Optimal control of quasistatic plasticity with linear kinematic hardening II: regularization and differentiability
Summary: We consider an optimal control problem governed by an evolution 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 quasilinear PDEs whose principal parts depend on the gradient of the state. We show the Fréchet differentiability of the solution map of this quasilinear system. As a consequence, we obtain a first order necessary optimality system. Moreover, we address certain convergence properties of the regularization. Editorial remark: for part I, see [Zbl 1258.49008].
scientific article; zbMATH DE number 6510071
scientific article