Force fluctuations in granular materials

TL;DR

This paper derives a continuum model for force fluctuations in granular materials, analyzing how boundary conditions affect force distribution and fluctuations, with results validated against previous studies and simulations.

Contribution

It introduces a continuum equation based on a discrete model to study force fluctuations, incorporating boundary condition effects, which is a novel approach in this context.

Findings

Average weight increases linearly with depth under periodic boundaries.

Weight saturates at a constant value with absorbing boundaries.

Analytical results align with previous work and 1D simulations.

Abstract

Force fluctuations in granular materials are investigated. A continuum equation is derived starting from a discrete model proposed in the literature. The influence of boundary conditions is investigated. For periodic boundary conditions the average weight is found to increase linearly with depth while it saturates to a constant value for absorbing boundary conditions, which models the existence of walls. The scale dependencies of the saturation weight, the saturation depth and the average squared fluctuations are obtained. The analytical results are compared with previous works and with numerical simulations in one dimension.