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

TL;DR

This study tests a visco-plastic theory of dense granular flows against simulations of rotating drums, confirming some predictions while revealing significant tensor misalignments that challenge the theory's assumptions.

Contribution

It provides a critical evaluation of visco-plastic theory in complex granular flows, highlighting where it succeeds and where it fails due to tensor misalignment.

Findings

The stress-strain relation holds over a wide strain rate range.

Stress and strain rate tensors are misaligned throughout the flow.

Misalignment may be linked to transient dilatancy effects.

Abstract

We confront a recent visco-plastic description of dense granular flows [P. Jop et al, Nature, {\bf 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.