Stress in frictionless granular material: Adaptive Network Simulations

TL;DR

This paper introduces an adaptive network simulation method for force transmission in frictionless granular materials, revealing stable force networks, force chains, and stress constraints under shear loading.

Contribution

It presents a novel adaptive contact removal/addition procedure to simulate force networks without modifying particle positions, aligning with recent theoretical stress constraints.

Findings

Force networks satisfy linear stress constraints.

Force distribution follows an exponential decay.

Force response concentrates along specific rays.

Abstract

We present a minimalistic approach to simulations of force transmission through granular systems. We start from a configuration containing cohesive (tensile) contact forces and use an adaptive procedure to find the stable configuration with no tensile contact forces. The procedure works by sequentially removing and adding individual contacts between adjacent beads, while the bead positions are not modified. In a series of two-dimensional realizations, the resulting force networks are shown to satisfy a linear constraint among the three components of average stress, as anticipated by recent theories. The coefficients in the linear constraint remain nearly constant for a range of shear loadings up to about .6 of the normal loading. The spatial distribution of contact forces shows strong concentration along ``force chains". The probability of contact forces of magnitude f shows an exponential falloff with f. The response to a local perturbing force is concentrated along two characteristic rays directed downward and laterally.