Rheology and shear jamming of frictional ellipses

Understanding and predicting dense granular flows is of importance in geology and industrial applications. Still, most theoretical work has been limited to flows and packings composed of discs or spheres, a narrow subset of all possible packings. To advance our understanding of more realistic flows we here study the granular rheology of ellipses in steady-state flow with a focus on the effects of elongation and interparticle friction. We carry out novel numerical simulations of amorphous granular flows in a shear cell under confining pressure, at constant shear rate and at various aspect ratios. Both frictionless and frictional particles are considered. The various rheological curves follow the semi-empirical constitutive relations previously found for granular flows composed of discs or spheres. At the shear jamming point one finds well-defined packings, all characterised by their own set of critical parameters such as critical packing fraction, effective friction, etc. Packings composed of frictionless or almost frictionless particles are found to have a non-monotonic dependence of the macroscopic friction but a monotonic increase in packing fraction as the aspect ratio increases. For packings composed of particles with high interparticle friction the reverse is found. While frictionless packings are found to be hypostatic (except in the disc limit) frictional packings are remarkably close to the isostaticity point of having three contacts per particle. Both frictional and frictionless packings are found to have an increasing nematic ordering as the aspect ratio increases. The onset of a rolling, rather than sliding, motion between very frictional particles diminish this nematic ordering substantially. These findings put new and previously unknown bounds on the packing ratios and yield criteria for these amorphous packings at shear jamming.