# American Institute of Mathematical Sciences

May  2012, 11(3): 1185-1203. doi: 10.3934/cpaa.2012.11.1185

## Analysis of a contact problem for electro-elastic-visco-plastic materials

 1 Department of Mathematics, University of Craiova, A.I. Cuza Street 13, 200585 Craiova, Romania 2 Departement of Mathematics, University of Craiov, A.I. Cuza Street 13, 200585, Craiova 3 Laboratoire de Mathématiques et Physique pour les Systèmes, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan

Received  December 2010 Revised  September 2011 Published  December 2011

We consider a mathematical model which describes the quasistatic frictionless contact between a piezoelectric body and a foundation. The novelty of the model consists in the fact that the foundation is assumed to be electrically conductive, the material's behavior is described with an electro-elastic-visco-plastic constitutive law, the contact is modelled with normal compliance and finite penetration and the problem is studied in an unbounded interval of time. We derive a variational formulation of the problem and prove existence, uniqueness and regularity results. The proofs are based on recent results on history-dependent quasivariational inequalities obtained in [21].
Citation: Maria-Magdalena Boureanu, Andaluzia Matei, Mircea Sofonea. Analysis of a contact problem for electro-elastic-visco-plastic materials. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1185-1203. doi: 10.3934/cpaa.2012.11.1185
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