Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening Part I: Existence and Discretization in Time

TL;DR

This paper investigates the optimal control of quasistatic plasticity with linear kinematic hardening, establishing existence results and proposing a time discretization method that approximates continuous solutions.

Contribution

It provides new theoretical insights into the existence of optimal controls and introduces a discretization scheme for quasistatic plasticity problems.

Findings

Existence of optimal control proven

Time discretization scheme developed

Approximation of continuous minimizers shown

Abstract

In this paper we consider an optimal control problem governed by a time-dependent variational inequality arising in quasistatic plasticity with linear kinematic hardening. We address certain continuity properties of the forward operator, which imply the existence of an optimal control. Moreover, a discretization in time is derived and we show that every local minimizer of the continuous problem can be approximated by minimizers of modified, time-discrete problems.