Adhesive and adhesiveless contact mechanics of elastic layers on slightly wavy rigid substrates

The behavior of an elastic layer in contact with a wavy rigid substrate is analyzed depending on layer thickness, substrate geometry, energy of adhesion, for given value of remote applied load or penetration. Two different slab configurations are considered: (i) a free layer with uniform pressure acting on the upper boundary, and (ii) a confined layer with uniform displacement assigned to the upper boundary. These two different geometries have been considered as exemplar cases which are of great relevance in a large number of applications of crucial importance as structural adhesives, pressure sensitive adhesives, coatings and protective adhesives. Our study shows that the layer thickness affects the contact behavior differently depending on the constraints configuration. In particular, reducing the thickness of the layer makes the latter more or less compliant depending on the considered configuration. Thus, the free layer becomes more sticky and, as the layer thickness is reduced, an increasingly large amount of external work needs to be provided to detach the layer from the substrate. On the contrary, the confined layer significantly stiffens by decreasing the layer thickness. This leads to an increase of the pull-off force for detachment accompanied by a decrease of the energy needed to bring the layer and substrate apart.