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 Sigma in two and three spatial dimensions. To find a mechanically stable (MS) packing that can support the applied Sigma, isotropically prepared states with size L must undergo a total strain gamma(ms)(Sigma, L). The number density of MS packings (alpha gamma(-1)(ms)) vanishes for Sigma > Sigma(c) approximate to 0.11 according to a critical scaling formwith a length scale xi alpha vertical bar Sigma-Sigma(c)vertical bar(-nu), where nu approximate to 1.7-1.8. Above the yield stress (Sigma-Sigma(c)), no MS packings that can support Sigma exist in the large-system limit L/xi >> 1. MS packings generated via shear possess anisotropic force and contact networks, suggesting that Sigma(c) is associated with an upper limit in the degree to which these networks can be deformed away from those for isotropic packings.
