  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].

Statistical Mechanics;Soft Condensed Matter