Measurement of higher-order stress-strain effects in granular materials undergoing non-uniform deformation

Discrete element (DEM) simulations demonstrate that granular materials are non-simple, meaning that the incremental stiffness of a granular assembly depends on the gradients of the strain increment as well as on the strain increment itself. In quasi-static simulations, two-dimensional granular assemblies were stiffer when the imposed deformation was non-uniform than for uniform deformation. The contacts between particles were modeled as linear-frictional contacts with no contact moments. The results are interpreted in the context of a higher-order micro-polar continuum, which admits the possibility of higher-order stress and couple-stress. Although the behavior was non-simple, no evidence was found for a couple-stress or an associated stiffness. The experimental results apply consistently to three particle shapes (circles, ovals, and a non-convex cluster shape), to assemblies of three sizes (ranging from 250 to 4000 particles), and at pre-peak and post-peak strains.