Existence of solutions past collisions for viscoelastic solids

In this talk, we will consider 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, e.g. 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. Our presentation will additionally delve into the latest developments concerning solids with Lipschitz boundaries.