Unilateral contact with adhesion and friction between two hyperelastic bodies

In the present paper, we consider a thermodynamic model using the contact kinematics developed by A. Curnier, Q.C. He and J.J. Téléga [C. R. Acad. Sci. Paris Sér. II 314 (1992) 1] involving unilateral contact, adhesion and Coulomb friction between two homogeneous, isotropic and hyperelastic bodies. Adhesion is described by an internal state variable βϕ introduced by M. Frémond [C. R. Acad. Sci. Paris Sér. II 295 (1982) 913; J. Theor. Appl. Mech. 6 (1987) 383]. Taking the case of contact between a hyperelastic solid and a plane support, we formulate the associated boundary value problem as a minimization problem when no friction is involved. When the intensity of the adhesion obeys a `static' law, we obtain an existence result for this problem.