The force network ensemble for granular packings

TL;DR

This paper reviews the force network ensemble approach for granular packings, analyzing how packing geometry and anisotropy influence force distributions and responses, supported by detailed numerical and emerging analytical results.

Contribution

It introduces and reviews the force network ensemble method, highlighting its ability to predict force distributions and responses in granular packings based on geometry and anisotropy.

Findings

Force distribution $P(f)$ depends on packing dimension and anisotropy.

The response to shear and point forcing can be predicted within this framework.

Analytical approaches effectively capture the form of force distributions.

Abstract

For packings of hard but not perfectly rigid particles, the length scales that govern the packing geometry and the contact forces are well separated. This separation of length scales is explored in the force network ensemble, where one studies the space of allowed force configurations for a given, frozen contact geometry. Here we review results of this approach, which yields nontrivial predictions for the effect of packing dimension and anisotropy on the contact force distribution $P(f)$, the response to overall shear and point forcing, all of which can be studied in great numerical detail. Moreover, there are emerging analytical approaches that very effectively capture, for example, the form of force distributions.