A unilateral contact problem with slip-dependent friction

Volume 43 / 2016

Arezki Touzaline Applicationes Mathematicae 43 (2016), 105-116 MSC: 74B20, 74M15, 49J40. DOI: 10.4064/am2258-11-2015 Published online: 26 November 2015

Abstract

We consider a mathematical model which describes a static contact between a nonlinear elastic body and an obstacle. The contact is modelled with Signorini's conditions, associated with a slip-dependent version of Coulomb's nonlocal friction law. We derive a variational formulation and prove its unique weak solvability. We also study the finite element approximation of the problem and obtain an optimal error estimate under extra regularity for the solution. Finally, we establish the convergence of an iterative method to the finite element problem.

Authors

  • Arezki TouzalineFaculté de Mathématiques, USTHB
    Laboratoire de Systèmes Dynamiques
    BP 32 El Alia
    Bab-Ezzouar, 16111, Algeria
    e-mail

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