Optimal Control of Static Elastoplasticity in Primal Formulation

An optimal control problem of static plasticity with linear kinematic hardening and von Mises yield condition is studied. The problem is treated in its primal formulation, where the state system is a variational inequality of the second kind. First-order necessary optimality conditions are obtained by means of an approximation by a family of control problems with state system regularized by Huber-type smoothing, and a subsequent limit analysis. The equivalence of the optimality conditions with the C-stationarity system Herzog et al. [2012] for the equivalent dual formulation of the problem is proved. Numerical experiments are presented, which demonstrate the viability of the Huber-type smoothing approach.