Topology optimization for quasistatic elastoplasticity

TL;DR

This paper develops a phase-field based topology optimization method for quasistatic elastoplastic materials, proving existence of optimal shapes and deriving optimality conditions through a sequence of approximations.

Contribution

It introduces a novel phase-field approach for elastoplastic topology optimization, establishing existence and optimality conditions at both discrete and continuous levels.

Findings

Existence of optimal shapes proven at discrete and continuous levels.

First-order optimality conditions derived and shown to pass to the limit.

Phase-field approximation converges to sharp-interface limit via variational methods.

Abstract

Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic medium under kinematic hardening. We adopt a phase-field approach and argue by subsequent approximations, first by discretizing time and then by regularizing the flow rule. Existence of optimal shapes is proved both at the time-discrete and time-continous level, independently of the regularization. First order optimality conditions are firstly obtained in the regularized time-discrete setting and then proved to pass to the nonregularized time-continuous limit. The phase-field approximation is shown to pass to its sharp-interface limit via an evolutive variational convergence argument.