalavenues.F- thermore, the ?eld is truly multidisciplinary in nature, drawing on the expertise of specialists in materials science, various branches of engineering, mathematics, and physics, and bene?ting from integrative approaches to the solution of problems. The objective of the IUTAM Symposium on Theoretical, Modelling and C- putational Aspects of Inelastic Media, held in Cape Town over the period 14-18 January 2008, was to provide a forum in which experts engaged in a spectrum of activities underthe theme of inelastic media could discussrecent developments, and also identify key open problem

This book focuses on the theoretical aspects of small strain theory of elastoplasticity with hardening assumptions. It provides a comprehensive and unified treatment of the mathematical theory and numerical analysis. It is divided into three parts, with the first part providing a detailed introduction to plasticity, the second part covering the mathematical analysis of the elasticity problem, and the third part devoted to error analysis of various semi-discrete and fully discrete approximations for variational formulations of the elastoplasticity. This revised and expanded edition includes material on single-crystal and strain-gradient plasticity. In addition, the entire book has been revised to make it more accessible to readers who are actively involved in computations but less so in numerical analysis. Reviews of earlier edition: "The authors have written an excellent book which can be recommended for specialists in plasticity who wish to know more about the mathematical theory, as well as those with a background in the mathematical sciences who seek a self-contained account of the mechanics and mathematics of plasticity theory." (ZAMM, 2002) "In summary, the book represents an impressive comprehensive overview of the mathematical approach to the theory and numerics of plasticity. Scientists as well as lecturers and graduate students will find the book very useful as a reference for research or for preparing courses in this field." (Technische Mechanik) "The book is professionally written and will be a useful reference to researchers and students interested in mathematical and numerical problems of plasticity. It represents a major contribution in the area of continuum mechanics and numerical analysis." (Math Reviews)

Inelastic media constitute a rich source of interesting and important problems in theoretical, experimental and computationalmechanics. Signi?cantinsightshavebeengainedthroughstudiesofthemathematicalchar- teristics of new models. New constitutive theories have lead to variational and other formulations that are generally more complex, often highly nonlinear, and requ- ing new tools for their successful resolution. Likewise, there have been signi?cant advances of a computational nature, coupled to the development of new algorithms for solving such problems in discrete form. It is clear, therefore, that research in the broad area of inelastic media offers c- temporary investigators a range of challenges which are most fruitfully addressed througha combinationof theoretical, experimentaland computationalavenues.F- thermore, the ?eld is truly multidisciplinary in nature, drawing on the expertise of specialists in materials science, various branches of engineering, mathematics, and physics, and bene?ting from integrative approaches to the solution of problems. The objective of the IUTAM Symposium on Theoretical, Modelling and C- putational Aspects of Inelastic Media, held in Cape Town over the period 14-18 January 2008, was to provide a forum in which experts engaged in a spectrum of activities underthe theme of inelastic media could discussrecent developments, and also identify key open problem