Patterned Nonaffine Motion in Granular Media

Vortex-like flow patterns are often observed in experiments on granular media for which uniform strain is expected based on the loading boundary conditions. These deformations become apparent when the motion associated with uniform strain is subtracted from the total particle motion. Besides presenting an interesting phenomenon that begs explanation, these vortex patterns suggest multiscale structure for nonaffine motion as suggested by modern continuum theories. Further, the authors note that the rotational velocity field added to a uniform strain field produces a planar slip field. Thus, these structures are associated with the slip-band fields that eventually form, which are generally associated with bifurcations in the solution path of the governing partial differential equations. The authors present a procedure to extract these motion fields from discrete-element simulations along with conjugate forces associated with these motions. A key finding from the simulations is that the motions that eventually lead to shear band formation develop throughout the loading history rather than arising as a distinct bifurcation. Further, the pattern of rotational fields, and hence the shear banding pattern, are controlled by the boundary conditions. A question, only partly resolved here, is the origin of forces driving the rotational fields.