Relevance of visco-plastic theory in a multi-directional inhomogeneous granular flow

Abstract

We confront a recent visco-plastic description of dense granular flows (Jop P. et al., Nature, 441 (2006) 727) with multi-directional inhomogeneous steady flows observed in non-smooth contact dynamics simulations of 2D half-filled rotating drums. Special attention is paid to check separately the two underlying fundamental statements into which the considered theory can be recast, namely i) a single relation between the invariants of stress and strain rate tensors and ii) the alignment between these tensors. Interestingly, the first prediction is fairly well verified over more than four decades of small strain rate, from the surface rapid flow to the quasi-static creep phase, where it is usually believed to fail because of jamming. On the other hand, the alignment between stress and strain rate tensors is shown to fail over the whole flow, what yields an apparent violation of the visco-plastic rheology when applied without care. In the quasi-static phase, the particularly large misalignment is conjectured to be related to transient dilatancy effects.