B6.: A space-time formulation for thermodynamic topology optimization for inelastic materials

Topology optimization is an important and prominent tool for computational design of construction parts. The computation of a topology optimization has become a standard in nowadays engineering. However, a still unsolved problem is to account for inelastic material behavior such as plasticity, for metals, or visco-elasticity, for 3D-printed parts, for instance. The question here is: how to (efficiently) incorporate the path-dependent material behavior during topology optimization?

In recent publications, it could be demonstrated that Hamilton’s principle of stationary action yields a holistic space-time framework for material modeling. Furthermore, the thermodynamic topology optimization follows from the very same Hamilton principle. Consequently, a space-time formulation of thermodynamic topology optimization for inelastic materials is at hand. For evaluation of the space-time dependent coupled system of differential equalities with inequality constraints, a suitable numerical scheme needs to be developed to enable (efficient) simulations. The project thus aims to conduct research on a virtual element method for space-time thermodynamic topology optimization.

Supervision: Supervision: Prof. Junker (UH), Prof. Wick (LUH) and Prof. Néron (ENS)