Compression-driven jamming of athermal frictionless spherocylinders in two dimensions

Abstract

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}<z_{iso}=2d_{f}=6 the isostatic value. We show that, for moderately elongated spherocylinders, there is no orientational ordering upon athermal compression through jamming. We analyze in detail the eigenmodes of the dynamical matrix close to the jamming point for a few different values of the aspect ratio, from nearly circular to moderately elongated. We find that there are low frequency bands containing N(z_{iso}-z_{J})/2 modes, such that the frequencies of these modes vanish as ϕ→ϕ_{J}. We consider the extended versus localized nature of these low frequency modes, and the extent to which they involve translational or rotational motion, and find many low frequency sliding modes where particles can move with little rotation. We highlight the importance of treating side-to-side contacts, along flat sides of the spherocylinder, properly for the correct determination of z_{J}. We note the singular nature of taking the α→0 limit. We discuss the similarities and differences with previous work on jammed ellipses and ellipsoids, to illustrate the effects that different particle shapes have on configurations at jamming.

Shear-driven flow of athermal, frictionless, spherocylinder suspensions in two dimensions: Stress, jamming, and contacts

“…We see (as reported earlier by us for sheared 2D spherocylinders and 3D ellipsoids [67]) that as α decreases, the peak on the flat side at ϑ = π/2 increases in magnitude, while the width of this peak ∆ϑ = 2 arctan(α) decreases. Similar results have been previously reported for static jammed configurations of 2D spherocylinders and ellipses obtained by isotropic compression [19,25]. Evidence suggesting such an effect has also been reported for both frictionless and frictional 2D ellipses with a Bagnoldian rheology [40], though the effect seems to be reduced as the friction coefficient increases; similar conclusions were found for Bagnoldian 3D spherecylinders [41].…”

“…Passing through the configuration to remove such rattlers, we then iterate the process until no further rattlers are found. We note that for compression-driven jamming, we have found [25] that the fraction of rattlers in the system at jamming decreases significantly as the asphericity α increases, varying from roughly 3.3% for For the current study, with our system sheared at a finite rateγ > 0, there is yet another complication because our flowing configurations are not in mechanically stable states; only in the limitγ → 0 do we arrive at mechanically stable states. The Z that we seek should therefore be taken as theγ → 0 limit of the Z computed at finitė γ.…”

“…In Fig. 9 we also plot, for comparison, the values of φ J vs α that we have previously found [25] for the compression-driven jamming of this same system, when we isotropically compressed at a slow rate from random configurations at an initial small φ init . We see that at small α 0.5 the φ J from compression are quite close to, though systematically slightly smaller than, the φ J from shearing.…”

“…Fitting σ(γ) to a Herschel-Bulkley form at different φ for Packing fraction at the jamming transition φJ vs particle asphericity α for shear-driven jamming and for jamming by isotropic compression (from Ref [25]…”

Vibrational properties of two-dimensional dimer packings near the jamming transition

“…Jammed systems composed of various shapes of nonspherical particles, such as ellipsoidal particles [9][10][11][12][13][14][15][16][17][18][19], sphero-cylinders [20][21][22][23][24], and composites of spherical par- * kumpeishiraishi@g.ecc.u-tokyo.ac.jp ticles [25][26][27][28], have also been studied numerically, theoretically, and experimentally. One of the most studied nonspherical particles is the ellipsoidal particle.…”