Anisotropy in granular media: classical elasticity and directed force chain network
arXiv:cond-mat/0211015 · doi:10.1103/PhysRevE.67.031302
Abstract
A general approach is presented for understanding the stress response function in anisotropic granular layers in two dimensions. The formalism accommodates both classical anisotropic elasticity theory and linear theories of anisotropic directed force chain networks. Perhaps surprisingly, two-peak response functions can occur even for classical, anisotropic elastic materials, such as triangular networks of springs with different stiffnesses. In such cases, the peak widths grow linearly with the height of the layer, contrary to the diffusive spreading found in `stress-only' hyperbolic models. In principle, directed force chain networks can exhibit the two-peak, diffusively spreading response function of hyperbolic models, but all models in a particular class studied here are found to be in the elliptic regime.
34 pages, 17 figures (eps), submitted to PRE, figures amended, partially to compare better to recent exp. work
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