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Comptes Rendus Mathématique
Volume 341, n° 6
pages 393-398 (septembre 2005)
Doi : 10.1016/j.crma.2005.06.034
Received : 12 May 2005 ;  accepted : 28 June 2005
Contacts et auto-contacts sans frottement
Frictionless contact and self-contact
 

Olivier Pantz
Centre de mathématiques appliquées, École polytechnique, 91128 Palaiseau cedex, France 

Résumé

Soit M une sous-variété de   ( ) considérée comme configuration de référence dʼun solide hyperélastique. Une contrainte topologique est imposée aux déformations admissibles   du solide afin de satisfaire une condition de non interpénétration. Nous montrons que le problème de minimisation associé possède au moins une solution. A lʼexception du cas particulier des solides bidimensionnels évoluant dans lʼespace  , ce problème de minimisation est un modèle mathématique de solide pouvant réaliser des auto-contacts sans frottement. Une application numérique est présentée. Pour citer cet article : O. Pantz, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Abstract

Let M be a submanifold of   ( ) considered as the reference configuration of a hyperelastic solid. A topological constraint is imposed on the admissible deformations   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   or  , 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).

The full text of this article is available in PDF format.


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