OPTIMAL CONTROL OF QUASISTATIC PLASTICITY WITH LINEAR KINEMATIC HARDENING PART II: REGULARIZATION AND DIFFERENTIABILITY

Abstract. We consider an optimal control problem governed by a time-dependent variational inequality arising in quasistatic plasticity with linear kinematic hardening. A regularization of the time-discrete problem is derived. The regularized forward problem can be interpreted as system of coupled quasi-linear PDEs whose principal parts depend on the gradient of the state. We show the Fréchet differentiability of the solution map of this quasilinear sys-tem. As a consequence, we obtain a first order necessary optimality system. Moreover, we address certain convergence properties of the regularization.