Granular Matter

, 21:90 | Cite as

Jamming transition in non-spherical particle systems: pentagons versus disks

  • Yiqiu ZhaoEmail author
  • Jonathan Barés
  • Hu Zheng
  • Cacey Stevens Bester
  • Yuanyuan Xu
  • Joshua E. S. Socolar
  • Robert P. Behringer
Original Paper
Part of the following topical collections:
  1. In Memoriam of Robert P. Behringer, late Editor in Chief of Granular Matter


We investigate the jamming transition in a quasi-2D granular material composed of regular pentagons or disks subjected to quasistatic uniaxial compression. We report six major findings based on experiments with monodisperse photoelastic particles with static friction coefficient \(\mu \approx 1\). (1) For both pentagons and disks, the onset of rigidity occurs when the average coordination number of non-rattlers, \(Z_{nr}\), reaches 3, and the dependence of \(Z_{nr}\) on the packing fraction \(\phi\) changes again when \(Z_{nr}\) reaches 4. (2) Though the packing fractions \(\phi _{c1}\) and \(\phi _{c2}\) at these transitions differ from run to run, for both shapes the data from all runs with different initial configurations collapses when plotted as a function of the non-rattler fraction. (3) The averaged values of \(\phi _{c1}\) and \(\phi _{c2}\) for pentagons are around \(1\%\) smaller than those for disks. (4) Both jammed pentagons and disks show Gamma distribution of the Voronoi cell area with same parameters. (5) The jammed pentagons have similar translational order for particle centers but slightly less orientational order for contacting pairs compared to jammed disks. (6) For jammed pentagons, the angle between edges at a face-to-vertex contact point shows a uniform distribution and the size of a cluster connected by face-to-face contacts shows a power-law distribution.


Granular matter Jamming transition Pentagon-shaped particle Packing structure 



This work is dedicated to Bob Behringer, whom we are deeply indebted to and will forever miss. Though the paper was written after his passing, his role in supporting and mentoring this research justifies including him as a coauthor. Discussions with Yuchen Zhao, Émilien Azéma, Dong Wang, Ryan Kozlowski and Aghil Abed Zadeh are highly appreciated. This work was funded by NSFC Grant No. 4167 2256 (HZ), NSF Grant Nos. DMR1206351 and DMR1809762, ARO No. W911NF-18-1-0184, NASA Grant No. NNX15AD38G, DARPA Grant No. 4-34728, the William M. Keck Foundation, and a Duke University Provost’s Postdoctoral fellowship (CSB).

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Physics and Center for Non-linear and Complex SystemsDuke UniversityDurhamUSA
  2. 2.Laboratoire de Mécanique et Génie CivilUniversité de Montpellier, CNRSMontpellierFrance
  3. 3.Department of Geotechnical Engineering, College of Civil EngineeringTongji UniversityShanghaiChina
  4. 4.Department of Physics and AstronomySwarthmore CollegeSwarthmoreUSA
  5. 5.Department of Physics and AstronomyJohns Hopkins UniversityBaltimoreUSA

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