Analysis of an Antiplane Contact Problem with Adhesion for Electro-Viscoelastic Materials

• Main Authors: M. Sofonea, L. Chouchane, L. Selmani
• Format: Article
• Language: English
• Published: Vilnius University Press 2008-07-01
• Series: Nonlinear Analysis
• Subjects: antiplane shear; electro-viscoelastic material; contact process; adhesion; fixed point; weak solution
• Online Access: http://www.journals.vu.lt/nonlinear-analysis/article/view/14563
• ISSN: 1392-5113; 2335-8963

We consider a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The adhesion of the contact surfaces, caused by the glue, is taken into account. The material is assumed to be electro-viscoelastic and the foundation is assumed to be electrically conductive. We derive a variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field, a time-dependent variational equation for the electric potential field and a differential equation for the bonding field. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of evolution equations with monotone operators and fixed point.