The Stress Distribution in Polydisperse Granular Packings in Two Dimensions

We study the effect of size polydispersity on the stress distributions and structural properties of static frictionless packings under isotropic compressions. More than 50 isostatic packings with constant mean stress of 1 kPa are generated for each size polydispersity s with a uniform distribution of diameter between (d₀ ? s/2) and (d₀ + s/2). In order to vary the degree of positional order, the size polydispersity s ranges from 0 to 0.5. Several typical structural characterizations, (i.e., the height of the first pair correlation peak, the global and the local order parameters), the probability distribution of the normalized mean stress and the stress-stress correlation are calculated. The result shows that (i) the stress distribution scales as a power law in the limit of small stresses, and the distribution displays a Gaussian tail in the limit of large stresses; (ii) s has no evident influence on the structural and mechanical properties when s> 0.2.