Mixed Formulation for a Signorini Problem

Problem statement: This study deals with the study of a Signorini Problem (SP) of unilateral contact between two a linear or non linear elastic bodies. Approach: We present two variational formulations noted P₁, P₂, of the considered problem, where P1 depends on the displacement field and P₂ depends on the stress field. In the linear case, under assumptions, then the considered problem was equivalent to a mixed variational formulation problem, where the unknowns are the displacement field and the normal constraint stress on the contact area. Results: Problems P1 and P2 were formally equivalent to the Signorini Problem (SP) and using Lions-Stampachia Theorem, we shown the existence and uniqueness result. Conclusion: The Signorini problem (PS) has a unique variational solution.