Topology optimization in quasi-static plasticity with hardening using a level-set method

We study topology optimization in quasi-static plasticity with linear kinematic and linear isotropic hardening using a level-set method. We consider the primal variational formulation for the plasticity problem. This formulation is subjected to penalization and regularization, resulting in an approximate problem that is shape-differentiable. The shape derivative for the approximate problem is computed using the adjoint method. Thanks to the proposed penalization and regularization, the time discretization of the adjoint problem is proved to be well-posed. For comparison purposes, the shape derivative for the original problem is computed in a formal manner. Finally, shape and topology optimization is performed numerically using the level-set method, and 2D and 3D case studies are presented. Shapes are captured exactly using a body-fitted mesh at every iteration of the optimization algorithm.