Electron. J. Diff. Eqns., Vol. 2006(2006), No. 58, pp. 1-9.

A quasistatic bilateral contact problem with friction for nonlinear elastic materials

Arezki Touzaline

We consider a mathematical model describing the bilateral contact between a deformable body and a foundation. We use a nonlinear elastic constitutive law. The contact takes into account the effects of friction, which are modelled with the regularized friction law. We derive a variational formulation of the problem and establish the existence of a weak solution under a smallness assumption of the friction coefficient. The proof is based on arguments of compactness, lower semicontinuity and time discretization.

Submitted December 26, 2005. Published May 1, 2006.
Math Subject Classifications: 35J85, 49J40, 47J20, 58E35.
Key Words: Nonlinear elasticity; bilateral contact; friction; variational inequality; weak solution.

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Arezki Touzaline
Faculté de Mathématiques, USTHB
BP 32 EL ALIA, Bab-Ezzouar, 16111, Algérie
email: atouzaline@yahoo.fr

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