Title: Isostaticity at Frictional Jamming

Author (Talk): Stefanos Papanikolaou, Yale University

Abstract:

Jamming as a transition achieved for frictionless, density-driven systems at zero temperature, has been intrinsically tied to mechanical stability, known as the isostaticity argument. However, such a general, protocol-independent argument has been missing for frictional systems, even when in the dear proximity to frictionless systems. We propose a model of static friction where friction is modeled geometrically using uniform circular asperities on each disc surface. First, we show that the predictions of the Geometric Asperity (GA) model are clearly consistent with the predictions of the well accepted Hertz-Mindlin (HM) model including the hypostaticity of the coarse grained particle contacts. Then, we show that the number of actual contacts (potential energy overlaps) satisfy “exact” isostaticity, in precise correspondence to the frictionless result, while the particle contacts show the same behavior as predicted by the HM model, displaying a transition to hypostatic behavior at high friction. We explain this transition by studying the geometric cross-sections of the different contact types in the GA model and we use our insight to connect our geometric explanation to the different weights of low and high plasticity HM contacts. Finally, we show the vibrational density of states as a function of friction, with clear signatures of weakening as friction is decreased, using no additional assumptions for the friction microscopics.