Advertisement

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

Abstract

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.

Keywords

Granular matter Jamming transition Pentagon-shaped particle Packing structure 

Notes

Acknowledgements

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.

References

  1. 1.
    O’Hern, C.S., Silbert, L.E., Liu, A.J., Nagel, S.R.: Jamming at zero temperature and zero applied stress: the epitome of disorder. Phys. Rev. E 68, 011306 (2003)CrossRefADSGoogle Scholar
  2. 2.
    Liu, A.J., Nagel, S.R.: The jamming transition and the marginally jammed solid. Ann. Rev. Condens. Matter Phys. 1(1), 347–369 (2010)ADSGoogle Scholar
  3. 3.
    Silbert, L.E.: Jamming of frictional spheres and random loose packing. Soft Matter 6(13), 2918–2924 (2010)ADSGoogle Scholar
  4. 4.
    Bi, D., Henkes, S., Daniels, K.E., Chakraborty, B.: The statistical physics of athermal materials. Ann. Rev. Condens. Matter Phys. 6(1), 63–83 (2015)ADSGoogle Scholar
  5. 5.
    Bi, D., Zhang, J., Chakraborty, B., Behringer, R.P.: Jamming by shear. Nature 480(7377), 355 (2011)CrossRefADSGoogle Scholar
  6. 6.
    Torquato, S., Stillinger, F.H.: Jammed hard-particle packings: from Kepler to Bernal and beyond. Rev. Mod. Phys. 82(3), 2633 (2010)ADSGoogle Scholar
  7. 7.
    Parisi, G., Zamponi, F.: Mean-field theory of hard sphere glasses and jamming. Rev. Mod. Phys. 82(1), 789 (2010)ADSGoogle Scholar
  8. 8.
    Silbert, L.E., Ertaş, D., Grest, G.S., Halsey, T.C., Levine, D.: Analogies between granular jamming and the liquid-glass transition. Phys. Rev. E 65(5), 051307 (2002)ADSGoogle Scholar
  9. 9.
    Han, E., Peters, I.R., Jaeger, H.M.: High-speed ultrasound imaging in dense suspensions reveals impact-activated solidification due to dynamic shear jamming. Nat. Commun. 7, 12243 (2016)ADSGoogle Scholar
  10. 10.
    Peters, I.R., Majumdar, S., Jaeger, H.M.: Direct observation of dynamic shear jamming in dense suspensions. Nature 532(7598), 214 (2016)CrossRefADSGoogle Scholar
  11. 11.
    Sarkar, S., Chakraborty, B.: Shear-induced rigidity in athermal materials: a unified statistical framework. Phys. Rev. E 91(4), 042201 (2015)ADSGoogle Scholar
  12. 12.
    Donev, A., Cisse, I., Sachs, D., Variano, E.A., Stillinger, F.H., Connelly, R., Torquato, S., Chaikin, P.M.: Improving the density of jammed disordered packings using ellipsoids. Science 303(5660), 990–993 (2004)ADSGoogle Scholar
  13. 13.
    Donev, A., Connelly, R., Stillinger, F.H., Torquato, S.: Underconstrained jammed packings of nonspherical hard particles: ellipses and ellipsoids. Phys. Rev. E 75(5), 051304 (2007)MathSciNetADSGoogle Scholar
  14. 14.
    Azéma, E., Radjai, F., Peyroux, R., Saussine, G.: Force transmission in a packing of pentagonal particles. Phys. Rev. E 76(1), 011301 (2007)ADSGoogle Scholar
  15. 15.
    Athanassiadis, A.G., Miskin, M.Z., Kaplan, P., Rodenberg, N., Lee, S.H., Merritt, J., Brown, E., Amend, J., Lipson, H., J., Heinrich, M.: Particle shape effects on the stress response of granular packings. Soft Matter 10(1), 48–59 (2014)ADSGoogle Scholar
  16. 16.
    Zhao, Y., Liu, K., Zheng, M., Barés, J., Dierichs, K., Menges, A., Behringer, R.P.: Packings of 3d stars: stability and structure. Granul. Matter 18(2), 24 (2016)Google Scholar
  17. 17.
    VanderWerf, K., Jin, W., Shattuck, M.D., O’Hern, C.S.: Hypostatic jammed packings of frictionless nonspherical particles. Phys. Rev. E 97(1), 012909 (2018)ADSGoogle Scholar
  18. 18.
    Smith, K.C., Fisher, T.S., Alam, M.: Isostaticity of constraints in amorphous jammed systems of soft frictionless platonic solids. Phys. Rev. E 84(3), 030301 (2011)ADSGoogle Scholar
  19. 19.
    Zhang, L., Feng, G., Zeravcic, Z., Brugarolas, T., Liu, A.J., Lee, D.: Using shape anisotropy to toughen disordered nanoparticle assemblies. ACS nano 7(9), 8043–8050 (2013)Google Scholar
  20. 20.
    Schaller, F.M., Neudecker, M., Saadatfar, M., Delaney, G.W., Schröder-Turk, G.E., Schröter, M.: Local origin of global contact numbers in frictional ellipsoid packings. Phys. Rev. Lett. 114(15), 158001 (2015)ADSGoogle Scholar
  21. 21.
    Saint-Cyr, B., Szarf, K., Voivret, C., Azéma, E., Richefeu, V., Delenne, J.-Y., Combe, G., Nouguier-Lehon, C., Villard, P., Sornay, P., et al.: Particle shape dependence in 2d granular media. EPL (Europhys. Lett.) 98(4), 44008 (2012)ADSGoogle Scholar
  22. 22.
    Torquato, S., Jiao, Y.: Exact constructions of a family of dense periodic packings of tetrahedra. Phys. Rev. E 81(4), 041310 (2010)MathSciNetADSGoogle Scholar
  23. 23.
    Azéma, E., Radjai, F.: Force chains and contact network topology in sheared packings of elongated particles. Phys. Rev. E 85(3), 031303 (2012)ADSGoogle Scholar
  24. 24.
    Jaeger, H.M.: Celebrating soft matter’s 10th anniversary: toward jamming by design. Soft Matter 11(1), 12–27 (2015)ADSGoogle Scholar
  25. 25.
    Börzsönyi, T., Stannarius, R.: Granular materials composed of shape-anisotropic grains. Soft Matter 9(31), 7401–7418 (2013)ADSGoogle Scholar
  26. 26.
    Mailman, M., Schreck, C.F., O’ Hern, C.S., Chakraborty, B.: Jamming in systems composed of frictionless ellipse-shaped particles. Phys. Rev. Lett. 102(25), 255501 (2009)ADSGoogle Scholar
  27. 27.
    Azéma, E., Radjaï, F.: Stress–strain behavior and geometrical properties of packings of elongated particles. Phys. Rev. E 81(5), 051304 (2010)ADSGoogle Scholar
  28. 28.
    Jiao, Y., Stillinger, F.H., Torquato, S.: Optimal packings of superballs. Phys. Rev. E 79(4), 041309 (2009)MathSciNetADSGoogle Scholar
  29. 29.
    Torquato, S., Jiao, Y.: Dense packings of the platonic and archimedean solids. Nature 460(7257), 876 (2009)ADSGoogle Scholar
  30. 30.
    Han, Y., Lee, J., Choi, S.Q., Choi, M.C., Kim, M.W.: Shape-controlled percolation transition in 2d random packing of asymmetric dimers. EPL (Europhys. Lett.) 109(6), 66002 (2015)ADSGoogle Scholar
  31. 31.
    Tang, J., Behringer, R .P.: Orientation, flow, and clogging in a two-dimensional hopper: ellipses vs. disks. Europhys. Lett. 114(3), 34002 (2016)ADSGoogle Scholar
  32. 32.
    Zheng, H., Wang, D., Barés, J., Behringer, R.P.: Jamming by compressing a system of granular crosses. In: EPJ Web of Conferences, vol. 140, p. 06014. EDP Sciences (2017)Google Scholar
  33. 33.
    Xu, Y., Barés, J., Zhao, Y., Behringer, R.P.: Jamming transition: heptagons, pentagons, and discs. In: EPJ Web of Conferences, vol. 140, p. 06010. EDP Sciences (2017)Google Scholar
  34. 34.
    Estrada, N., Azéma, E., Radjai, F., Taboada, A.: Identification of rolling resistance as a shape parameter in sheared granular media. Phys. Rev. E 84(1), 011306 (2011)ADSGoogle Scholar
  35. 35.
    Schilling, T., Pronk, S., Mulder, B., Frenkel, D.: Monte carlo study of hard pentagons. Phys. Rev. E 71(3), 036138 (2005)ADSGoogle Scholar
  36. 36.
    Duparcmeur, Y.L., Gervois, A., Troadec, J.P.: Crystallization of pentagon packings. J. Phys. Condens. Matter 7(18), 3421 (1995)ADSGoogle Scholar
  37. 37.
    Daniels, K.E., Kollmer, J.E., Puckett, J.G.: Photoelastic force measurements in granular materials. Rev. Sci. Instrum. 88(5), 051808 (2017)ADSGoogle Scholar
  38. 38.
    Majmudar, T.S., Sperl, M., Luding, S., Behringer, R.P.: Jamming transition in granular systems. Phys. Rev. Lett. 98(5), 058001 (2007)ADSGoogle Scholar
  39. 39.
    Zadeh, A.A., Barés, J., Brzinski, T., Daniels, K.E., Dijksman, J., Docqiuer, N., Everitt, H., Kollmer, J., Lantsoght, O., Wang, D., Workamp, M., Zhao, Y., Zheng, H.: Photoelastic methods wiki (2019). https://git-xen.lmgc.univ-montp2.fr/PhotoElasticity/Main/wikis/home. Accessed 28 Feb 2019
  40. 40.
    Cox, M., Wang, D., Barés, J., Behringer, R.P.: Self-organized magnetic particles to tune the mechanical behavior of a granular system. EPL (Europhys. Lett.) 115(6), 64003 (2016)ADSGoogle Scholar
  41. 41.
    Barés, J., Mora, S., Delenne, J.-Y., Fourcaud, T.: Experimental observations of root growth in a controlled photoelastic granular material. In: EPJ Web of Conferences, vol. 140, p. 14008. EDP Sciences (2017)Google Scholar
  42. 42.
    Geng, J., Howell, D., Longhi, E., Behringer, R.P., Reydellet, G., Vanel, L., Clément, E., Luding, S.: Footprints in sand: the response of a granular material to local perturbations. Phys. Rev. Lett. 87(3), 035506 (2001)ADSGoogle Scholar
  43. 43.
    Zhao, Y., Zheng, H., Wang, D., Wang, M., Behringer, R.P.: Particle scale force sensor based on intensity gradient method in granular photoelastic experiments. New J. Phys. 21(2), 023009 (2019)ADSGoogle Scholar
  44. 44.
    Bandi, M.M., Rivera, M.K., Krzakala, Florent, Ecke, R.E.: Fragility and hysteretic creep in frictional granular jamming. Phys. Rev. E 87(4), 042205 (2013)ADSGoogle Scholar
  45. 45.
    Wang, C., Dong, K., Aibing, Y.: Structural characterization of the packings of granular regular polygons. Phys. Rev. E 92(6), 062203 (2015)ADSGoogle Scholar
  46. 46.
    van Hecke, M.: Jamming of soft particles: geometry, mechanics, scaling and isostaticity. J. Phys. Condens. Matter 22(3), 033101 (2009)Google Scholar
  47. 47.
    Henkes, S., van Hecke, M., van Saarloos, W.: Critical jamming of frictional grains in the generalized isostaticity picture. EPL (Europhys. Lett.) 90(1), 14003 (2010)ADSGoogle Scholar
  48. 48.
    Roux, J.-N.: Geometric origin of mechanical properties of granular materials. Phys. Rev. E 61(6), 6802 (2000)MathSciNetADSGoogle Scholar
  49. 49.
    Azéma, E., Radjai, F., Dubois, F.: Packings of irregular polyhedral particles: strength, structure, and effects of angularity. Phys. Rev. E 87(6), 062203 (2013)ADSGoogle Scholar
  50. 50.
    Marschall, T., Teitel, S.: Compression-driven jamming of athermal frictionless spherocylinders in two dimensions. Phys. Rev. E 97(1), 012905 (2018)ADSGoogle Scholar
  51. 51.
    Nguyen, D.-H., Azéma, É., Radjai, F., Sornay, P.: Effect of size polydispersity versus particle shape in dense granular media. Phys. Rev. E 90(1), 012202 (2014)ADSGoogle Scholar
  52. 52.
    Cheng, X.: Packing structure of a two-dimensional granular system through the jamming transition. Soft Matter 6(13), 2931–2934 (2010)ADSGoogle Scholar
  53. 53.
    Aste, T., Di Matteo, T., Saadatfar, M., Senden, T.J., Schröter, M., Swinney, H.L.: An invariant distribution in static granular media. EPL (Europhys. Lett.) 79(2), 24003 (2007)ADSGoogle Scholar
  54. 54.
    Aste, T., Di Matteo, T.: Emergence of gamma distributions in granular materials and packing models. Phys. Rev. E 77(2), 021309 (2008)ADSGoogle Scholar

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

Personalised recommendations