Criticality of the "critical state" of granular media: Dilatancy angle in the tetris model

Details Criticality of the "critical state" of granular media: Dilatancy angle in the tetris model Criticality of the "critical state" of granular media: Dilatancy angle in the tetris model

1999-10-06

arxiv.org/abs/cond-mat/9910078v1

Physics

Condensed Matter

Statistical Mechanics

7 pages RevTex, 8eps figure, to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.61.2813

The dilatancy angle describes the propensity of a granular medium to dilate under an applied shear. Using a simple spin model (the ``tetris'' model) which accounts for geometrical ``frustration'' effects, we study such a dilatancy angle as a function of density. An exact mapping can be drawn with a directed percolation process which proves that there exists a critical density $\rho_c$ above which the system expands and below which it contracts under shear. When applied to packings constructed by a random deposition under gravity, the dilatancy angle is shown to be strongly anisotropic, and it constitutes an efficient tool to characterize the texture of the medium.

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