no. 4
Mathematical Problems in Mechanics
Existence of a solution to a dynamic unilateral contact problem for a cracked viscoelastic body
[Existence d'une solution à un problème dynamique de contact unilatéral pour un milieu viscoélastique fissuré]

Présenté par : Philippe G. Ciarlet

Cocou, Marius1 ; Scarella, Gilles2
1 Laboratoire de mécanique et d'acoustique CNRS, 31, chemin Joseph-Aiguier, 13402 Marseille cedex 20, et Université de Provence, UFR MIM, Marseille, France
2 INRIA Rocquencourt, Domaine de Voluceau, BP 105, 78153 Le Chesnay cedex, France
Comptes Rendus. Mathématique, Tome 338 (2004) no. 4, pp. 341-346.

Dans ce travail, on s'intéresse à un problème dynamique de contact unilatéral avec frottement non local pour un milieu viscoélastique fissuré, suivant une loi de comportement de Kelvin–Voigt. L'existence d'une solution du problème est obtenue par une méthode de pénalisation. Le passage à la limite est justifié par plusieurs estimations et par quelques résultats de compacité.

In this paper we study a dynamic unilateral contact problem with friction for a cracked viscoelastic body. The viscoelastic model is characterized by Kelvin–Voigt's law and a nonlocal friction law is investigated here. The existence of a solution to the problem is obtained by using a penalty method. Several estimates are obtained on the solution to the penalized problem, which enable us to pass to the limit by using compactness results.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.12.013
Cocou, Marius 1 ; Scarella, Gilles 2

1 Laboratoire de mécanique et d'acoustique CNRS, 31, chemin Joseph-Aiguier, 13402 Marseille cedex 20, et Université de Provence, UFR MIM, Marseille, France
2 INRIA Rocquencourt, Domaine de Voluceau, BP 105, 78153 Le Chesnay cedex, France 
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Cocou, Marius; Scarella, Gilles. Existence of a solution to a dynamic unilateral contact problem for a cracked viscoelastic body. Comptes Rendus. Mathématique, Tome 338 (2004) no. 4, pp. 341-346. doi : 10.1016/j.crma.2003.12.013. http://www.numdam.org/articles/10.1016/j.crma.2003.12.013/

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