Effects of Grain Shape on the Response of a Two-Dimensional Granular Material Under Constant Shear Rate

We present a study on the effects of particle shape (disks, hexagons, and pentagons) on the macroscopic coefficient of friction of a two-dimensional, monodisperse, single-shaped, granular system, subjected to shear. We found that the mechanism of stress relaxation in disks is based on the sliding of adjacent planes parallel to the applied deformation direction. In hexagons, stress is relaxed through the creation of rigid pivots, which require hexagonal domains to nucleate and are responsible for the large fluctuations in the dilatancy and shear force. In pentagons the stress relaxation mechanism is through the rotation of individual pentagons, which is a consequence of their permanent misalignment, and are responsible for the small but relatively rapid fluctuations in the shear force. We observed that the friction coefficient is larger for polygonal particles than for the rounded ones. A maximum in the friction coefficient is observed in hexagon granulates with an initial width around 6.5 grains caused by the increased frequency in nucleation of rigid pivots. In mixtures of disks and hexagons we observed three different friction coefficient behaviors, which depended on the relative concentration of hexagons; in low concentrations of hexagons, <20%, the friction coefficient corresponds to that obtained in solely disks, at intermediate concentrations, <80%, the coefficient varies linearly with concentration, and at larger concentrations the friction coefficient corresponds to the values obtained for solely hexagons. On the contrary, mixtures of pentagons and hexagons showed two regimes; a low constant friction regime at concentrations lower than 60%, and an increased in friction observed with higher concentrations of hexagons. © 2014 American Physical Society.