A HISTORY-DEPENDENT CONTACT PROBLEM WITH UNILATERAL CONSTRAINT

We consider a mathematical model which describes the quasistaticcontact between a viscoplastic body and a foundation. The contactis frictionless and is modelled with a new and nonstandard conditionwhich involves both normal compliance, unilateral constraint and memoryeffects. We derive a variational formulation of the problem thenwe prove its unique weak solvability. The proof is based on argumentson history-dependent variational inequalities.