Plasticity

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.

Contenu

Continuum Mechanics and Elastoplasticity Theory.- Preliminaries.- Continuum Mechanics and Linear Elasticity.- Elastoplastic Media.- The Plastic Flow Law in a Convex-Analytic Setting.- The Variational Problems of Elastoplasticity.- Results from Functional Analysis and Function Spaces.- Variational Equations and Inequalities.- The Primal Variational Problem of Elastoplasticity.- The Dual Variational Problem of Elastoplasticity.- Numerical Analysis of the Variational Problems.- to Finite Element Analysis.- Approximation of Variational Problems.- Approximations of the Abstract Problem.- Numerical Analysis of the Primal Problem.- Numerical Analysis of the Dual Problem.