Critical Scaling near Yield in Granular Materials

APS March Meeting 2018, Volume 63, Number 1, Monday–Friday, March 5–9, 2018; Los Angeles, CaliforniaThe item of record as published may be found at http://meetings.aps.org/link/BAPS.2018.MAR.S48.1We show that the yielding transition in granular media displays second-order critical-point scaling behavior, independent from jamming. We use discrete element simulations in the overdamped limit for frictionless spherical grains undergoing simple shear at fixed Σ, which is the ratio of the applied shear stress to normal stress. To find a mechanically stable (MS) packing that can support the applied Σ, isotropically prepared states with size L must travel over a strain γms(Σ,L). The density of MS packings, which is inversely proportional to γms(Σ,L), vanishes for Σ = Σc ≈ 0.11 according to a critical scaling form with a length scale ξ ~ |Σ - Σc|-ν, where ν ≈ 1.8. For Σ > Σc, no MS packings that can support Σ exist as L/ξ becomes large. For MS packings obtained by shear, the packing fraction is independent of Σ, but the anisotropy in force and contact networks increases with Σ. This suggests that Σc is associated with an upper limit in how far these networks can be deformed away from an isotropic configuration.This research was sponsored by the Army Research Laboratory and was accomplished under Grant Numbers W911NF-14-1-0005 and W911NF-17-1-0164 (A.H.C., N.T.O., and C.S.O.). M.D.S. acknowledges support from the National Science Foundation Grant No.~CMMI-1463455.This research was sponsored by the Army Research Laboratory and was accomplished under Grant Numbers W911NF-14-1-0005 and W911NF-17-1-0164 (A.H.C., N.T.O., and C.S.O.). M.D.S. acknowledges support from the National Science Foundation Grant No.~CMMI-1463455