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We use previous results from discrete element simulations of simple shear flows ofrigid, identical spheres in the collisional regime to show that the volume fractiondependenceof the stresses is singular at the shear rigidity. Here, we identify the shearrigidity, which is a decreasing function of the interparticle friction, as the maximumvolume fraction beyond which a random collisional assembly of grains cannot besheared without developing force chains that span the entire domain. In the frameworkof extended kinetic theory, i.e., kinetic theory that accounts for the decreasing inthe collisional dissipation due to the breaking of molecular chaos at volume fractionslarger than 0.49, we also show that the volume fraction-dependence of the correlationlength (measure of the velocity correlation) is singular at random close packing,independent of the interparticle friction. The difference in the singularities ensuresthat the ratio of the shear stress to the pressure at shear rigidity is different from zeroeven in the case of frictionless spheres: we identify that with the yield stress ratioof granular materials, and we show that the theoretical predictions, once the differentsingularities are inserted into the functions of extended kinetic theory, are in excellentagreement with the results of numerical simulations.

Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows