Eur. Phys. J. E 6, 99-105 (2001)

Robust propagation direction of stresses in a minimal granular packing

D.A. Head¹, A.V. Tkachenko² and T.A. Witten<sup>3

1</sup>  Department of Physics and Astronomy, JCMB King's Buildings, University of Edinburgh, Edinburgh EH9 3JZ, UK
²  Bell Labs, Lucent Technologies, 600-700 Mountain Ave., Murray Hill, NJ 07974, USA
³  The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA

dhead@nat.vu.nl

(Received 30 April 2001 and Received in final form 16 August 2001)

Abstract
By employing the adaptive network simulation method, we demonstrate that the ensemble-averaged stress caused by a local force for packings of frictionless rigid beads is concentrated along rays whose slope is consistent with unity: forces propagate along lines at 45 degrees to the horizontal or vertical. This slope is shown to be independent of polydispersity or the degree to which the system is sheared. Further confirmation of this result comes from fitting the components of the stress tensor to the null stress "constitutive equation" . The magnitude of the response is also shown to fall off with the -1/2 power of distance. We argue that our findings are a natural consequence of a system that preserves its volume under small perturbations.

PACS
45.70.Cc - Static sandpiles; granular compaction.
83.80.Fg - Granular solids.


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001