Analysis of a Dynamic Frictional Contact Problem for Thermo-Elastic-Viscoplastic Materials with Damage

We consider a dynamic frictional contact problem with normal domped response. The material is elastic-viscoplastic with two internal variables which may describe the damage of the system caused by plastic deformations and a temperature parameter. We derive a weak formulation of the system consisting of a motion equation, an energy equation, and an evolution damage inclusion. We prove existence and uniqueness of the weak solution, and the positivity of the temperature. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic type inequalities, fixed-point arguments and differential equations.