Plasticity: Mathematical Theory and Numerical Analysis (Interdisciplinary Applied Mathematics Book 9)

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) The theory of elastoplastic media is now a mature branch of solid and structural mechanics, having experienced significant development during the latter half of this century. This monograph focuses on theoretical aspects of the small-strain theory of hardening elastoplasticity. It is intended to provide a reasonably comprehensive and unified treatment of the mathematical theory and numerical analysis, exploiting in particular the great advantages to be gained by placing the theory in a convex analytic context. The book is divided into three parts. The first part provides a detailed introduction to plasticity, in which the mechanics of elastoplastic behavior is emphasized. The second part is taken up with mathematical analysis of the elastoplasticity problem. The third part is devoted to error analysis of various semi-discrete and fully discrete approximations for variational formulations of the elastoplasticity. The work is intended for a wide audience: this would include 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. Front Matter....Pages i-xv Front Matter....Pages 1-1 Preliminaries....Pages 3-13 Continuum Mechanics and Linearized Elasticity....Pages 15-39 Elastoplastic Media....Pages 41-94 The Plastic Flow Law in a Convex-Analytic Setting....Pages 95-122 Front Matter....Pages 123-123 Basics of Functional Analysis and Function Spaces....Pages 125-150 Variational Equations and Inequalities....Pages 151-185 The Primal Variational Problem of Elastoplasticity....Pages 187-223 The Dual Variational Problem of Classical Elastoplasticity....Pages 225-248 Front Matter....Pages 249-249 Introduction to Finite Element Analysis....Pages 251-267 Approximation of Variational Problems....Pages 269-283 Approximations of the Abstract Problem....Pages 285-317 Numerical Analysis of the Primal Problem....Pages 319-370 Numerical Analysis of the Dual Problem....Pages 371-404 Back Matter....Pages 405-421 "The theory of elastoplastic media is now a mature branch of solid and structural mechanics, having experienced significant development during the latter half of this century. This monograph focuses on theoretical aspects of the small-strain theory of hardening elastoplasticity. It is intended to provide a reasonably comprehensive and unified treatment of the mathematical theory and numerical analysis, exploiting in particular the great advantages to be gained by placing the theory in a convex analytic context." "The work is intended for a wide audience: this would include 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."--Jacket

focussing On Theoretical Aspects Of The Small-strain Theory Of Hardening Elastoplasticity, This Monograph Provides A Comprehensive And Unified Treatment Of The Mathematical Theory And Numerical Analysis, Exploiting In Particular The Great Advantages Gained By Placing The Theory In A Convex Analytic Context. Divided Into Three Parts, The First Part Of The Text Provides A Detailed Introduction To Plasticity, In Which The Mechanics Of Elastoplastic Behaviour Is Emphasised, While The Second Part Is Taken Up With Mathematical Analysis Of The Elastoplasticity Problem. The Third Part Is Devoted To Error Analysis Of Various Semi-discrete And Fully Discrete Approximations For Variational Formulations Of The Elastoplasticity.

Preface to the Second Edition Preface to the First Edition.-Preliminaries Continuum Mechanics and Linearized Elasticity Elastoplastic Media The Plastic Flow Law in a Convex-Analytic Setting Basics of Functional Analysis and Function Spaces Variational Equations and Inequalities The Primal Variational Problem of Elastoplasticity The Dual Variational Problem of Classical Elastoplasticity Introduction to Finite Element Analysis Approximation of Variational Problems Approximations of the Abstract Problem Numerical Analysis of the Primal Problem References Index

. In its revised and expanded second edition, this book examines the theoretical aspects of small strain theory of elastoplasticity with hardening assumptions, offering a comprehensive and unified treatment of mathematical theory and numerical analysis.