Analysis and numerical simulation of dynamic contact problem with friction in thermo-viscoelasticity

Abstract

The focus of our study is a dynamic frictional contact model that involves a viscoelastic body and a conductive foundation. We use Coulomb's law to describe the frictional behavior, while a normal compliance model is employed to simulate the contact. We formulate a variational formulation for the problem, and we establish the existence of its unique weak solution using the Banach fixed point theorem. We propose a fully discrete scheme, using the finite element method for the spatial approximation and the Euler scheme for the discretization of the time derivatives. The errors on the solutions are derived, and the linear convergence is obtained under suitable regularity hypotheses. Some numerical simulations are included to show the performance of method.