Elasticity from the Force Network Ensemble in Granular Media

TL;DR

This paper investigates force transmission in static granular materials using the force network ensemble, revealing a transition from nonlinear, peaked responses near the load to linear, elastic-like behavior at larger scales, influenced by overload magnitude and friction.

Contribution

It provides a numerical analysis of force response in granular packings, highlighting the crossover from nonlinear to elastic behavior and its dependence on overload and friction.

Findings

Near overload application, response is nonlinear with two peaks.

At larger scales, response becomes linear and elastic-like.

Crossover depth depends on overload magnitude and friction.

Abstract

Transmission of forces in static granular materials are studied within the framework of the force network ensemble, by numerically evaluating the mechanical response of hexagonal packings of frictionless grains and rectangular packings of frictional grains. In both cases, close to the point of application of the overload, the response is non-linear and displays two peaks, while at larger length-scales it is linear and elastic-like. The cross-over between these two behaviors occurs at a depth that increases with the magnitude of the overload, and decreases with increasing friction.