Elements of meso-scale continuum theory of granular matter

Owing to its disordered multiphase microstructure, dense granular matter exhibits characateristic behavior, including: (1) Transition between solid and fluid state, (2) Dilatancy: volume increase when sheared under constant pressure, (3) Localization in shear bands with characteristic width, and, (4) Vortex flow within shear bands, and in the bulk.

We analyze the mechanisms which produce the above phenomena on the level of discrete model. The kinematics is described by the graph theory representation. The transition from solid to fluid state is accompanied by dilatancy, but the fluid state includes compacting flow which leads to minimum fluid density state – the Critical state. We uncover the mechanisms of dilatancy and compaction and define intrinsic stress as the key variable that determines the behaviour. Strain localization in the form of shear bands is accompanied by accompanied by massive rolling of particle, which is energetically preferred over frictional sliding, but constrained by neighbors. The result is a characteristic rotation correlation length, which depends on direction relative to the force chain direction. By means of simple model we demonstrate that the vortex flow in shear bands minimizes the dissipation (and shear resistance) in the shear band.