Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 257, pp. 1-21.
A quasistatic electro-elastic 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 electro-elastic 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 time-dependent 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; electro-elastic; frictional contact;
Coulomb's law; adhesion; normal compliance;
quasi-variational 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
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Salah Drabla
Department of Mathematics, Faculty of Sciences
University Farhat Abbas of Setif1
Setif 19000, Algeria
email: drabla_s@univ-setif.dz
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