Percolation and Jamming in Random Heterogeneous Materials with Competing Length Scales

Abstract

Dense packings of particles of different size and shape are simulated by the mechanical contraction method (MCM). The effect of particle shape and particle size disparity on the packing density and micro-structure of two-component composite materials with competing length scales is investigated. We propose a simple analytical model to calculate the maximum packing fraction of such a mixture, which considers two co-existing random networks of large and small particles. The model predicts a non-monotonic behavior of the total packing fraction as a function of the mixture composition with the absolute maximum in packing fraction when the two sub-systems of large and small particles simultaneously jam. The mechanical contraction simulations corroborate this finding and also provide additional results for arbitrary particle size disparity. The simulated granular materials composed of frictionless spherical and rod-like particles also exhibit a non-monotonic dependence of the onset of rigidity percolation or jamming transition on the rod elongation.