Mechanics of rough contacts in elastic and viscoelastic thin layers

Contact mechanics between rough solids usually relies on the half-space approximation, which assumes that the contact area dimension is much smaller than the thickness of the layers of materials that characterize the surfaces of the contacting bodies. However, such simplifying assumption is often inadequate when industrially relevant applications are considered, in particular those of biomechanical interest. Indeed, a large variety of systems, including not only classical engineering applications such as gear boxes, shafts, tyres, etc., but also biological tissues such as human skin, is characterized by superficial coatings; very often the mechanical properties of these coatings are very different from those of the bulk region of the bodies in contact. The aim of this paper is to shed light on the role played by the thickness of the layer of material used as a coating, with specific focus on the contact between a rigid rough surface and a thin deformable layer bonded to a rigid substrate. Starting from a recently developed boundary element formulation (Carbone and Putignano, 2013), we derive a methodology which accounts for finite thickness by a corrective coefficient modulating the classical Greens function, and extends our analyses to periodic domains. This enables to avoid border effects and provides an innovative tool to tackle viscoelastic contacts with realistic roughness. This is exploited to perform a thorough investigation of the mechanisms responsible for frictional losses in layered systems characterized by different materials, thickness and loading conditions. Results show that decreasing the layer thickness corresponds to an increase in the contact stiffness. Furthermore, in the case of viscoelastic layer, particular attention has to be paid to the changes in the viscoelastic dissipation due to the finite thickness of the surface layer.