Topology optimization for quasistatic elastoplasticity

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.