Stress Propagation in Two Dimensional Frictional Granular Matter

Abstract

The stress profile and reorientation of grains, in response to a point force applied to a preloaded two dimensional granular system, are calculated in the context of a continuum theory that incorporates the texture of the packing. When high friction prevents slip at the inter-grain contacts, an anisotropic packing propagates stress along two peaks which amalgamate into a single peak as the packing is disordered into a less anisotropic structure; this single peak may be wider or narrower than in the isotropic case, depending on the preparation of the packing. At lower frictions, an effective treatment of slipping contacts yields sharpened peaks, and ultimately a singular limit in which stress propagates along straight rays. Recent experiments, as well as aspects of hyperbolic models, are discussed in light of these results.