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 gradient and stress are computed and evaluated with the goal to formulate objective constitutive relations for the powder flow behavior. From a single simulation, by applying timeand (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, approaching the maximum according to a stretched exponential with a specific rate that is consistent with a shear path of about one particle diameter. Introduction Granular Matter consists of many independent particles with peculiar collective flow behavior. Knowing the interaction laws and inserting those into a discrete element model (DEM), one can follow the particles by integrating Newtons equations of motion (Herrmann et al., 1998; Kishino, 2001; Luding et al., 2001; Luding, 2004b; Luding, 2008b). One goal is to derive continuum constitutive relations – as needed for industrial application. Methods and tools for a so-called micro-macro transition