Existence and uniqueness results for a class of dynamic elasto-plastic contact problems

Abstract

This paper focuses on a dynamical model for the motion of a visco-elasto-plastic body in contact with an elasto-plastic obstacle. The elastoplastic constitutive laws as well as the contact boundary condition are stated in terms of hysteresis operators. Under appropriate regularity assumptions on the initial data, we show that the resulting partial differential equation with hysteresis possesses a unique solution which is constructed by Galerkin approximations and the Minty trick. In the 1D case, the existence and uniqueness proof can be carried out without the viscosity assumption, and the necessary a priori estimates are derived from a hysteresis second order energy inequality.