Plasticity: Mathematical Theory and Numerical Analysis

Shai M. J. Haran3540783784, 9783540783787

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.

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Table of contents :
front-matter……Page 1
1Preliminaries……Page 12
2Continuum Mechanics and Linear Elasticity……Page 23
3Elastoplastic Media……Page 49
4The Plastic Flow Law in a Convex-Analytic Setting……Page 79
5Results from Functional Analysis and Function Spaces……Page 102
6Variational Equations and Inequalities……Page 129
7The Primal Variational Problem of Elastoplasticity……Page 154
8The Dual Variational Problem of Elastoplasticity……Page 179
9Introduction to Finite Element Analysis……Page 205
10Approximation of Variational Problems……Page 223
11Approximations of the Abstract Problem……Page 237
12Numerical Analysis of the Primal Problem……Page 271
13Numerical Analysis of the Dual Problem……Page 319
back-matter……Page 355