Variational analysis of fully coupled electro‐elastic frictional contact problems |
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| Authors: | Stanislaw Migorski Anna Ochal Mircea Sofonea |
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| Institution: | 1. Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. S. Lojasiewicza 6, 30348 Krakow, Poland;2. Phone: +48 126646668, Fax: +48 126646673;3. Laboratoire de Mathématiques et Physique pour les Systèmes, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan, France;4. Phone: +33468661765, Fax: +33468661760 |
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| Abstract: | We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a foundation. The material behavior is described with a nonlinear electro‐elastic constitutive law. The novelty of the model consists in the fact that the foundation is assumed to be electrically conductive and both the frictional contact and the conductivity on the contact surface are described with subdifferential boundary conditions which involve a fully coupling between the mechanical and electrical variables. We derive a variational formulation of the problem which is in the form of a system coupling two hemivariational inequalities for the displacement and the electric potential fields, respectively. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proofs are based on recent results for inclusions of subdifferential type in Sobolev spaces (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | piezoelectricity electro‐elastic material static process frictional contact conductive foundation hemivariational inequality Clarke subdifferential weak solution |
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