Shear flow of frictional spheroids: Comparison between elongated and flattened particles

TL;DR

The paper addresses how friction and non-spherical particle shapes govern dense granular shear flows by comparing oblate and prolate spheroids under quasi-2D shear. Using discrete element method simulations with superquadric particles, Lees-Edwards boundary conditions, and pressure-controlled shear, they map a regime diagram for energy dissipation by partitioning the total power into normal and tangential components, $\mathcal P_n$ and $\mathcal P_t$, across inertial number $I$ and microscopic friction $\mu_p$, and quantify alignment, velocity fluctuations, and fabric. Key findings include an extended sliding regime for oblate particles, non-monotonic dissipation transitions at small $|r_g|$, and stronger fabric anisotropy and correlated motion for oblate grains, with dissipation clustering along the major axis aligned with the flow. The results advance understanding of how 3D particle geometry shapes macroscopic rheology and micro-contact networks, informing anisotropic constitutive modeling for industrial and geophysical granular flows.

Abstract

The rheology of dense granular shear flows is influenced by friction and particle shape. We investigate numerically the impact of non-spherical particle geometries under shear on packing fraction, stress ratios, velocity fluctuations, force distribution, and dissipation mechanisms, for a wide range of inertial numbers, friction coefficients and aspect ratios. We obtain a regime diagram for the dissipation which shows that lentil-like (oblate) particles exhibit an extended sliding regime compared to rice-like (prolate) particles with the same degree of eccentricity. Additionally, we identify non-monotonic behaviour of slightly aspherical particles at low friction, linking it to their higher fluctuating rotational kinetic energy. We find that angular velocity fluctuations are generally reduced when particles align with the flow, except in highly frictional rolling regimes, where fluctuations collapse onto a power-law distribution and motion becomes less correlated. Moreover, for realistic friction coefficients power dissipation tends to concentrate along the major axis aligned with the flow, where slip events are more frequent. We also show that flat particles develop stronger fabric anisotropy than elongated ones, influencing macroscopic stress transmission. These findings provide new insights into the role of particle shape in granular mechanics, with implications for both industrial and geophysical applications.

Figures (18)

• Figure 1: (a) Snapshot of the simulation box. Oblate grains $\alpha = 0.33, \, r_g=-0.5$ and prolate ones $\alpha = 3.0, \, r_g=0.5$ are displayed on the left and right respectively. A constant shear rate in the $xy$ plane, $\dot{\gamma}$, is applied by tilting the box, while the normal stress $\sigma_{yy}=P$ is controlled by shrinking the box in the $y$ direction. (b) Illustration of ellipsoids' shapes in this study from flattened to elongated left to right. (c) Absolute value of the shape ratio $|r_g|$ and $M_\alpha = \max(\alpha, \alpha^{-1})$ as a function of aspect ratio $\alpha$.
• Figure 2: (a) Nematic order parameter, (b) mean angle with the shear flow, and (c) average grain angular velocity in the vorticity direction. All data in this figure is measured at $I\approx 0.01$ and is nearly constant over the range of $I$ in this study. Dotted lines indicate the behavior towards ill-defined quantities for spheres.
• Figure 3: Dissipation regime diagram of granular shear flow as a level set curve where the frictional and normal dissipation are equal. Left lines mark the transition between the normal dissipation and the sliding frictional regime, while right ones the transition to the rolling regime, where virtually all contacts are sticking. The black dashed line has slope 2 as predicted by degiuli2016phase for spheres. For all non-spherical particles the sliding regime is wider than for spherical ones, indicating non-spherical particles slide over a larger range of parameters. (Inset) Slice of $I_c$ at the normal dissipation-sliding transition for $\mu_p=0.01$, showing non monotonicity in $\alpha$. Slightly aspherical particles display a reduced normal dissipation regime.
• Figure 4: (a) Normalized normal and (b) tangential dissipation for $I\approx10^{-2}$ and different values of microscopic friction. On the left, data at $\mu_p<0.4$, on the right $\mu_p\geq0.4$. In panel (a.1), the red (black) line represents the best-fit power law for frictionless prolate (oblate) particles, with a slope of $-0.90$, $(0.96)$. For particles with $\mu_p=0.1$, panel (b.1), the corresponding slopes are $-0.30$ for prolate and $+0.33$ for oblate particles. From (b.1, b.2), it is evident that the tangential dissipation increases up to a value of $\mu_p$ between $0.1$ and $1.0$, depending on the shape, and then reduces for higher values.
• Figure 5: (a) Ratio of the streamline-wise velocity fluctuation $\delta v_x$ to the gradient-wise velocity fluctuation $\delta v_y$, (b) and to spanwise vorticity $\delta v_z$. (c) Ratio of rotational to translational kinetic energy, where the dashed line indicates a ratio of one. Different microscopic friction coefficients, with the same color legend as in Figure \ref{['fig:dissipation_normal_tangential']}. For low values of friction the flow component of the fluctuation dominates for prolate particles, whereas for oblate ones, both the flow and the vorticity ones are dominant. In the sliding regime the fluctuations in the vorticity direction are reduced, as friction stabilizes that translation. For low values of friction and eccentricity the rotational fluctuations dominate. At high values of friction energy tends to be equally distributed between translation and rotation, as well as between the translational degrees of freedom. Data taken at $I\approx 0.01$.