A frictionless contact problem for elastic-viscoplastic materials with internal state variables

This paper deals with an initial and boundary value problem describing the quasistatic evolution of a rate-type viscoplastic material with internal state variables which is in frictionless contact. Two variational formulations of the problem are proposed, and existence and uniqueness results established. The equivalence of the variational formulation is studied and a strong convergence result involving penalized problems is proved.