A non-local rheology for granular flows across yield conditions

TL;DR

This paper introduces a non-local rheological model for dense granular flows that applies across yield conditions, revealing a divergence in relaxation length near the yield point.

Contribution

It develops a non-local constitutive relation for granular flows that remains valid below the yield stress, extending the understanding of flow behavior.

Findings

Relaxation length diverges as inverse square-root of distance to yield point

Flow can occur below yield stress with the same rheology as above yield

Model applies to both frictional and frictionless granular materials

Abstract

The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A non-local constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is found to diverge as the inverse square-root of the distance to the yield point, on both sides of that point.