On the use of DMT approximations in adhesive contacts, with remarks on random rough contacts

TL;DR

This paper examines the applicability of DMT approximations in modeling adhesive contacts of rough surfaces, highlighting their limitations and the conditions under which they may or may not provide accurate results.

Contribution

It provides a critical analysis of DMT models in adhesive contact problems, especially for rough and cylindrical surfaces, and discusses the validity of approximate models like Pastewka & Robbins' under specific parameters.

Findings

DMT overestimates adhesion in spherical contacts except at pull-off.

In cylindrical contacts, DMT underestimates adhesion for larger areas.

Pastewka & Robbins' model accuracy depends on error cancellation within certain parameters.

Abstract

The contact between rough surfaces with adhesion is an extremely difficult problem, and the approximation of the DMT theory (to neglect deformations due to attractive forces), originally developed for spherical contact of very small radius, are receiving some new interest. The DMT approximation leads to extremely large overestimate of the adhesive forces in the case of spherical contact, except at pull-off. For cylindrical contact, the opposite trend is found for larger contact areas. These findings suggest some caution in solving rough contacts with DMT models, unless the Tabor parameter is really low. Further approximate models like that of Pastewka & Robbins' may be explained to work only for a coincidence of error cancellation in their range of parameters.