Sheared force-networks: anisotropies, yielding and geometry

TL;DR

This paper investigates how shear stress induces anisotropy in force networks within granular materials, leading to yielding characterized by a transition to an isostatic state and predictable scaling of the force network subspace.

Contribution

It introduces a framework linking force network anisotropy and yielding in granular matter, predicting yield stress based on contact number and force network properties.

Findings

Force networks become highly anisotropic with increasing shear stress.

Yielding occurs when the network becomes effectively isostatic.

Scaling laws predict the yield stress for different contact numbers.

Abstract

A scenario for yielding of granular matter is presented by considering the ensemble of force networks for a given contact network and applied shear stress $\tau$. As $\tau$ is increased, the probability distribution of contact forces becomes highly anisotropic, the difference between average contact forces along minor and major axis grows, and the allowed networks span a shrinking subspace of all force-networks. Eventually, contacts start to break, and at the yielding shear stress, the packing becomes effectively isostatic. The size of the allowed subspace exhibits simple scaling properties, which lead to a prediction of the yield stress for packings of arbitrary contact number.