Reduction of the bulk modulus with polydispersity in non-cohesive granular solids

TL;DR

This study investigates how increasing grain size variation in non-cohesive granular solids reduces their bulk modulus, using simulations to analyze force networks and contact lengths.

Contribution

It reveals that higher polydispersity leads to lower bulk modulus and more anisotropic force networks, providing insights into the mechanics of granular materials.

Findings

Higher polydispersity correlates with lower bulk modulus.

Large grains carry the strongest forces and contact lengths.

Force networks become more anisotropic with increased polydispersity.

Abstract

We study the effect of grain polydispersity on the bulk modulus in non-cohesive two dimensional granular solids. Molecular dynamics simulations in two dimensions are used to describe polydisperse samples that reach a stationary limit after a number of hysteresis cycles. For stationary samples, we obtain that the packing with the highest polydispersity has the lowest bulk modulus. We compute the correlation between normal and tangential forces with grain size using the concept of {\it branch vector/contact length}. Classifying the contact lengths and forces by their size compared to the average length and average force respectively, we find that strong normal and tangential forces are carried by large contact lengths, generally composed of at least one large grain. This behavior is more dominant as polydispersity increases, making force networks more anisotropic and removing the support, from small grains, in the loading direction thus reducing the bulk modulus of the granular pack. Our results for two dimensions describe qualitatively the results of three dimensional experiments.