CONTACT PROBLEM WITH ADHESION AND WEAR IN ELECTRO-VISCOELASTICITY WITH DAMAGE
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Published:2023-03
Issue:1
Volume:11
Page:29-48
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ISSN:2306-6172
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Container-title:Eurasian Journal of Mathematical and Computer Applications
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language:
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Short-container-title:EJMCA
Author:
Azeb Ahmed Abdelaziz, ,Yazid Fares,Djeradi Fatima Siham,
Abstract
We consider a mathematical model which describes the dynamic process of con- tact between a piezoelectric body and two obstacles. The behavior of the material is modeled with a nonlinear electro-viscoelastic constitutive with law long memory and damage. The mechanical damage of the material, caused by excessive stess or strains, is described by a damage function whose evolution is modeled by an inclusion of parabolic type. The contact is modeled with adhesion and wear. The adhesion field, whose evolution is described by a first order differential equation. The evolution of the wear function is described with Ar- chard’s law. For the variational formulation of the contact problem, we present and prove the existence of a unique weak solution to the problem. The proof is based on arguments of time dependent variational inequalities, parabolic inequalities, differential equations and fixed point arguments.
Publisher
L. N. Gumilyov Eurasian National University
Subject
Applied Mathematics,Computational Mathematics,Computer Science Applications,Mathematical Physics,Modeling and Simulation,Information Systems