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

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, is receiving some new interest. The DMT approximation leads to extremely large overestimations 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 due to a coincidence of error cancellation in their range of parameters.