Electron. J. Diff. Eqns., Vol. 2007(2007), No. 161, pp. 1-14.

Antiplane frictional contact of electro-viscoelastic cylinders

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.

Show me the PDF file (285 KB), TEX file, and other files for this article.

Mohamed Dalah
Département de Mathématiques, Faculté des Sciences
Université de Mentouri - Constantine
25 000 Constantine, Algérie
email: mdalah17@yahoo.fr
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

Return to the EJDE web page