Effects of Friction and Disorder on the Quasi-Static Response of Granular Solids to a Localized Force

TL;DR

This study uses numerical simulations to explore how friction and disorder influence stress transmission in granular solids, revealing size-dependent responses and the effects of friction and polydispersity on elasticity and anisotropy.

Contribution

It demonstrates how system size, friction, and disorder affect the elastic and anisotropic stress responses in granular materials through detailed simulations.

Findings

Large systems exhibit elastic, isotropic responses.

Small systems or large forces induce anisotropic, non-elastic responses.

Higher friction extends elastic behavior and reduces anisotropy.

Abstract

The response to a localized force provides a sensitive test for different models of stress transmission in granular solids. The elasto-plastic models traditionally used by engineers have been challenged by theoretical and experimental results which suggest a wave-like (hyperbolic) propagation of the stress, as opposed to the elliptic equations of static elasticity. Numerical simulations of two-dimensional granular systems subject to a localized external force are employed to examine the nature of stress transmission in these systems as a function of the magnitude of the applied force, the frictional parameters and the disorder (polydispersity). The results indicate that in large systems (typically considered by engineers), the response is close to that predicted by isotropic elasticity whereas the response of small systems (or when sufficiently large forces are applied) is strongly anisotropic. In the latter case the applied force induces changes in the contact network accompanied by frictional sliding. The larger the coefficient of static friction, the more extended is the range of forces for which the response is elastic and the smaller the anisotropy. Increasing the degree of polydispersity (for the range studied, up to 25%) decreases the range of elastic response. This article is an extension of a previously published letter [1].