Adhesive sliding contact of viscoelastic layers on a wavy rigid counterface

We study thin viscoelastic layers with different constraints in steady-state adhesive sliding contact against wavy indenters. This is crucial for many applications involving compliant films and coatings, where adhesion, friction, and confinement may strongly interact, leading to distinct results compared to half-space geometries. Both a confined layer bonded to a rigid substrate and a free layer subjected to uniform pressure are considered. The problem is formulated within a rigorous energy- based framework for non-conservative viscoelastic materials. The results show that varying the thickness induces distinct responses on the two configurations for pull-off force, friction, and contact stability, with specific dependence on sliding speed due to different scale-dependent dissipation mechanisms. At low sliding speeds, small-scale dissipation localized at contact edges enhances effective adhesion. For thinner layers, this effect is suppressed by confinement and strongly amplified in free layers. Conversely, pull-off forces increase (decrease) in confined (free) layers. The friction coefficient under load control is independent of layer thickness and boundary conditions. At higher speeds, bulk viscoelasticity dominates, and friction decreases (increases) for confined (free) layers due to different bulk deformation mechanisms. A full-contact instability at intermediate velocities leads to discontinuous friction – velocity curves, a distinctive feature of adhesive viscoelastic contacts.