Solution multiplicity and stick configurations in continuous and finite element friction problems

This work is concerned with friction problems in linear elasticity. We consider the unilateral contact model with the static Coulomb friction law in the continuous and finite element contexts. Having at our disposal a solution of the problem where stick does not occur on the entire contact zone, we consider the simple problem which consists of checking if the stick configuration solves also the friction problem. We prove that this solution multiplicity phenomenon occurs in the continuous case when a solution with grazing contact exists. We perform the corresponding finite element computations as well as some ones dealing with separation solutions.