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Zeitschrift für Analysis und ihre Anwendungen


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Volume 35, Issue 1, 2016, pp. 81–118
DOI: 10.4171/ZAA/1556

Published online: 2015-12-23

Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening III: Optimality Conditions

Gerd Wachsmuth[1]

(1) Technische Universität Chemnitz, Germany

In this paper we consider an optimal control problem governed by a rate-independent variational inequality arising in quasistatic plasticity with linear kinematic hardening. Since the solution operator of a variational inequality is not diff erentiable, the Karush-Kuhn-Tucker system is not a necessary optimality condition. We show a system of weakly stationary type by passing to the limit with the optimality system of a regularized and time-discretized problem.

Keywords: Complementarity condition, quasistatic plasticity, time-dependent variational inequality, mathematical program with complementarity constraints, evolution variational inequality, rate-independent

Wachsmuth Gerd: Optimal Control of Quasistatic Plasticity with Linear Kinematic Hardening III: Optimality Conditions. Z. Anal. Anwend. 35 (2016), 81-118. doi: 10.4171/ZAA/1556