Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session J13: Focus Session: Jamming Theory and Experiment II |
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Sponsoring Units: GSNP Chair: Leonardo Silbert, Southern Illinois University Room: D225/226 |
Tuesday, March 22, 2011 11:15AM - 11:51AM |
J13.00001: Jammed particulate systems are inherently nonharmonic Invited Speaker: Normal mode analysis in the harmonic approximation underlies most of solid-state physics and applies well to both ordered and dis- ordered systems. Naturally, researches apply this analysis to jammed particulate systems, such as granular media, colloids, and foams, that interact via one-sided interactions, which are nonzero only when particles overlap. However, we find that systems with one-sided repulsive interactions possess no linear, harmonic response regime for large systems ($N\rightarrow\infty$) at finite pressures $P$, and for all $N$ near jamming onset $P\rightarrow 0$. We perform simulations on 2D frictionless bidisperse mechanically stable disk packings over a range of packing fractions $\Delta \phi = \phi-\phi_J$ above jamming onset $\phi_J$. We apply perturbations with amplitude $\delta$ to the packings along each eigen-direction from the dynamical matrix and determine whether the response of the system evolving at constant energy remains in the original eigenmode of the perturbation. For $\delta > \delta_c$, a single contact breaks and fluctuations abruptly spread to all discrete harmonic modes. As $\delta$ increases further all harmonic modes disappear into a continuous frequency band. We find that $\delta_c \sim \Delta \phi/N$, and thus jammed particulate systems are inherently nonharmonic with no linear vibrational response regime as $N\rightarrow \infty$ over the full range of $\Delta \phi$, and as $\Delta \phi \rightarrow 0$ at any $N$. This breakdown of harmonic behavior dramatically affects all aspects of system response including heat capacity, density of states, elastic moduli, and energy propagation. [Preview Abstract] |
Tuesday, March 22, 2011 11:51AM - 12:03PM |
J13.00002: Vibrational density of states for granular solids Carl Schreck, Thibault Bertand, Mark Shattuck, Corey O'Hern It was recently shown that granular packings composed of frictionless particles with purely repulsive contact interactions are strongly anharmonic. When perturbed along an eigenmode of the static packing (in the harmonic approximation), energy leaks from the original mode of vibration to a continuum of frequencies even when the system is under significant compression due to the breaking of the weakest contact. In light of this, we perform numerical simulations to measure the displacement matrix averaged over fluctuations and the associated eigenspectrum of weakly vibrated frictionless packings, which possess well-defined equilibrium positions that are different than those of the nearest static packing. We find that there is an increase in the number of low-frequency eigenmodes of the displacement matrix in the harmonic approximation (over the number of low-frequency modes in the static case) and these modes provide a more accurate description of the system dynamics. We also investigate the extent to which these results hold for systems with continuous potentials with repulsive and attractive interactions. [Preview Abstract] |
Tuesday, March 22, 2011 12:03PM - 12:15PM |
J13.00003: Spatiotemporally resolved granular acoustics Eli Owens, Karen Daniels Acoustic techniques provide a non-invasive method of characterizing granular material properties; however, there are many challenges in formulating accurate models of sound propagation due to the inherently heterogeneous nature of granular materials. In order to quantify acoustic responses in space and time, we perform experiments in a photoelastic granular material in which the internal stress pattern (in the form of force chains) is visible. We utilize two complementary methods, high-speed imaging and piezoelectric transduction, to provide particle-scale measurements of the amplitude of the acoustic wave. We observe that the average wave amplitude is largest within particles experiencing the largest forces. The force-dependence of this amplitude is in qualitative agreement with a simple Hertzian-like model for contact area. In addition, we investigate the power spectrum of the propagating signal using the piezoelectric sensors. For a Gaussian wave packet input, we observe a broad spectrum of transmitted frequencies below the driving frequency, and we quantify the characteristic frequencies and corresponding length scales of our material as the system pressure is varied. [Preview Abstract] |
Tuesday, March 22, 2011 12:15PM - 12:27PM |
J13.00004: Edge Effects in Jammed Systems Carl Goodrich, Wouter Ellenbroek, Andrea Liu Packings of spheres at zero temperature and shear stress exhibit a
jamming/unjamming transition as a function of density. For spheres
that repel when they overlap and do not otherwise interact, packings
are jammed with a nonzero static shear modulus at high densities. As
density decreases towards the unjamming transition, the number of
interacting neighbors per particle, $z$, decreases towards a critical
value $z_c$, so that at the unjamming transition the system just has
the minimum number of interacting neighbors to be mechanically stable.
In 2005, Wyart, et al. [1] proposed that there is a diverging length
scale, $l^*$, associated with this transition, that can be understood
from a ``cutting argument." Thus, if one cuts a cluster of linear
dimension $L$, the cluster will have zero-frequency vibrational modes
(soft modes) only for $L |
Tuesday, March 22, 2011 12:27PM - 12:39PM |
J13.00005: Dislocations jam at any density Georgios Tsekenis, Nigel Goldenfeld, Karin Dahmen Crystalline materials deform in an intermittent way via dislocation-slip avalanches. Below a critical stress, the dislocations are jammed due to long-range interactions and the material exhibits plastic response, while above this critical stress the dislocations are mobile (the unjammed phase) and the material fails. We use dislocation dynamics and scaling arguments to show that the critical stress grows with the square root of the dislocation density. Consequently, dislocations jam at any density, in contrast to granular materials, which only jam below a critical density. [Preview Abstract] |
Tuesday, March 22, 2011 12:39PM - 12:51PM |
J13.00006: Jammed packings of bumpy spherical particles Dominic Kwok, K. Vijay Kumar, Carl Schreck, Corey O'Hern, Mark Shattuck Static packings of soft frictionless spheres are a simple model to understand the jamming transition in granular media, and have provided great insight. However, friction in granular media plays an important role in determining the structural and mechanical properties of jammed packings. In particular, the number and location of contacts near the Coulomb sliding threshold is strongly correlated with plastic rearrangements. To better understand friction, we numerically generate jammed packings of bumpy spherical particles as a function of the rms roughness of the particles without incorporating {\it ad hoc} single contact frictional forces between particles, {\it i.e.} frictional contacts in the Hertz-Mindlin (HM) model. The frictional interactions in the bumpy particle model emerge in a natural way via the interdigitation of bumps between contacting particles. We calculate the number of contacts, packing fraction, interparticle forces, eigenmodes of the dynamical matrix, and mechanical properties of jammed packings of bumpy particles and compare our results with those obtained using the HM model. [Preview Abstract] |
Tuesday, March 22, 2011 12:51PM - 1:03PM |
J13.00007: Shock Waves in Jammed Solids Leopoldo Gomez, Ari Turner, Martin van Hecke, Vincenzo Vitelli We study shock propagation in two-dimensional jammed packings of soft repulsive spheres with Herzian contacts. The critical amplitude above which acoustic waves propagate as shocks displays power law scaling with density and vanishes as the jamming point is approached. Thus close to jamming elastic energy is mainly propagated in the form of shock waves. We determine the characteristic speed and attenuation of the resulting shocks as a function of the amplitude of the initial impulse and applied load. [Preview Abstract] |
Tuesday, March 22, 2011 1:03PM - 1:15PM |
J13.00008: Jamming: A Peek Behind the Curtain Martin van Hecke We will discuss two of the ``dirty little secrets'' concerning the (anomalous) scaling of the elastic moduli near jamming. First, there is no linear response near jamming, and we propose a novel scaling law for the onset of rearrangements as function of number of particles and distance to the jamming point. Second, the elastic moduli obtained from the dynamical matrix have a very broad distribution, and we discuss how to deal with packings with negative elastic moduli. [Preview Abstract] |
Tuesday, March 22, 2011 1:15PM - 1:27PM |
J13.00009: Local anisotropy in globally isotropic granular packings Kamran Karimi, Craig Maloney We study local stresses and elastic moduli defined at various coarse-graining scales, $R$, and volume fractions, $\phi$, in a two dimensional (2D) mixture of frictionless granular particle packings. We measure the average deviatoric stress normalized by pressure, $\tau/p$, and normalized anisotropic component of the shear modulus, $\delta\mu/\mu$, as a function of $R$. As the packings are prepared isotropically, both $\tau/p$ and $\delta\mu/\mu$ vanish at large $R$. However, in local regions, where single force chains dominate, the response can be quite anisotropic. We show that $\tau/p$ exhibits two power-law regimes in $R$ with a cross-over that is only weakly dependent on $\phi$. In contrast, $\delta\mu/\mu$, behaves like a pure power law up to $R\sim640D$ (where $D$ is the characteristic particle diameter) at all $\phi$. [Preview Abstract] |
Tuesday, March 22, 2011 1:27PM - 1:39PM |
J13.00010: Thermodynamic stability of dense packings of hard, regular tetrahedra Amir Haji-Akbari, Michael Engel, Sharon C. Glotzer The question of how densely regular tetrahedra can pack in three dimensions has attracted many researchers in recent years. In the first thermodynamic study of dense phases of the hard tetrahedron system, we recently reported the spontaneous formation of a dodecagonal quasicrystal [1]. The (3.4.3$^2$.4) approximant of the quasicrystal, with an 82-particle unit cell, was compressed to a packing fraction of 85.03$\%$ [1]. Very shortly after, a much simpler crystal of tetrahedron dimers [2] with a slightly higher packing fraction of 85.63$\%$ was discovered [3], the current densest packing [3]. Since the dimer crystal packs more densely than the quasicrystal and its approximant, it is thermodynamically favored in the limit of infinite pressure. However, which structure is stable at finite pressures is an open question. Here, we explore the relative thermodynamic stability of these very different ordered phases as a function of packing density. \\[4pt] [1] Haji-Akbari A, Engel M, Keys A S, Zhang X Y, Petschek R, Palffy-Muhoray P, Glotzer S C, Nature 462: 773-777 (2009). \\[0pt] [2] Kallus Y, Elser V, Gravel S, Disc. Comp. Geom 44(2):245-252 (2010). \\[0pt] [3] Chen E R, Engel M, Glotzer S C, Disc. Comp. Geom. 44(2):253-280 (2010). [Preview Abstract] |
Tuesday, March 22, 2011 1:39PM - 1:51PM |
J13.00011: Jamming of frictional tetrahedra Max Neudecker, Stephan Ulrich, Stephan Herminghaus, Matthias Schr\"{o}ter We present experimental results on the packing of polypropylene tetrahedra with 7mm side length. Analysis via X-ray-tomography allows for a detailed analysis of the radial distribution function and the number and type of geometrical contacts. We focus particularly on the dependence of these packing properties on the bulk packing fraction. [Preview Abstract] |
Tuesday, March 22, 2011 1:51PM - 2:03PM |
J13.00012: Rheology of Minimally Jammed Frictionless Rodpiles James Graham, Scott Franklin The ability of large aspect ratio granular particles to form solid plugs is now well-documented but, apart from a general phenomenological explanation of geometric entanglement, remains unexplained. Recent experiments on the collapse of granular columns~[1] suggest that rods with even moderate aspect ratios can maintain angles of repose of 90$^{\circ}$ or larger, implying that the shear modulus increases continuously with aspect ratio. Our simulations generate minimally jammed packings of frictionless, aspect ratio 1-48 spherocylinders through an energy-minimization process. Once the minimally jammed state is reached, we continue the process to larger packing fractions in order to determine the bulk modulus. Packings are then subjected to infinitesimal strain in order to calculate the shear modulus as a function of particle aspect ratio. Shear simulations can be extended to large strain and used to investigate the long-time reordering of rod-like particles that accompanies macroscopic shear. \\[4pt] [1] M. Trepanier and S. V. Franklin, Phys. Rev. E {\bf 82}, 011308 (2010). [Preview Abstract] |
Tuesday, March 22, 2011 2:03PM - 2:15PM |
J13.00013: Couette Shear for Elliptical Particles Near Jamming Somayeh Farhadi We have performed 2D Couette shear experiments on systems of photoelastic particles. The particles are identical ellipses with aspect ratio 2. We use the photoelastic property of the disks to obtain the forces acting on a particle. We use two cameras to simultaneously image the particle motion and the photoelastic force response. Using ellipses enables us to understand the effect of particle shape asymmetry on the large-scale behavior on the rheological behavior of granular systems near jamming. Of particular interest are the nematic ordering of the ellipses, the formation of shear bands and the nature of force transmission. [Preview Abstract] |
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