Critical scaling near the yielding transition in granular media

Abstract

We show that the yielding transition in granular media displays second-order critical-point scaling behavior. We carry out discrete element simulations in the low inertial number limit for frictionless, purely repulsive spherical grains undergoing simple shear at fixed nondimensional shear stress $Σ$ in two and three spatial dimensions. To find a mechanically stable (MS) packing that can support the applied $Σ$, isotropically prepared states with size $L$ must undergo a total strain $γ_{\rm ms}(Σ,L)$. The number density of MS packings ($\propto γ_{\rm ms}^{-1}$) vanishes for $Σ> Σ_c \approx 0.11$ according to a critical scaling form with a length scale $ξ\propto |Σ- Σ_c|^{-ν}$, where $ν\approx 1.7-1.8$. Above the yield stress ($Σ>Σ_c$), no MS packings that can support $Σ$ exist in the large system limit, $L/ξ\gg 1$. MS packings generated via shear possess anisotropic force and contact networks, suggesting that $Σ_c$ is associated with an upper limit in the degree to which these networks can be deformed away from those for isotropic packings.