Discontinuous rigidity transition associated with shear jamming in granular simulations

The rigidity transition associated with isotropic and shear jamming have in the past been investigated through the analysis of constraints. Whereas the transition is discontinuous for isotropic jamming, with the sudden percolation of a rigid contact network when the isostatic condition is crossed, previous work has suggested that the transition is more continuous in the case of shear jamming of frictional grain assemblies. To understand better this apparent difference, we investigate the rigidity transition associated with shear jamming in frictional, as well as frictionless disk packings [1,2] in the quasi-static regime and at low shear rates. We find that while the transition appears continuous for finite shear rates, it is sharper for lower shear rates, and with quasi-static shearing the transition is discontinuous with an instantaneous emergence of a system spanning rigid cluster at the transition. We also show that the same picture holds for frictionless shear jamming at high densities under quasi-static shearing. Thus, our results suggest that the rigidity transition associated with shear jamming in both frictional and frictionless packings is discontinuous, and therefore similar to the transition for isotropic jamming.