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Register a new userThe missing stress-geometry equation in granular media
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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 $ abla_{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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