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Title: Instabilities of Jammed Packings of Frictionless Spheres Under Load

Authors:
; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1409469
Grant/Contract Number:
FG02-05ER46199; FG02-03ER46088; 2030020028
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 119; Journal Issue: 21; Related Information: CHORUS Timestamp: 2017-11-20 10:04:40; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English

Citation Formats

Xu, Ning, Liu, Andrea J., and Nagel, Sidney R. Instabilities of Jammed Packings of Frictionless Spheres Under Load. United States: N. p., 2017. Web. doi:10.1103/PhysRevLett.119.215502.
Xu, Ning, Liu, Andrea J., & Nagel, Sidney R. Instabilities of Jammed Packings of Frictionless Spheres Under Load. United States. doi:10.1103/PhysRevLett.119.215502.
Xu, Ning, Liu, Andrea J., and Nagel, Sidney R. 2017. "Instabilities of Jammed Packings of Frictionless Spheres Under Load". United States. doi:10.1103/PhysRevLett.119.215502.
@article{osti_1409469,
title = {Instabilities of Jammed Packings of Frictionless Spheres Under Load},
author = {Xu, Ning and Liu, Andrea J. and Nagel, Sidney R.},
abstractNote = {},
doi = {10.1103/PhysRevLett.119.215502},
journal = {Physical Review Letters},
number = 21,
volume = 119,
place = {United States},
year = 2017,
month =
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on November 20, 2018
Publisher's Accepted Manuscript

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  • We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness.more » Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature.« less
  • We derive the first nontrivial rigorous bounds on the mean distance between nearest neighbors [lambda] in ergodic, isotropic packings of hard [ital D]-dimensional spheres that depend on the packing fraction and nearest-neighbor distribution function. Several interesting implications of these bounds for equilibrium as well as nonequilibrium ensembles are explored. For an equilibrium ensemble, we find accurate analytical approximations for [lambda] for [ital D]=2 and 3 that apply up to random close packing. Our theoretical results are in excellent agreement with available computer-simulation data.
  • The probability of finding a nearest neighbor at some radial distance from a given particle in a system of interacting particles is of fundamental importance in a host of fields in the physical as well as biological sciences. A procedure is developed to obtain analytical expressions for nearest-neighbor probability functions for random isotropic packings of hard {ital D}-dimensional spheres that are accurate for all densities, i.e., up to the random close-packing fraction. Using these results, the mean nearest-neighbor distance {lambda} as a function of the packing fraction is computed for such many-body systems and compared to rigorous bounds on {lambda}more » derived here. Our theoretical results are found to be in excellent agreement with available computer-simulation data.« less
  • The effective sintering rates and viscosities of three-dimensional composite packings have been studied using a discrete numerical model. The packings consist of random mixtures of hard and soft spheres of the same size. With increasing substitution of hard particles for soft particles in the packing, the viscosity increases and the sintering rate decreases. This is particularly abrupt at well-defined rigidity thresholds where there is a transition from softlike to hardlike behavior. The site fraction of hard particles at which the transition occurs depends on the nature of the interaction between hard particles. When the contact between hard particles resists allmore » six relative degrees of freedom (relative velocities and spins). the bonded case, the rigidity threshold coincides with the percolation threshold (site fraction {approx}0.32). When the contact between hard particles resists only interpenetration. the sliding case, the threshold occurs at a site fraction of hard particles very close to unity. Results for the variation of effective properties with site fraction of hard particles are presented for these and other cases. These results can also be applied to the study of elastic percolating networks.« less