Injectivité presque partout, auto-contact, et non-interpénétrabilité en élasticité non linéaire tridimensionnelle (Almost everywhere injectiveness, self-contact, and non-interpenetration in nonlinear three-dimensional elasticity). (French) Zbl 0585.73018

Generalizing previous existence results of J. Ball [Arch. Ration. Mech. Anal. 63, 337-403 (1977; Zbl 0368.73040)] for the minimization problem of the total energy in nonlinear elasticity for a mixed traction- displacement problem, the authors, imposing an additional condition on the global volumetric behavior of the admissible deformation, are able to show that any deformation satisfying the boundary conditions and the orientation-preserving condition, which minimizes the total energy of the body, is almost everywhere injective, and that the associated minimization problem is a mathematical problem of self-contact without friction and non-interpenetration of matter. The proofs make use of previous results of no-friction unilateral problems and passing to the limit when considering a minimizing sequence of the energy. The full developments will be given elsewhere.
Reviewer: G.A.Maugin


74B20 Nonlinear elasticity
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics


Zbl 0368.73040