On the Contact Area of Nominally Flat Hertzian Contacts

In a recent paper, Pastewka and Robbins (Appl Phys Lett 108:221-601, 2016) state an analytical expression for the real contact area of a Hertzian tip with smallscale roughness. We confirm that their formula predicts real contact areas quite well-with less than 10 % error. Nonetheless, the complementary contact area does not show the proper scaling to the continuum results at large loads. This shortcoming is fixed in the present work by abandoning a mean-field approximation made in the original work. Analytical results can even be made essentially perfect with a relation giving the accurate dependence of contract area on pressure for contacts between solids with nominally flat surfaces.