Nanocontacts and Gaussian Filters: Insights into the idea of Filtering contact stress fields for removing the effects of surface roughness at the atomic scale

The inherent surface roughness at atomic scale contacts has profound effects on their local stresses, contact areas, and so on, which yield deviations from the predictions of continuum models. While these deviations can be interpreted as a breakdown of the models, attempts have been made to reconcile the two via different paths, e.g. proposing new methods for estimating the contact area, or ltering the contact stress fields. The applicability of the latter to randomly rough
nanocontacts, however, has not yet been explored hitherto. Here, we show that this new method should be employed with care. Investigating two smooth and rough contacts, we find that the filtering method can make the stresses resemble each other by varying the filter's resolution. Our results demonstrate that the filtering method improves comparisons between atomistic contacts and Hertz theory, while accounting for roughness in the rough contact results in more accurate solutions.