Force distribution in a scalar model for non-cohesive granular material

TL;DR

This paper investigates force distribution in a scalar lattice model of non-cohesive granular materials, revealing a power-law stress-strain relationship and Gaussian force distributions, with correlations affecting theoretical deviations.

Contribution

It introduces a scalar lattice model that captures force distributions and stress behavior, highlighting the role of correlations in non-cohesive granular materials.

Findings

Stress follows a power-law dependence on strain with a system-dependent exponent.

Force distributions are Gaussian at all compression stages.

Correlations influence deviations from existing theories.

Abstract

We study a scalar lattice model for inter-grain forces in static, non-cohesive, granular materials, obtaining two primary results. (i) The applied stress as a function of overall strain shows a power law dependence with a nontrivial exponent, which moreover varies with system geometry. (ii) Probability distributions for forces on individual grains appear Gaussian at all stages of compression, showing no evidence of exponential tails. With regard to both results, we identify correlations responsible for deviations from previously suggested theories.