Thermodynamic topology optimization including plasticity

In this contribution, we present an extension of the thermodynamic topology optimization that accounts for a non-linear material behavior due to the evolution of plastic strains. Physically, a plastic material behavior is characterized by a hysteresis in the stress/strain diagram after loading and unloading. In contrast, topology optimization is usually employed for a time-invariant load and the optimized component will only be loaded during physical use. Still, a virtual increase and decrease of strains, i.e., an unphysical evolution of the strains during the optimization process, is locally observed due to the evolution of the structure and thus modulation of the stiffness. If a classical plasticity model is employed for this unphysical ``loading'' and ``unloading'', incorrect strain and stress states are computed due to the apparent energy dissipation and hysteresis in the stress/strain diagram. Therefore, this problem is usually resolved by recomputing the physical behavior for each optimization step: the initial conditions are refreshed by deleting all plastic strains computed for the previous optimization step. This restores the virgin state for the updated topology. The plastic strains are subsequently determined by evaluating the classical plasticity model which requires a discretization of the loading which results in several finite element simulations. After the correct plastic strains have been found, the next update step for the topology optimization is performed. To avoid this time-consuming procedure, we develop a novel surrogate material model that allows to correctly account for the physical state in terms of the plastic strains. Hence, finite element simulations purely for the plastic material behavior become obsolete such that the optimization of plastic materials now consumes comparable computation times as the optimization of elastic materials.