A note on the pull-off force for a pattern of contacts distributed over a halfspace

We consider a series of flat contact spots distributed over a half-space, for which the pull-off force is proportional to the square root of the total contact area over the elastic compliance. By using an electro-mechanical analogy to compute the compliance using the well-known Greenwood–Holm equation, we show how the pull-off decays for fractal patterns of contact spots with simple scaling laws, tending to zero in a fractal limit, as the contact area goes to zero. Moreover, a qualitative assessment is made for contact of fractal rough surfaces, and it is shown that pull-off in this case is dominated by the value of the contact area reached during the loading process, which depends on the applied load, suggesting pressure-sensitive adhesion.