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Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 7
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Research Article

Analysis of a doubly-history dependent variational–hemivariational inequality arising in adhesive contact problem

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Pages 1224-1240 | Received 25 Jun 2022, Accepted 02 Apr 2023, Published online: 21 Jul 2023
 

Abstract

This paper is devoted to studying a dynamic adhesive contact model where the body is composed of a viscoelastic material with long memory. The adhesion process is modeled by a bonding field on part of the contact surface and on which the contact and the friction are modeled by nonmonotone Clarke subdifferential conditions with adhesion. Meanwhile, on another part of the contact surface, the contact is comprised of a normal compliance contact condition while the memory effects of the obstacle are considered, the friction is modeled by a version of Coulomb's law of dry friction and the friction bound is dependent on the normal stress. The variational form of the model generates a system of a doubly-history dependent variational–hemivariational inequality as well as a differential equation. Then, on the basis of the proof of abstract variational–hemivariational inequality, the existence and uniqueness results of the contact problem are established.

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Disclosure statement

No potential conflict of interest was reported by the author(s).

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