Stress Propagation in Granular Materials: Robert Behringer, Duke University
Granular materials present a host of challenging questions at the most basic level. In dense granular materials, complex force structures, known as force chains dominate the transmission of force. Competing models to describe force propagation include purely diffusive, elastic, and wave-like behavior. One way to address the issue of how stresses propagate is to carry out experimental determinations of the Green's function, i.e. the response of a material to a local force perturbation. We have recently carried out such measurements using 2D photoelastic particles that allow us to determine the local force at the particle scale. These measurements indicate that the ensemble-averaged response depends significantly of the amount of order in the packing. In highly ordered packings, the response is consistent with a wave-like propagation of forces, whereas in disordered packings, the response is elastic. Notably, any given realization is typically complex, with large deviations from the ensemble-averaged response. When dense materials are deformed, the stress chains break and reform, leading to large-scale fluctuations.  In Couette shear experiments, we have found that there is a novel transition with second-order-like properties as the density of the sample is varied. Conventional Coulomb models for stresses in shearing materials indicate that the forces should be independent of shear rate. However, we have recently found a slow dependence on shear rate that is not accounted for by conventional models.