Analyse numérique d'un problème de contact viscoélastique sans frottement avec adhérence et endommagement

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).