Contacts et auto-contacts sans frottement

Let M be a submanifold of ${\mathbb{R}}^n$ ($n=2,3$) considered as the reference configuration of a hyperelastic solid. A topological constraint is imposed on the admissible deformations $\psi :M\to {\mathbb{R}}^n$ 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 $\dim (M)\ne 2$ or $n\ne 3$, 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).