Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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VARIATIONAL ANALYSIS OF AN ELECTRO-VISCOELASTIC CONTACT PROBLEM WITH FRICTION AND ADHESION

  • CHOUGUI, NADHIR (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCES UNIVERSITY FARHAT ABBAS OF SETIF1) ;
  • DRABLA, SALAH (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCES UNIVERSITY FARHAT ABBAS OF SETIF1) ;
  • HEMICI, NACERDINNE (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCES UNIVERSITY FARHAT ABBAS OF SETIF1)
  • Received : 2014.09.29
  • Published : 2016.01.01
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Abstract

We consider a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and an electrically conductive obstacle, the so-called foundation. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with Signorini's conditions and a version of Coulomb's law of dry friction in which 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 system for the displacements, the electric potential and the adhesion. Under a smallness assumption which involves only the electrical data of the problem, 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.

Keywords

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