Unilateral contact with adhesion and friction between two hyperelastic bodies

• Published in: International journal of engineering science Vol. 39; no. 18; pp. 2015 - 2032
• Main Authors: Bretelle, A.-S., Cocou, M., Monerie, Y.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-12-2001; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mechanical contact (friction...); Mechanics; Physics; Solid mechanics; Structural and continuum mechanics; Structural mechanics; Tribology and mechanical contacts; High strain; Quasi static theory; Mechanical contact; Adhesion; Modeling; Dry friction; Hyperelasticity; Boundary value problem; Thermodynamic model; Kinematics; Unilateral; Internal variable material; Isotropic material
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/S0020-7225(01)00052-0

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
β
ϕ
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.