In this talk, we will examine the time evolution of viscoelastic solids within a framework that allows for collisions and self-contact. In the static and quasi-static regimes, corresponding existence results have been shown through variational descriptions of the problem. For the fully dynamical case, however, collisions have so far either been ignored or handled using a simplified model (for example, using repulsive terms). In contrast to this, by employing a newly developed variational technique, we are able to prove the existence of solutions for arbitrary times. In the second part of the talk, we will delve into the latest developments concerning solids with Lipschitz boundaries and discuss technical and conceptual difficulties that arise due to the presence of corners.

Zoom meeting: link