  We introduce a two time-scale scheme which allows to extend the method of
minimizing movements to hyperbolic problems. This method is used to show the
existence of weak solutions to a fluid-structure interaction problem between a
nonlinear, visco-elastic, $n$-dimensional bulk solid governed by a hyperbolic
evolution and an incompressible fluid governed by the ($n$-dimensional)
Navier-Stokes equations for $n\geq 2$.
