Mohamed Dalah, Mircea Sofonea
Abstract:
We study a mathematical model that describes the antiplane
shear deformation of a cylinder in frictional contact with
a rigid foundation. The material is assumed to be electro-viscoelastic,
the process is quasistatic, friction is modelled with Tresca's law
and the foundation is assumed to be electrically conductive.
We derive a variational formulation of the model which is in
a form of a system coupling a first order evolutionary variational
inequality for the displacement field with a time-dependent
variational equation for the electric potential field.
Then, we prove the existence of a unique weak solution to the model.
The proof is based on arguments of evolutionary variational
inequalities and fixed points of operators.
Also, we investigate the behavior of the solution as the viscosity
converges to zero and prove that it converges to the solution of
the corresponding electro-elastic antiplane contact problem.
Submitted September 2, 2007. Published November 21, 2007.
Math Subject Classifications: 74M10, 74F15, 74G25, 49J40.
Key Words: Antiplane problem; electro-viscoelastic material;
contact process; Tresca's friction law;
evolutionary variational inequality; weak solution.
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Mohamed Dalah Département de Mathématiques, Faculté des Sciences Université de Mentouri - Constantine 25 000 Constantine, Algérie email: mdalah17@yahoo.fr |
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Mircea Sofonea Laboratoire de Mathématiques et Physique pour les Systémes, University of Perpignan, 52 avenue Paul Alduy 66860 Perpignan, France email: sofonea@univ-perp.fr |
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