Topology optimization for quasistatic elastoplasticity

¹ Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, via Cintia, 80126 Napoli, Italy
² Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
³ Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währingerstraße 17, 1090 Wien, Austria
⁴ Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, via Ferrata 1, 27100 Pavia, Italy

^* Corresponding author: ulisse.stefanelli@univie.ac.at

Received: 18 June 2021
Accepted: 2 May 2022

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-continuous 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.