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Granular packings display the remarkable phenomenon of dilatancy [1], whereintheir volume increases upon shear deformation. Conventional wisdom and previousresults suggest that dilatancy, as also the related phenomenon of shear-inducedjamming, requires frictional interactions [2, 3]. Here, we investigate theoccurrence of dilatancy and shear jamming in frictionless packings. We showthat the existence of isotropic jamming densities {\phi}j above the minimaldensity, the J-point density {\phi}J [4, 5], leads both to the emergence ofshear-induced jamming and dilatancy. Packings at {\phi}J form a significantthreshold state into which systems evolve in the limit of vanishing pressureunder constant pressure shear, irrespective of the initial jamming density{\phi}j. While packings for different {\phi}j display equivalent scalingproperties under compression [6], they exhibit striking differences inrheological behaviour under shear. The yield stress under constant volume shearincreases discontinuously with density when {\phi}j > {\phi}J, contrary to thecontinuous behavior in generic packings that jam at {\phi}J [4, 7].

Is friction essential for dilatancy and shear jamming in granular matter?