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We discuss a topology optimization problem for an elastoplastic medium. The distribution of material in a region is optimized with respect to a given target functional taking into account compliance. The incremental elastoplastic problem serves as state constraint. We prove that the topology optimization problem admits a solution. First-order optimality conditions are obtained by considering a regularized problem and passing to the limit.

Topology Optimization for Incremental Elastoplasticity: A Phase-Field Approach