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We consider a dynamic contact problem between an elastic-viscoplastic body and a rigid obstacle. The contact is frictional and bilateral, the friction is modeled with Tresca's law with heat exchange. We employ the elastic-viscoplastic with damage constitutive law for the material . The evolution of the damage is described b y an inclusion of parabolic type.We establish a variational formulation for the model and we prove the existence of a unique weak solution to the problem. The proof is based on a classical existence and uniquness result on parabolic inequalities, differentiel equations and fixed point argument.

A dynamic Tresca's frictional contact problem with damage for thermo elastic-viscoplastic bodies