A penalized viscoplastic contact problem with unilateral constraints

In this paper we study a mathematical model which describes the quasistatic contact between a viscoplastic body and a foundation. The contact is frictionless and is modelled with a new and nonstandard condition which involves both normal compliance, unilateral constraint and memory eects. We present a penalization method in the study of this problem. We start by introducing the penalized problem, then we prove its unique solvability as well as the convergence of its solution to the solution of the original problem, as the penalization parameter converges to zero.