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    STUDIA MATHEMATICA - Issue no. 1 / 2009  
         
  Article:   ANALYSIS OF A ELECTRO-ELASTIC CONTACT PROBLEM WITH FRICTION AND ADHESION.

Authors:  SALAH DRABLA, ZILOUKHA ZELLAGUI. 		 
       
         
  Abstract:  We consider a mathematical model which describes the quasistaticfrictional contact between a piezoelectric body and an obstacle, the so-called foundation. A nonlinear electro-elastic constitutive law is used to model the piezoelectric material. The contact is modelled with Signorini’s conditions and the associated with a regularized Coulomb’s law of dry friction in witch the adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation for the model, in the form of a coupled system for the displacements, the electric potential and the adhesion. Under a smallness assumption on the coefficient of friction, we prove the existence of a unique weak solution of the model. The proof is based on arguments of time-dependent quasi-variational inequalities, differential equations and Banach’s fixed point theorem.

Key words and phrases: piezoelectric material, electro-elastic, erictional contact, nonlocal Coulomb’s law, adhesion; quasi-variational inequality, weak solution, fixed point.

  
         
     
         
         
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