Numerical Study of the Stress Response of Two-Dimensional Dense Granular Packings

TL;DR

This study uses computer simulations to analyze stress transmission in two-dimensional dense granular packings, finding that isotropic elasticity models best predict stress distribution across various conditions, challenging hyperbolic and parabolic models.

Contribution

It provides a detailed numerical validation of elasticity theory for dense granular packings, highlighting its applicability and limitations near the jamming transition.

Findings

Stress distribution aligns with isotropic elasticity predictions.

Hyperbolic and parabolic models do not accurately predict stress in studied regions.

Stress profile width scales linearly with depth.

Abstract

We investigate the Green function of two-dimensional dense random packings of grains in order to discriminate between the different theories of stress transmission in granular materials. Our computer simulations allow for a detailed quantitative investigation of the dynamics which is difficult to obtain experimentally. We show that both hyperbolic and parabolic models of stress transmission fail to predict the correct stress distribution in the studied region of the parameters space. We demonstrate that the compressional and shear components of the stress compare very well with the predictions of isotropic elasticity for a wide range of pressures and porosities and for both frictional and frictionless packings. However, the states used in this study do not include the critical isostatic point for frictional particles, so that our results do not preclude the fact that corrections to elasticity may appear at the critical point of jamming, or for other sample preparation protocols, as discussed in the main text. We show that the agreement holds in the bulk of the packings as well as at the boundaries and we validate the linear dependence of the stress profile width with depth.