Existence and local uniqueness of solutions to contact problems in elasticity with nonlinear friction laws

Abstract

In this paper, we show how the use of interface models greatly facilitates the mathematical analysis of static friction phenomena. Such models have already found extensive arguments in their support, from both the experimental and numerical sides. They are then not conveniently introduced for purely mathematical purposes. Nevertheless, they also appear to provide a satisfactory substitute to the classical approach in terms of a variational problem with unilateral constraint. Indeed, we have been able to prove, with relatively simple arguments, the existence and uniqueness results that the classical theory has been unable to generate despite numerous attempts. In addition, in the case with no friction, the solution obtained through the classical theory is shown to be recovered in the limiting case of an infinite normal stiffness, thus giving one more justification of the validity of such models.