Adhesion between a thin elastic plate and a hard randomly rough substrate

In this paper we discuss the adhesion of a thin elastic plate to a randomly rough hard substrate. It is shown that at small magnification (long length scales) the plate, because of its higher compliance, is able to adhere in apparent full contact to the long wavelength corrugation of the underlying surface. That is, at length scales longer than the plate thickness, the gain in the adhesion energy upon the contact with the substrate overcomes the repulsive elastic energy produced by the elastic deformations, and the plate is able to fill out the large cavities of the rigid substrate. This produces a larger area of contact and an enhanced capability to adhere to a rough surface in comparison to the semi-infinite elastic solid case. However, at large enough magnification (small length scales) the plate behaves as a semi-infinite solid, and, depending on the roughness statistical properties, the area of true atomic contact may be much smaller than the nominal contact area.