Numerical study of stress distribution in sheared granular material in two dimensions
We simulate the response of dense granular material to shear. Our simulations use a micromechanical model which includes realistic material models for each deformable grain, and a Coulomb friction model for interactions between grains. We measure the probability density function (PDF) governing the volume distribution of stress for monodisperse and polydisperse samples, circular and polygonal grains, and various values of microscopic friction coefficients, yield stresses, and packing fractions. Remarkably, PDF's are similar in form for all cases simulated, and similar to those observed in experiments with granular materials under both compression and shear. Namely, the simulations yield an exponential probability of large stresses above the mean. The relationship between distributions of boundary tractions and volume distributions of stress is discussed. The ratio of normal and tangential components of traction on the boundary defines a bulk frictional response, which is shown to increase with the intergranular friction coefficient. However, the bulk friction is always larger than the intergranular friction for densely packed samples. Bulk friction is also strongly dependent on grain size distribution and shape. New observations of force-chain banding during recrystallization, of slip systems in monodisperse samples, and of the effects of plastic yield, are also presented.