Elasto-plastic contact problems with heat exchange

This paper deals with a dynamical model for the motion of a one-dimensional visco-elasto-plastic body in contact with an elasto-plastic obstacle and undergoing thermal expansion. The problem for the unknown displacement and temperature is rewritten in accordance with the formalism of hysteresis operators as solution operators of the underlying variational inequalities. The system consists of the momentum balance and energy balance equations. The existence result for this thermodynamically consistent problem is obtained by using some a priori estimates established for the space discretized problem while the uniqueness result follows from the Lipschitz continuity of the nonlinearities.