The contact mechanics of elastic and viscoelastic thin layers

In contact mechanics it is usual to assume the contacting bodies as semi-infinite solids. Although this assumption holds true for a large class of problems, where the size of the contact area is sufficiently small compared with the thickness of the bodies involved in the contact, it has been recently pointed out that dealing with relatively thin elastic layers strongly affects the overall results of the contact problem. Indeed, in the case of finite sized bodies, significant differences have been reported in terms of the main contact quantities (e.g. contact area, penetration, mean pressure, etc.). Nowadays, there exists a wide range of industrial applications demanding for this kind of studies, such as seals leakage predictions or pressure-sensitive coatings for electrical applications. In this talk, we focus on the exemplar class of contact involving rigid sinusoidal profiles and elastic or viscoelastic layers with finite thickness. Specifically, we will investigate the effect on the layer behavior of two different boundary condition applied on the non-contacting surface: (a) a rigid constrain and (b) a uniform pressure. We will pass through the contact formulation, which relying on the Green's functions approach, allows to reduce the problem to a Fredholm equation of the first kind, to be then numerically solved. In the specific case of elastic layers, the formulation has been focused on both adhesive and adhesiveless conditions at the interface, whereas for viscoelastic layers only the latter condition has been studied. Therefore, two different closure conditions will be presented, depending on the specific case: adhesive contacts are addressed by looking for a stationary point of the system potential energy with respect to the unknown contact area; whereas adhesiveless conditions analysis exploits the fracture mechanics Griffith's criterion by requiring a vanishing stress intensity factor K1. The key role played by the layer thickness on the overall contact results will be shown in detail for both the elastic adhesive and adhesiveless layer contacts in terms of contact area, contact penetration, and mean contact pressure. Moreover, the effect on pull-off force and penetration will be reported. Further, in the case of viscoelastic layers, a devoted study of the viscoelastic frictional response as a function of the layer thickness and boundary conditions will be presented, showing interesting results recently generalized to randomly rough profiles.