Analysis of an evolutionary variational inequality arising in elasticity quasi-static contact problems

Abstract

In this paper, we present the strong and the variational form of a dynamic contact problem with friction. We derive the result and obtain an incremental formulation by space discretization with finite element method and by time discretization with finite difference method of the dynamic contact problem. As well we describe the solution strategies for spatially discrete system and the condition for stability of the solution. Difficulties caused by the discontinuity of the Coulomb's friction law (passage from sliding to adhesion), are tried to be passed over using the Newton-Raphson iterative techniques, and their success depends also on the small value of the parameter, from the regularized friction law.