Granular packings display the remarkable phenomenon of dilatancy [1], wherein their volume increases upon shear deformation. Conventional wisdom and previous results suggest that dilatancy, as also the related phenomenon of shear-induced jamming, requires frictional interactions [2, 3]. Here, we investigate the occurrence of dilatancy and shear jamming in frictionless packings. We show that the existence of isotropic jamming densities { \phi}j above the minimal density, the J-point density { \phi}J [4, 5], leads both to the emergence of shear-induced jamming and dilatancy. Packings at { \phi}J form a significant threshold state into which systems evolve in the limit of vanishing pressure under constant pressure shear, irrespective of the initial jamming density { \phi}j. While packings for different { \phi}j display equivalent scaling properties under compression [6], they exhibit striking differences in rheological behaviour under shear. The yield stress under constant volume shear increases discontinuously with density when { \phi}j > { \phi}J, contrary to the continuous behavior in generic packings that jam at { \phi}J [4, 7].
Categories: cond-mat.stat-mech cond-mat.soft