Elasticity Does Not Necessarily Break Down in Nanoscale Contacts

Abstract

Atomistic structures can have (sharp) features that are not accounted for in standard continuum theories. A prominent example is a Hertzian contact in which, however, the indenting tip is cut out of a crystal, whereby the tip acquires a discretized height profile. The microscopic stresses observed for such quantized indenters show sharp stress peaks at the edges of the height steps so that the stress profiles differ from those produced by smooth, parabolic indenters. Such deviations are frequently misinterpreted as the breakdown of continuum theory at the nanoscale. In this Letter, the stress peaks are confirmed to also occur in a continuum treatment containing steps. In addition, it is shown that analytical solutions for smooth tips can compare extremely well to those with steps if both stress fields are passed through the same (Gaussian) filter smearing out the features in real space with a resolution close to the broadest terrace of the quantized tip. Related statements are shown to also hold for the stress distribution function of randomly rough indenters with quantized height profiles.