Contact problems with friction: models and simulations

This article deals with the modeling and the numerical simulation of contact and friction problems. Some friction formulations are proposed and numerical methods of resolution by finite elements are presented. Two methods are more particularly developed. The first one is based on a formulation using displacements and the second one is based on a mixed formulation using displacements and contact forces. Then, some improvements of these two methods as well as a comparison of their respective performances are presented.