Hypostatic jammed packings of frictionless nonspherical particles

Kyle VanderWerf, Weiwei Jin, Mark D. Shattuck, and Corey S. O'Hern
Phys. Rev. E 97, 012909 – Published 19 January 2018

Abstract

We perform computational studies of static packings of a variety of nonspherical particles including circulo-lines, circulo-polygons, ellipses, asymmetric dimers, dumbbells, and others to determine which shapes form packings with fewer contacts than degrees of freedom (hypostatic packings) and which have equal numbers of contacts and degrees of freedom (isostatic packings), and to understand why hypostatic packings of nonspherical particles can be mechanically stable despite having fewer contacts than that predicted from naive constraint counting. To generate highly accurate force- and torque-balanced packings of circulo-lines and cir-polygons, we developed an interparticle potential that gives continuous forces and torques as a function of the particle coordinates. We show that the packing fraction and coordination number at jamming onset obey a masterlike form for all of the nonspherical particle packings we studied when plotted versus the particle asphericity A, which is proportional to the ratio of the squared perimeter to the area of the particle. Further, the eigenvalue spectra of the dynamical matrix for packings of different particle shapes collapse when plotted at the same A. For hypostatic packings of nonspherical particles, we verify that the number of “quartic” modes along which the potential energy increases as the fourth power of the perturbation amplitude matches the number of missing contacts relative to the isostatic value. We show that the fourth derivatives of the total potential energy in the directions of the quartic modes remain nonzero as the pressure of the packings is decreased to zero. In addition, we calculate the principal curvatures of the inequality constraints for each contact in circulo-line packings and identify specific types of contacts with inequality constraints that possess convex curvature. These contacts can constrain multiple degrees of freedom and allow hypostatic packings of nonspherical particles to be mechanically stable.

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  • Received 25 November 2017

DOI:https://doi.org/10.1103/PhysRevE.97.012909

©2018 American Physical Society

Physics Subject Headings (PhySH)

Polymers & Soft MatterStatistical Physics & Thermodynamics

Authors & Affiliations

Kyle VanderWerf1, Weiwei Jin2,3, Mark D. Shattuck4, and Corey S. O'Hern1,3,5,6

  • 1Department of Physics, Yale University, New Haven, Connecticut 06520, USA
  • 2Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China
  • 3Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA
  • 4Benjamin Levich Institute and Physics Department, The City College of New York, New York, New York 10031, USA
  • 5Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
  • 6Graduate Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut 06520, USA

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Issue

Vol. 97, Iss. 1 — January 2018

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