A doubly history‐dependent quasivariational inequality arising in viscoelastic frictional contact problems with wear
Abderrahmane Oultou, Othmane Baiz, Hicham Benaissa
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Source: Crossref
Published: May 25, 2024
DOI: 10.1002/zamm.202400012
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Abstract We aim here to investigate a new mathematical model that describes the contact between a viscoelastic body, accounting for long memory and wear effects, and an obstacle referred to as the foundation. The contact model is governed by a normal compliance condition, coupled with Coulomb's law of dry friction for sliding, and wear effects. We derive the variational formulation of the model, which involves coupling of a quasi‐variational inequality with a nonlinear equation. By pursuing the abstract history‐dependent quasi‐variational inequalities and leveraging the fixed point theorem, we establish results concerning both existence and uniqueness.
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