  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.
