In this talk we consider the interaction of a Stokes/Navier-Stokes flow with a viscoelastic body. The elastic body is allowed to undergo large deformations (but no self-collisions). In order to handle this situation correctly, we devise a variational approximation scheme in the spirit of DeGiorgi to the combined problem. Moreover, by using a two-scale scheme, we also extend this approach to the hyperbolic regime including inertia of the solid body. These variational approaches allow us to prove proper energetic estimates while also controling the geometric restictions posed on the solid body and, eventually, to establish existence of weak solutions.