An elastic-viscoplastic contact problem with internal state variable, normal damped response and unilateral constraint

In this manuscript, we study a contact problem between an elastic-viscoplastic body and an obstacle. The contact is quasistatic and it is described with a normal damped response condition with friction and unilateral constraint. Moreover, we use an elastic-viscoplastic constitutive law with internal state variable to model the material's behavior. We present the classical problem then we derive its variational formulation. Finally, we prove that the associated variational problem has a unique solution. The proof is based on arguments of quasivariational inequalities and fixed points.