Comptes Rendus
Numerical approximation of a viscoelastic frictional contact problem
Comptes Rendus. Mécanique, Volume 334 (2006) no. 5, pp. 279-284.

We consider a fully discrete scheme for a quasistatic frictional contact problem between a viscoelastic body and an obstacle. The contact is bilateral, the friction is modeled with Tresca's law and the behavior of the material is described with a viscoelastic constitutive law with long memory. We state an existence and uniqueness result for the discrete solution, followed by error estimate results. Then, we present numerical simulations in the study of a two-dimensional test example.

Nous considérons un schéma totalement discrétisé pour un problème quasistatique de contact avec frottement entre un corps viscoélastique et un obstacle. Le contact est bilatéral, le frottement est modélisé à l'aide de la loi de Tresca et le comportement du matériau est décrit à l'aide d'une loi viscoélastique à mémoire longue. Nous présentons un résultat d'existence et d'unicité pour la solution discrète, suivi des résultats d'estimation de l'erreur. Nous présentons aussi des simulations numériques dans l'étude d'un exemple test en dimension deux.

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Accepted:
Published online:
DOI: 10.1016/j.crme.2006.03.013
Keywords: Friction, Viscoelastic frictional contact, Fully discrete scheme, Finite element method, Error estimates, Duality-penalization algorithm, Numerical simulations
Mot clés : Frottement, Contact viscoélastique avec frottement, Schéma totalement discrétisé, Méthode des élements finis, Estimation de l'erreur, Algorithme de dualité-pénalisation, Simulations numériques

Ángel Rodríguez-Arós 1; Mircea Sofonea 2; Juan Viaño 1

1 Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Avda. Lope Gómez de Marzoa S/N, Facultade de Matemáticas, 15782 Santiago de Compostela, Spain
2 Laboratoire de Mathématiques et Physique pour les Systèmes, Université de Perpignan, 52, avenue Paul-Alduy, 66860 Perpignan cedex, France
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Ángel Rodríguez-Arós; Mircea Sofonea; Juan Viaño. Numerical approximation of a viscoelastic frictional contact problem. Comptes Rendus. Mécanique, Volume 334 (2006) no. 5, pp. 279-284. doi : 10.1016/j.crme.2006.03.013. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.03.013/

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