Optimal Control of Plasticity with Inertia

TL;DR

This paper develops an optimal control framework for elasto-plasticity with inertia, transforming the governing equations into an evolution variational inequality and deriving optimality conditions through regularization techniques.

Contribution

It introduces a novel approach to control elasto-plastic systems with inertia by reformulating the problem as an EVI and applying Yosida regularization for optimality analysis.

Findings

Successful formulation of the control problem as an EVI.

Derivation of optimality conditions via Yosida approximation.

Enhanced understanding of controlling plasticity with inertia.

Abstract

The paper is concerned with an optimal control problem governed by the equations of elasto plasticity with linear kinematic hardening and the inertia term at small strain. The objective is to optimize the displacement field and plastic strain by controlling volume forces. The idea given in [10] is used to transform the state equation into an evolution variational inequality (EVI) involving a certain maximal monotone operator. Results from [27] are then used to analyze the EVI. A regularization is obtained via the Yosida approximation of the maximal monotone operator, this approximation is smoothed further to derive optimality conditions for the smoothed optimal control problem.