Journal of Applied Mathematics
Volume 2006 (2006), Article ID 64217, 25 pages
Analysis of electroelastic frictionless contact problems with
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.