Analysis of electroelastic frictionless contact problems with
adhesion

Sofonea, Mircea; Arhab, Rachid; Tarraf, Raafat

doi:https://doi.org/10.1155/JAM/2006/64217

Journal of Applied Mathematics

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Volume 2006 | Article ID 064217 | https://doi.org/10.1155/JAM/2006/64217

Analysis of electroelastic frictionless contact problems with adhesion

Mircea Sofonea,¹Rachid Arhab,¹and Raafat Tarraf¹

Received24 Jan 2006

Revised29 May 2006

Accepted05 Jun 2006

Published17 Aug 2006

Abstract

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.

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Copyright

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.

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