We numerically simulate the uniform athermal shearing of bidisperse, frictionless, two dimensional spherocylinders and three dimensional prolate ellipsoids. We focus on the orientational ordering of particles as an asphericity parameter α → 0 and particles approach spherical. We find that the nematic order parameter S2 is non-monotonic in the packing fraction φ, and that as α → 0 S2 stays finite at jamming and above. The approach to spherical particles thus appears to be singular. We also find that sheared particles continue to rotate above jamming, and that particle contacts preferentially lie along the narrowest width of the particles, even as α → 0.Models of athermal (T = 0) granular materials have often focused on the simplest case of spherical particles. Recently, however, more attention has been paid to the case of elongated particles with lower rotational symmetry [1]. The question then arises whether such elongated particles will orientationally order as the particle density increases, so as to pack more efficiently. While elongated particles in thermal equilibrium are known to have a nematic orientational ordering transition [2, 3], recent works have found that such particles do not orientationally order upon athermal isotropic compression [4][5][6][7][8].Orientational ordering is, however, found when elongated particles are placed in an athermal uniform shear flow. In this case, drag forces between the particle and the flow will cause the particle to tumble [9]. If the particle is asymmetrical, with unequal eigenvalues of its moment of inertia tensor, tumbling will have a non-uniform rotational velocity; the torque from drag forces will vary with the particle's orientation, and the particle will on average align with the flow direction. For a finite density of colliding particles, nematic ordering remains but the nematic director becomes oriented at a finite angle with respect to the flow direction [10][11][12][13][14][15][16][17][18].Here we investigate the nematic ordering of frictionless, aspherically shaped particles, athermally sheared at constant strain rateγ, putting the system into a steady state of simple shear flow. We consider behavior as an asphericity parameter α → 0, and the particles approach spherical. We find the surprising result that a finite nematic ordering persists even as α → 0, suggesting that the shear driven jamming of aspherical particles has a singular limit as α → 0. Since most particles in nature are not truly spherical, our result may have broad implications for granular shear flows.Models: We consider two different numerical models: (i) spherocylinders in two dimensions (2D), and (ii) prolate ellipsoids in three dimensions (3D). In both cases we take a bidisperse distribution of particle sizes, with equal numbers of big and small particles. We use softcore particles with a one-sided harmonic elastic repulsion. The system length is L in all directions, with periodic boundary conditions along the flow directionx, and Lees-Edwards boundary conditions [19] with a uniform stra...

We simulate numerically the compression-driven jamming of athermal, frictionless, soft-core spherocylinders in two dimensions, for a range of particle aspect ratios α. We find the critical packing fraction ϕ_{J}(α) for the jamming transition and the average number of contacts per particle z_{J}(α) at jamming. We find that both are nonmonotonic, with a peak at α≈1. We find that configurations at the compression-driven jamming point are always hypostatic for all α, with z_{J}

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady state shear strain applied at a fixed finite rate. Energy dissipation occurs via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension and resulting in a Newtonian rheology. We study the resulting pressure p and deviatoric shear stress σ of the interacting spherocylinders as a function of packing fraction φ, strain rateγ, and a parameter α that measures the asphericity of the particles; α is varied to consider the range from nearly circular disks to elongated rods. We consider the direction of anisotropy of the stress tensor, the macroscopic friction µ = σ/p, and the divergence of the transport coefficient ηp = p/γ as φ is increased to the jamming transition φJ . From a phenomenological analysis of Herschel-Bulkley rheology above jamming, we estimate φJ as a function of asphericity α and show that the variation of φJ with α is the main cause for differences in rheology as α is varied; when plotted as φ/φJ rheological curves for different α qualitatively agree. However a detailed scaling analysis of the divergence of ηp for our most elongated particles suggests that the jamming transition of spherocylinders may be in a different universality class than that of circular disks. We also compute the number of contacts per particle Z in the system and show that the value at jamming ZJ is a non-monotonic function of α that is always smaller than the isostatic value. We measure the probability distribution of contacts per unit surface length P(ϑ) at polar angle ϑ with respect to the spherocylinder spine, and find that as α → 0 this distribution seems to diverge at ϑ = π/2, giving a finite limiting probability for contacts on the vanishingly small flat sides of the spherocylinder. Finally we consider the variation of the average contact force as a function of location on the particle surface.

We carry out numerical simulations of soft, U-shaped, frictionless particles in d = 2 dimensions in order to explore the effects of complex particle shape on the jamming transition. We consider both cases of uniform compression-driven and shear-driven jamming as packing fraction φ and compression or shear rate is varied. Upon slow compression, jamming is found to occur when the isostatic condition is satisfied. Under driven steady state shearing, jamming occurs at a higher packing fraction φJ than observed in compression. A growing relaxation time and translational correlation length is found as φ increases towards φJ . We consider the orientational ordering and rotation of particles induced by the shear flow. Both nematic and tetratic ordering are found, but these decrease as φ increases to φJ . At the jamming transition, the nematic ordering further decreases, while the tetratic ordering increases, but the orientational correlation lengths remain small throughout. The average angular velocity of the particles is found to increase as φ increases, saturating to a plateau just below φJ , but then increasing again as φ increases above φJ .[The final publication is available at Springer via http://dx.

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rateγ. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. Considering a range of packing fractions φ and particle asphericities α at smallγ, we study the angular rotationθi and the nematic orientational ordering S2 of the particles induced by the shear flow, finding a non-monotonic behavior as the packing φ is varied. We interpret this non-monotonic behavior as a crossover from dilute systems at small φ, where single-particle-like behavior occurs, to dense systems at large φ, where the geometry of the dense packing dominates and a random Poisson-like process for particle rotations results. We also argue that the finite nematic ordering S2 is a consequence of the shearing serving as an ordering field, rather than a result of long-ranged cooperative behavior among the particles. We arrive at these conclusions by consideration of (i) the distribution of waiting times for a particle to rotate by π, (ii) the behavior of the system under pure, as compared to simple, shearing, (iii) the relaxation of the nematic order parameter S2 when perturbed away from the steady state, and (iv) by construction a numerical mean-field model for the rotational motion of a particle. Our results also help to explain the singular behavior observed when taking the α → 0 limit approaching circular disks.