Abstract:
A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general Boltzmann equation for the densities of force chains in different directions is proposed and a complete solution is obtained for a special case in which chains lie along a discrete set of directions. The analysis and results demonstrate the necessity of including nonlinear terms in the Boltzmann equation. A line of nontrivial fixed-point solutions is shown to govern the properties of large systems. In the vicinity of a generic fixed point, the response to a localized load shows a crossover from a single, centered peak at intermediate depths to two propagating peaks at large depths that broaden diffusively.
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Received 16 January 2002
An Erratum for this chapter can be found at http://dx.doi.org/10.1140/epje/i2002-10030-4
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Socolar, J., Schaeffer, D. & Claudin, P. Directed force chain networks and stress response in static granular materials. Eur. Phys. J. E 7, 353–370 (2002). https://doi.org/10.1140/epje/i2002-10011-7
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DOI: https://doi.org/10.1140/epje/i2002-10011-7