Scales and shapes in continuum thermomechanics

We will propose a mathematically lucid setting for the derivation of reduced models from nonlinear continuum thermomechanics. We will justify linearized models in thermoviscoelasticity and viscoplasticity as limits of the nonlinear deformation theory employing variational convergence. We will also investigate lower-dimensional models as limit models of bulk structures subject to the injectivity constraints. We are going to investigate topology optimization problems in elastoplasticity, damage, and for fracture-undergoing and microstructural materials. Here, we include linear and nonlinear setting, time-incremental, and time-continuous models. Based on these results, new optimal control problems will be formulated and analyzed. Finally, efficient numerical approaches and computational simulations of the above-mentioned problems will complete our effort in establishing rigorous but also practically applicable models. In addition, we will derive discretization schemes of reduced models adapted to the structure of the so-called GENERIC framework.