Critical Scaling near Yield in Granular Materials*

We 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 γ_ms(Σ,L). The density of MS packings, which is inversely proportional to γ_ms(Σ,L), vanishes for Σ = Σ_c ≈ 0.11 according to a critical scaling form with a length scale ξ ~ |Σ - Σ_c|^-ν, where ν ≈ 1.8. For Σ > Σ_c, 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 Σ_c is associated with an upper limit in how far these networks can be deformed away from an isotropic configuration.