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Comptes Rendus Mathématique
Volume 341, n° 1
pages 63-68 (juillet 2005)
Doi : 10.1016/j.crma.2005.04.037
Received : 3 Mars 2004 ;  accepted : 27 April 2005
Analyse numérique dʼun problème de contact viscoélastique sans frottement avec adhérence et endommagement
Numerical analysis of a viscoelastic frictionless contact problem with adhesion and damage
 

José R. Fernández a , Kenneth L. Kuttler b , Meir Shillor c
a Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Facultade de Matemáticas, Campus Sur s/n, 15782 Santiago de Compostela, Espagne 
b Department of Mathematics, Brigham Young University, Provo, UT 84602, États-Unis 
c Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, États-Unis 

Résumé

On considère un problème quasi-statique de contact unilatéral sans frottement et avec adhérence entre deux corps viscoélastiques. Lʼendommagement qui résulte de la compression ou de la tension est aussi pris en compte dans la loi de comportement. Lʼadhérence est modélisée en utilisant une variable superficielle sur la frontière de contact. Le contact est décrit avec une loi de Signorini modifié et on inclut la contrainte tangentielle due à lʼadhérence. Le problème est formulé comme un système dʼéquations variationnelles dʼévolution qui est approché en la variable spatiale par des méthodes dʼéléments finis non conformes pour lʼopérateur de projection « mortar » et un schéma dʼEuler rétrograde pour la discrétisation temporelle. On démontre un résultat dʼestimation dʼerreur sous des hypothèses de régularité. Des résultats numériques correspondants sont présentés. Pour citer cet article : J.R. Fernández et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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Abstract

A model for quasistatic, adhesive, and frictionless contact between two viscoelastic bodies is described. Material damage, which results from tension or compression, is taken into account in the constitutive law. The adhesion process is modelled by introducing the bonding field on the contact surface as a dependent variable. Contact is described with a modified Signorini condition which includes the adhesive normal tensile force. The variational problem is formulated as a coupled system of evolution equations. It is discretized using an explicit scheme for the time derivatives and a nonconforming finite element method based on the mortar projection operator. Error estimates are obtained for the numerical scheme under additional regularity hypotheses. Finally, numerical results for a two-dimensional example are depicted. To cite this article: J.R. Fernández et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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