Large-scale frictionless jamming with power-law particle size distributions

TL;DR

This study uses advanced algorithms to simulate large, size-disperse frictionless sphere packings, revealing how particle size distributions influence packing structure and stability, with implications for understanding granular materials.

Contribution

We developed a neighbor binning algorithm enabling large-scale simulations of size-disperse sphere packings with power-law distributions, analyzing their structural and mechanical properties.

Findings

Densest packings occur at balanced size distributions.

Mean coordination number of load-bearing particles is always six.

Particles above a critical size dominate mechanical stability.

Abstract

Due to significant computational expense, discrete element method simulations of jammed packings of size-dispersed spheres with size ratios greater than 1:10 have remained elusive, limiting the correspondence between simulations and real-world granular materials with large size dispersity. Invoking a recently developed neighbor binning algorithm, we generate mechanically-stable jammed packings of frictionless spheres with power-law size distributions containing up to nearly four million particles with size ratios up to 1:100. By systematically varying the width and exponent of the underlying power laws, we analyze the role of particle size distributions on the structure of jammed packings. The densest packings are obtained for size distributions that balance the relative abundance of large-large/intermediate and small-small particle contacts. Although the proportion of rattler particles and mean coordination number strongly depend on the size distribution, the mean coordination of non-rattler particles attains the frictionless isostatic value of six in all cases. The size distribution of non-rattler particles that participate in the load-bearing network exhibits no dependence on the width of the total particle size distribution beyond a critical particle size for low-magnitude exponent power laws. This signifies that only particles with sizes greater than the critical particle size contribute to the mechanical stability. However, for high-magnitude exponent power laws, all particle sizes participate in the mechanical stability of the packing.