Boundary Element and Augmented Lagrangian Methods for Contact Problem with Coulomb Friction

Abstract

In this paper, boundary element and augmented Lagrangian methods for Coulomb friction contact problems are presented. Based on the projection technique, both unilateral contact and Coulomb friction conditions are reformulated as fixed point problems. The original problem is deduced to a variational formulation with boundary integral operators. Then, we propose a new augmented Lagrangian method which can be dealt with the semismooth Newton method. Short theoretical results and the algorithm description are given. Numerical simulations show the performance of the method proposed.

Nitsche method for contact with Coulomb friction: Existence results for the static and dynamic finite element formulations

“…In fact, it is well known that the finite element problem admits a solution and that the solution is unique if the friction coefficient is small enough, but the denomination small depends on the discretization parameter. Moreover, the improvement of numerical methods to solve contact with Coulomb friction represents still a very active research field (see for instance [3,51]). For Coulomb friction in elastodynamics, results are even more scattered (see [21] for a review).…”