On mixed-mode fracture mechanics models for contact area reduction under shear load in soft materials

The fundamental problem of friction in the presence of macroscopic adhesion, as in soft bodies, is receiving interest from many experimentalists. Since the first fracture mechanics ‘purely brittle’ model of Savkoor and Briggs, models have been proposed where the mixed mode toughness is interpreted with phenomenological fitting coefficients introducing weaker coupling between modes than expected by the “purely brittle” model. We compare here two such previously proposed models and introduce a third one to show that the transition to sliding is very sensitive to the form of the mixed-mode model. In particular, after a quadratic decay of the contact area with load for modest tangential loads, depending on the exact form of the mixed mode function, there is an inflexion point and an asymptotic limit, or a jump to the Hertzian contact area. We find also that the unstable points are different under load or displacement control. Hence, the form of the mixed mode function, and not only its parameter, is an extremely sensitive choice.