M. Shillor and M. Sofonea,
Communications in Applied Analysis, 5(1)(2001), 135-151.

We consider a nonstandard mathematical problem which
describes the frictional contact between an elastic-viscoplastic
body and a rigid obstacle. The frictional contact is modeled by
a general velocity dependent dissipation functional. We obtain
a weak formulation for the model and prove an existence and
uniqueness result. The proof is based on the theory of evolution
variational inequalities and the Banach fixed point theorem. We
describe a number of concrete friction conditions which may be
set in this form. We also obtain an existence and uniqueness result
for a model of an elastic-viscoplastic material with internal state
variables, which in particular, may describe the evolution of the
system's damage.