From force distribution to average coordination number in frictional granular matter

TL;DR

This paper investigates the joint distribution of normal and tangential forces in jammed granular media, revealing a universal scaling law that links force distribution to the average coordination number across different friction coefficients.

Contribution

It introduces a universal scaling law for force distributions in frictional granular matter and extends isostatic packing constraints to finite friction coefficients.

Findings

Universal scaling law for force distributions across friction coefficients

Link between force distribution and average coordination number

Extension of isostatic packing constraints to finite friction

Abstract

We study the joint probability distribution of normal and tangential frictional forces in jammed granular media, $P_{\mu}(f_t, f_n)$, for various friction coefficient $\mu$, especially when $\mu = \infty$. A universal scaling law is found to collapse the data for $\mu=0$ to $\infty$ demonstrating a link between force distribution $P_{\mu}(f_t, f_n)$ and average coordination number, $z^{\mu}_c$. The results determine $z_c^\mu$ for a finite friction coefficient, extending the constraints counting argument of isostatic granular packing to finite frictional packings.