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. In contrast to physical loading and unloading processes, a virtual unloading due to stiffness evolution during the optimization process must not result in a hysteresis in the stress/strain diagram. Therefore, this problem is usually resolved by simulating the entire load path for each optimization step. To avoid this time-consuming procedure, we develop a surrogate material model that yields identical results for the loading case but does not dissipate energy during the virtual unloading. The model is embedded into our strategy for topology optimization that routes back to thermodynamic extremal principles. We present the derivation of all model equations and suitable strategies for numerical solution. Then, we validate our model by means of solving optimization problems for several boundary value problems and empirically show that our novel material models yields very similar distributions of the plastic strains as classical elasto-plastic material models. Consequently, thermodynamic topology optimization allows to optimize elasto-plastic materials at low numerical costs without the need of computing the entire load history for each optimization step.