The aim of this paper is to study a quasistatic contact problem between a nonlinear elastic body and a foundation. The contact is adhesive and frictional and is modelled with a version of normal compliance condition and the associated Coulomb's law of dry friction. The evolution of the bonding field is described by a first order differential equation. We establish the variational formulation of the mechanical problem and prove an existence result of the weak solution if the coefficient of friction is sufficiently small by passing to the limit with respect to time. The proofs are based on arguments of time-discretization, compactness, lower semicontinuity and Banach fixed point.
Submitted April 15, 2008. Published September 23, 2008.
Math Subject Classifications: 35J85, 49J40, 47J20, 74M15.
Key Words: Nonlinear elastic materials; adhesion; normal compliance; time-discretization; fixed point; quasistatic; weak solution.
An addendum as attached on January 8, 2009. It corrects some misprints. See last page of this article.
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| Arezki Touzaline |
Laboratoire de Systèmes Dynamiques
Faculté de Mathématiques, USTHB
BP 32 El Alia, Bab-Ezzouar, 16111, Algérie
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