Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 257, pp. 121.
A quasistatic electroelastic contact problem with normal compliance,
friction and adhesion
Nadhir Chougui, Salah Drabla
Abstract:
In this article we consider a mathematical model which describes the contact
between a piezoelectric body and a deformable foundation. The constitutive
law is assumed linear electroelastic and the process is quasistatic. The
contact is adhesive and frictional and is modelled with a version of normal
compliance condition and the associated Coulomb's law of dry friction. 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
bonding field. Under a smallness assumption on the coefficient of friction,
we prove an existence result of the weak solution of the model. The proofs
are based on arguments of timedependent variational inequalities,
differential equations and Banach fixed point theorem.
Submitted July 3, 2014. Published December 10, 2014.
Math Subject Classifications: 74B20, 74H10, 74M15, 74F25, 49J40.
Key Words: Piezoelectric material; electroelastic; frictional contact;
Coulomb's law; adhesion; normal compliance;
quasivariational inequality; weak solution.
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Nadhir Chougui
Department of Mathematics, Faculty of Sciences
University Farhat Abbas of Setif1
Setif 19000, Algeria
email: chouguinadhir@yahoo.fr


Salah Drabla
Department of Mathematics, Faculty of Sciences
University Farhat Abbas of Setif1
Setif 19000, Algeria
email: drabla_s@univsetif.dz

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