Abstract: A dynamic contact problem for elastic-viscoplastic materials with thermal effects is investigated. The contact is bilateral, and the friction is modeled with Tresca’s friction law with heat exchange. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear first order evolution inequalities, the equations with monotone operators, and the fixed point arguments. Finally, the continuous dependence of the solution on the friction yield limit is studied.

Key words: thermo-elasto-viscoplastic material, dynamic process, bilateral contact, Tresca’s friction, evolution inequality, evolution equation, weak solution, fixed point, Galerkin meshless method, finite cover, partition of unity, numerical quadrature