Plasticity: Mathematical Theory and Numerical Analysis

✍ Scribed by Weimin Han, B. Daya Reddy (auth.)

• Publisher: Springer-Verlag New York
• Year: 2013
• Tongue: English
• Leaves: 372
• Series: Interdisciplinary Applied Mathematics 9
• Edition: 2
• Category: Library

✦ Synopsis

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)

✦ Table of Contents

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

✦ Subjects

Numerical Analysis; Theoretical and Applied Mechanics; Continuum Mechanics and Mechanics of Materials