Mohamed Dalah, Mircea Sofonea
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
| Mircea Sofonea |
Laboratoire de Mathématiques et Physique pour les Systémes,
University of Perpignan, 52 avenue Paul Alduy
66860 Perpignan, France
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