Models of stress propagation in granular media

Stress patterns in static granular media exhibit unusual features when compared to either liquids or elastic solids. Qualitatively, we attribute these features to the presence of `stress paths', whose geometry depends on the construction history and controls the propagation of stresses. Stress paths can cause random focussing of stresses (large fluctuations) as well as systematic deflections (arching). We describe simple physical models that capture some of these effects. In these models, the `stress paths' become identified with the characteristic `light rays' of wavelike (hyperbolic) equations for force propagation. Such models account for the `pressure dip' below conical sandpiles built by pouring from a point source, and explain qualitatively the large stress fluctuations observed experimentally in granular matter. The differences between this approach and more conventional modelling strategies (based on elastoplastic or rigid-plastic models) are highlighted, focusing on the role of boundary conditions. Our models provide a continuum picture in which granular materials are viewed as fragile matter, able to support without rearranging only a subset of the static external loadings admissible for a normal elastic solid.