A dynamic contact problem for thermo-electro-visoplastic materials with damage and internal state variable

This work studies a mathematical model involving a dynamic contact between two thermo-elasto-viscoplastic piezoelectric bodies with internal state variables and damage. The contact is modelled with normal compliance condition and adhesion effect of contact surfaces. We derive variational formulation of the problem and we prove an existence and uniqueness result of the weak solution. The proof is based on classical existence and uniqueness result on parabolic inequalities, differential equations and fixed-point arguments.