On the DMT adhesion theory: from the first studies to the modern applications in rough contacts

In the last years, increasing interest has been devoted to the study of the adhesion between rough media. The Derjaguin, Muller & Toporov (DMT) theory is one of the most known models to describe adhesion between hard elastic solids with long range adhesive interactions. However, many versions of the DMT theory can be found in the literature. In the first part of the present work, we try to make order about the various versions of the DMT theory appeared over the years. All models, often confusedly called with the same name "DMT theory", are based on the same assumption of neglecting deformations due to the adhesive forces. They predicts the same value of the detachment force at the pull-off, but only the so-called DMT force approach correctly captures the evolution trend of the adhesive force during the contact. In the second part of the work, we address the problem to include adhesion in the contact of rough surfaces according to the DMT theory. Specifically, we compare the Maugis' idea to add adhesion in the Greenwood and Williamson asperity theory, with more recent models: the Interacting and Coalescing Hertzian Asperities (ICHA) one and the Persson's theory. The two models, which both take account of adhesion according to the DMT force approach, give very similar results, showing that the pull-off force is negligibly affected by the shortest wavelength components of the surface roughness. On the contrary, the Maugis' model strongly underestimates adhesion and predicts a vanishing pull-off force when the upper cut-off spatial frequency of the surface is increased