A variational principle for hardening elastoplasticity

TL;DR

This paper introduces a variational principle for quasistatic elastoplastic evolution, enabling new insights into approximation, convergence, and error control in linear hardening materials.

Contribution

It presents a novel variational characterization that extends existing results and facilitates analysis of discretization convergence and error estimation.

Findings

Proves convergence of time and space-time discretizations.

Provides a framework for a posteriori error control.

Extends known results in elastoplasticity with a new variational approach.

Abstract

We present a variational principle governing the quasistatic evolution of a linearized elastoplastic material. In case of linear hardening, the novel characterization allows to recover and partly extend some known results and proves itself to be especially well-suited for discussing general approximation and convergence issues. In particular, the variational principle is exploited in order to prove in a novel setting the convergence of time and space-time discretizations as well as to provide some possible a posteriori error control.