Résumé
This work introduces a mathematical and numerical framework for modeling unilateral contact with adhesion and friction in the regime of large deformations, with applications to hyperelastic and viscoelastic materials. The model, formulated in the reference configuration, incorporates a cohesive-type adhesion law and a Kelvin-Voigt-type viscosity, while ensuring energy consistency through a persistent contact condition. We derive a finite element discretization combined with an implicit time integration scheme, and we propose a robust numerical solver based on a semi-smooth Newton method and the Primal-Dual Active Set (PDAS) approach. The preservation of the discrete energy balance is analyzed in detail. Numerical experiments are conducted on academic and applied scenarios, including the deployment of a biomedical stent into a deformable arterial wall. These simulations demonstrate the impact of adhesion and viscosity on the mechanical response, energy dissipation, and convergence properties of the scheme.