A mixed finite element method and solution multiplicity for Coulomb frictional contact Original Research Article

This paper is concerned with the discrete contact problem governed by Coulomb’s friction law. We propose and study a new technique using mixed finite elements with two multipliers in order to determine numerically critical friction coefficients for which multiple solutions to the friction problem exist. The framework is based on eigenvalue problems and it allows to exhibit non-uniqueness cases involving an infinity of solutions located on a continuous branch. The theory is illustrated with several computations which clearly show the accuracy of the proposed method.