Influence of polydispersity on micromechanics of granular materials

TL;DR

This paper investigates how polydispersity influences the mechanical behavior of granular materials, providing a mean-field theoretical framework that aligns well with simulation data.

Contribution

It introduces a mean-field approach linking microscopic particle size distribution moments to macroscopic properties of granular packings.

Findings

Fabric and stress tensor traces are proportional to packing properties and distribution moments.

The stiffness tensor elements follow similar proportionality in the linear regime.

Theoretical predictions match simulation results effectively.

Abstract

We study the effect of polydispersity on the macroscopic physical properties of granular packings in two and three dimensions. A mean-field approach is developed to approximate the macroscale quantities as functions of the microscopic ones. We show that the trace of the fabric and stress tensors are proportional to the mean packing properties (e.g. packing fraction, average coordination number, and average normal force) and dimensionless correction factors, which depend only on the moments of the particle-size distribution. Similar results are obtained for the elements of the stiffness tensor of isotropic packings in the linear affine response regime. Our theoretical predictions are in good agreement with the simulation results.