Journal of Applied Mathematics
Volume 2006 (2006), Article ID 64217, 25 pages

Analysis of electroelastic frictionless contact problems with adhesion

Mircea Sofonea, Rachid Arhab, and Raafat Tarraf

Laboratoire de Mathématiques et Physique pour les Systèmes, Université de Perpignan, 52 avenue Paul Alduy, Perpignan 66860, France

Received 24 January 2006; Revised 29 May 2006; Accepted 5 June 2006

Copyright © 2006 Mircea Sofonea et al. 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.


We consider two quasistatic frictionless contact problems for piezoelectric bodies. For the first problem the contact is modelled with Signorini's conditions and for the second one is modelled with normal compliance. In both problems the material's behavior is electroelastic and the adhesion of the contact surfaces is taken into account and is modelled with a surface variable, the bonding field. We provide variational formulations for the problems and prove the existence of a unique weak solution to each model. The proofs are based on arguments of time-dependent variational inequalities, differential equations, and fixed point. Moreover, we prove that the solution of the Signorini contact problem can be obtained as the limit of the solution of the contact problem with normal compliance as the stiffness coefficient of the foundation converges to infinity.