  We study the time evolution of non-linear viscoelastic solids in the presence
of inertia and (self-)contact. For this problem we prove the existence of weak
solutions for arbitrary times and initial data, thereby solving an open problem
in the field. Our construction directly includes the physically correct,
measure-valued contact forces and thus obeys conservation of momentum and an
energy balance. In particular, we prove an independently useful compactness
result for contact forces.
