VARIATIONAL ANALYSIS OF AN ELECTRO-VISCOELASTIC CONTACT PROBLEM WITH FRICTION AND ADHESION

- Journal title : Journal of the Korean Mathematical Society
- Volume 53, Issue 1, 2016, pp.161-185
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2016.53.1.161

Title & Authors

VARIATIONAL ANALYSIS OF AN ELECTRO-VISCOELASTIC CONTACT PROBLEM WITH FRICTION AND ADHESION

CHOUGUI, NADHIR; DRABLA, SALAH; HEMICI, NACERDINNE;

CHOUGUI, NADHIR; DRABLA, SALAH; HEMICI, NACERDINNE;

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

Piezoelectric material;electro-viscoelastic;frictional contact;nonlocal Coulomb`s law;adhesion;quasi-variational inequality;weak solution;fixed point theorem;

Language

English

Cited by

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