International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 686139, 13 pages
Research Article

Quasistatic Elastic Contact with Adhesion

1Laboratoire de Mathématiques Appliquées et Modélisation, Université Mentouri, Constantine 25000, Algeria
2Laboratoire de Mathématiques Appliquées et Modélisation, Université 20 Août 1955, Skikda 21000, Algeria

Received 11 June 2011; Accepted 22 August 2011

Academic Editor: Naseer Shahzad

Copyright © 2011 Boudjemaa Teniou and Sabrina Benferdi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this paper is the variational study of the contact with adhesion between an elastic material and a rigid foundation in the quasistatic process where the deformations are supposed to be small. The behavior of this material is modelled by a nonlinear elastic law and the contact is modelled with Signorini's conditions and adhesion. The evolution of bonding field is described by a nonlinear differential equation. We derive a variational formulation of the mechanical problem, and we prove the existence and uniqueness of the weak solution using a theorem on variational inequalities, the theorem of Cauchy-Lipschitz, a lemma of Gronwall, as well as the fixed point of Banach.