On the application of fracture mechanics mixed-mode models of sliding with friction and adhesion

As recently suggested in an interesting and stimulating paper by Menga, Carbone and Dini (MCD), applying fracture mechanics energy concepts for the case of a sliding adhesive contact, imposing also the shear stress is constant at the interface and equal to a material constant (as it seems in experiments), leads to a increase of contact area which instead is never observed. We add that the MCD theory also predicts a size effect and hence a distortion of the JKR curve during sliding which is also not observed in experiments. Finally, a simpler example with the pure mode I contact case, leads in the MCD theory to an unbounded contact area, rather than a perhaps more correct limit of the Maugis-Dugdale solution for the adhesive sphere when Tabor parameter is zero, that is DMT's solution. We discuss that the MCD theory does not satisfy equilibrium, and we propose some more correct formulations, although they may be rather academic: recent semi-empirical models, with an appropriate choice of the empirical parameters, seem more promising and robust in modelling actual experiments.