A bilateral contact problem with adhesion and damage between two viscoelastic bodies

Volume 9, Issue 3, pp 1216-1229 http://dx.doi.org/10.22436/jnsa.009.03.47

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Authors

Ammar Derbazi - Department of Mathematics, Faculty of MI, University Bachir El-Ibrahimi of Bordj Bou Arreridj, Bordj BBA: 34 000, Algeria. Souida Boukrioua - Department of Mathematics, University Kasdi Merbah of Ouargla, Ouargla 30 000, Algeria. Mohamed Dalah - Department of Mathematics, Faculty of Exact Sciences: FSE, University Mentouri of Constantine, Constantine 25 017, Algeria. Adel Aissaoui - Department of Mathematics, Faculty of Exact Sciences, University Hamma Lakhdar, El-Oued, El-Oued 39 000, Algeria. Allaoua Boudjedour - Department of Mathematics, Faculty of Exact Sciences: FSE, University Mentouri of Constantine, Constantine 25 017, Algeria. Amar Megrous - Department of Mathematics, EPSE-CSG of Constantine, Constantine 25 000, Algeria.

Abstract

This paper deals with the study of a mathematical model which describes the bilateral, frictionless adhesive contact between two viscoelastic bodies with damage. The adhesion of the contact surfaces is con- sidered and is modeled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. We establish a variational formulation for the problem and prove the existence and uniqueness result of the solution. The proofs are based on time-dependent variational equalities, a classical existence and uniqueness result on parabolic equations, differential equations, and fixed-point arguments.

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Keywords

• Bilateral frictionless contact
• adhesion
• viscoelastic materials
• fixed point
• damage
• weak solution.

MSC

•  74M15
•  74F99
•  74G25
•  74R99

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