The missing stress-geometry equation in granular media

Details The missing stress-geometry equation in granular media The missing stress-geometry equation in granular media

2001-03-16

arxiv.org/abs/cond-mat/0103346v1

Physica A 294, No.1-2, 545-553 (2001)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 4 figures, accepted by Physica A

Scientific paper

10.1016/S0378-4371(01)00102-9

The simplest solvable problem of stress transmission through a static granular material is when the grains are perfectly rigid and have an average coordination number of $\bar{z}=d+1$. Under these conditions there exists an analysis of stress which is independent of the analysis of strain and the $d$ equations of force balance $\nabla_{j} \sigma_{ij}({\vec r}) = g_{i}({\vec r})$ have to be supported by $\frac{d(d-1)}{2}$ equations. These equations are of purely geometric origin. A method of deriving them has been proposed in an earlier paper. In this paper alternative derivations are discussed and the problem of the "missing equations" is posed as a geometrical puzzle which has yet to find a systematic solution as against sensible but fundamentally arbitrary approaches.

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