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Register a new userPackings of frictionless spherocylinders
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Authors
Claus Heussinger
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We present simulation results on the properties of packings of frictionless spherocylindrical particles. Starting from a random distribution of particles in space, a packing is produced by minimizing the potential energy of inter-particle contacts until a force-equilibrated state is reached. For different particle aspect ratios $alpha=10ldots 40$, we calculate contacts $z$, pressure as well as bulk and shear modulus. Most important is the fraction $f_0$ of spherocylinders with contacts at both ends as it governs the jamming threshold $z_c(f_0)=8+2f_0$. These results highlight the important role of the axial sliding degree of freedom of a spherocylinder, which is a zero-energy mode but only if no end-contacts are present.
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At low volume fraction, disordered arrangements of frictionless spheres are found in un--jammed states unable to support applied stresses, while at high volume fraction they are found in jammed states with mechanical strength. Here we show, focusing on the hard sphere zero pressure limit, that the transition between un-jammed and jammed states does not occur at a single value of the volume fraction, but in a whole volume fraction range. This result is obtained via the direct numerical construction of disordered jammed states with a volume fraction varying between two limits, $0.636$ and $0.646$. We identify these limits with the random loose packing volume fraction $rl$ and the random close packing volume fraction $rc$ of frictionless spheres, respectively.
We perform computational studies of repulsive, frictionless disks to investigate the development of stress anisotropy in mechanically stable (MS) packings. We focus on two protocols for generating MS packings: 1) isotropic compression and 2) applied simple or pure shear strain $gamma$ at fixed packing fraction $phi$. MS packings of frictionless disks occur as geometric families (i.e. parabolic segments with positive curvature) in the $phi$-$gamma$ plane. MS packings from protocol 1 populate parabolic segments with both signs of the slope, $dphi/dgamma >0$ and $dphi/dgamma <0$. In contrast, MS packings from protocol 2 populate segments with $dphi/dgamma <0$ only. For both simple and pure shear, we derive a relationship between the stress anisotropy and dilatancy $dphi/dgamma$ obeyed by MS packings along geometrical families. We show that for MS packings prepared using isotropic compression, the stress anisotropy distribution is Gaussian centered at zero with a standard deviation that decreases with increasing system size. For shear jammed MS packings, the stress anisotropy distribution is a convolution of Weibull distributions that depend on strain, which has a nonzero average and standard deviation in the large-system limit. We also develop a framework to calculate the stress anisotropy distribution for packings generated via protocol 2 in terms of the stress anisotropy distribution for packings generated via protocol 1. These results emphasize that for repulsive frictionless disks, different packing-generation protocols give rise to different MS packing probabilities, which lead to differences in macroscopic properties of MS packings.
Simulated granular packings with different particle friction coefficient mu are examined. The distribution of the particle-particle and particle-wall normal and tangential contact forces P(f) are computed and compared with existing experimental data. Here f equivalent to F/F-bar is the contact force F normalized by the average value F-bar. P(f) exhibits exponential-like decay at large forces, a plateau/peak near f = 1, with additional features at forces smaller than the average that depend on mu. Computations of the force-force spatial distribution function and the contact point radial distribution function indicate that correlations between forces are only weakly dependent on friction and decay rapidly beyond approximately three particle diameters. Distributions of the particle-particle contact angles show that the contact network is not isotropic and only weakly dependent on friction. High force-bearing structures, or force chains, do not play a dominant role in these three dimensional, unloaded packings.
Using computer simulations we investigate the microscopic structure of the singular director field within a nematic droplet. As a theoretical model for nematic liquid crystals we take hard spherocylinders. To induce an overall topological charge, the particles are either confined to a two-dimensional circular cavity with homeotropic boundary or to the surface of a three-dimensional sphere. Both systems exhibit half-integer topological point defects. The isotropic defect core has a radius of the order of one particle length and is surrounded by free-standing density oscillations. The effective interaction between two defects is investigated. All results should be experimentally observable in thin sheets of colloidal liquid crystals.
Many experiments over the past half century have shown that, for a range of protocols, granular materials compact under pressure and repeated small disturbances. A recent experiment on cyclically sheared spherical grains showed significant compaction via homogeneous crystallization (Rietz et al., 2018). Here we present numerical simulations of frictionless, purely repulsive spheres undergoing cyclic simple shear with dissipative Newtonian dynamics at fixed vertical load. We show that for sufficiently small strain amplitudes, cyclic shear gives rise to homogeneous crystallization at a volume fraction $phi = 0.646 pm 0.001$. This result indicates that neither friction nor gravity is essential for homogeneous crystallization in driven granular media.
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