Constitutive relations for the shear-band evolution in granular matter under large strain

A so-called “split-bottom ring shear cell ” leads to wide shear bands under slow, quasi-static deformation. From discrete element simulations (DEM), several continuum fields like the density, velocity, deformation gra-dient and stress are computed and evaluated with the goal to formulate ob-jective constitutive relations for the powder flow behavior. From a single simulation, by applying time- and (local) space-averaging, a nonlinear yield surface is obtained with a peculiar stress dependence. The anisotropy is always smaller than the macroscopic friction coefficient. However, the lower bound of anisotropy increases with the strain rate, ap-proaching the maximum according to a stretched exponential with a specific rate that is consistent with a shear path of about one particle diameter