Contacts et auto-contacts sans frottement

Let M be a submanifold of Rn (n=2,3) considered as the reference configuration of a hyperelastic solid. A topological constraint is imposed on the admissible deformations ψ:M→Rn of the solid in order to satisfy a non penetration condition. We show that the associated minimization problem has at least one solution and, in the case dim(M)≠2 or n≠3, provides a mathematical model of body that allows frictionless self-contact. A numerical application is presented. To cite this article: O. Pantz, C. R. Acad. Sci. Paris, Ser. I 341 (2005).