Torsional shear flow of granular materials: shear localization and minimum energy principle

The rheological properties of granular matter submitted to torsional shear are investigated numerically by means of discrete element method. The shear cell is made of a cylinder filled by grains which are sheared by a bumpy bottom and submitted to a vertical pressure which is applied at the top. Regimes differing by their strain localization features are observed. They originate from the competition between dissipation at the sidewalls and dissipation in the bulk of the system. The effects of the (i) the applied pressure, (ii) sidewall friction, and (iii) angular velocity are investigated. A model, based on the purely local -rheology and a minimum energy principle is able to capture the effect of the two former quantities but unable to account the effect of the latter. Although, an ad hoc modification of the model allows to reproduce all the numerical results, our results point out the need for an alternative rheology.