Dynamic contact problem with adhesion and damage between thermo–electro–elasto-viscoplastic bodies

We study of a dynamic contact problem between two thermo–electro–elasto-viscoplastic bodies with damage and adhesion. The contact is frictionless and is modeled with normal compliance condition. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of evolutionary variational inequalities, parabolic inequalities, differential equations, and fixed point theorem.