A doubly history-dependent quasivariational inequality arising in viscoelastic frictional contact problems with wear

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.