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This paper deals with the study of a nonlinear problem of friction contact between two deformable bodies. The elastic constitutive law is a assumed to be nonlinear and the contact is modeled with Signorini’s conditions and version of Coulomb’s law of dry friction. 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. We establish existence and uniqueness results, using arguments of elliptic variational inequalities and a fixed point property and Lions, Stampachia theorem.

Mathematics Subject Classification (2010): 54AXX.

Keywords: Signorini’s conditions, elastic material, nonlinear constitutive law, Coulomb’s law of friction, contact problems, fixed point.