We thank Prof. Ciavarella and Dr. Papangelo for the supplemental discussion on the challenge of describing contact area and contact parameters between surfaces with fractal roughness. Their commentary brings up many points of debate in the literature on contact of surfaces with multiscale roughness, some of which were omitted from the original review because of its focus on nanoscale contacts.
There are four particular points that were raised in the commentary that underscore key themes in the initial review, and thus may be important for contacts at all size scales.
First, the commentary points out that debate has been ongoing for decades about how best to mathematically describe rough contacts using continuum mechanics. The vast majority of the proposed approaches focus on the contact of nominally flat systems, with different mathematical approximations to describe the character and behavior of the superimposed roughness. (For another useful description of this topic, the...
