Response of a Hexagonal Granular Packing under a Localized External Force

Details Response of a Hexagonal Granular Packing under a Localized External Force Response of a Hexagonal Granular Packing under a Localized External Force

2004-03-12

arxiv.org/abs/cond-mat/0403321v4

Europhys. Lett 71, 70 (2005).

Physics

Condensed Matter

Statistical Mechanics

4 pages, 9 figures, 2 colour figure, plot of standard deviation added, discussion expanded

Scientific paper

10.1209/epl/i2004-10530-9

We study the response of a two-dimensional hexagonal packing of rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each configuration of the contact forces is equally likely. We show that this problem is equivalent to a correlated $q$-model. We find that the response displays two peaks which lie precisely on the downward lattice directions emanating from the point of application of the force. With increasing depth, the magnitude of the peaks decreases, and a central peak develops. On the bottom of the pile, only the middle peak persists. The response of different system sizes exhibits self-similarity.

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