Bilateral contact problem with adhesion and damage

• Main Authors: Adel Aissaoui, Nacerdine Hemici
• Format: Article
• Language: English
• Published: University of Szeged 2014-05-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: dynamic process; viscoelastic material with damage; adhesion; bilateral frictionless contact; existence and uniqueness; fixed point
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=2874

We study a mathematical problem describing the frictionless adhesive contact between a viscoelastic material with damage and a foundation. The adhesion process is modeled by a bonding field on the contact surface. The contact is bilateral and the tangential shear due to the bonding field is included. We establish a variational formulation for the problem and prove the existence and uniqueness of the solution. The existence of a unique weak solution for the problem is established using arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result for parabolic inequalities, and Banach's fixed point theorem.