Granular Matter

, 18:24 | Cite as

Packings of 3D stars: stability and structure

  • Yuchen Zhao
  • Kevin Liu
  • Matthew Zheng
  • Jonathan Barés
  • Karola Dierichs
  • Achim Menges
  • Robert P. Behringer
Original Paper
Part of the following topical collections:
  1. Jamming-Based Aleatory Architectures

Abstract

We describe a series of experiments involving the creation of cylindrical packings of star-shaped particles, and an exploration of the stability of these packings. The stars cover a broad range of arm sizes and frictional properties. We carried out three different kinds of experiments, all of which involve columns that are prepared by raining star particles one-by-one into hollow cylinders. As an additional part of the protocol, we sometimes vibrated the column before removing the confining cylinder. We rate stability in terms of r, the ratio of the mass of particles that fall off a pile when it collapsed, to the total particle mass. The first experiment involved the intrinsic stability of the column when the confining cylinder was removed. The second kind of experiment involved adding a uniform load to the top of the column, and then determining the collapse properties. A third experiment involved testing stability to tipping of the piles. We find a stability diagram relating the pile height, h, versus pile diameter, \(\delta \), where the stable and unstable regimes are separated by a boundary that is roughly a power-law in h versus \(\delta \) with an exponent that is less than unity. Increasing vibration and friction, particularly the latter, both tend to stabilize piles, while increasing particle size can destabilize the system under certain conditions.

Keywords

Granular Cylindrical packing Star-shaped particle Stability Friction Vibration Aggregate 

Notes

Acknowledgments

We thank Dong Wang and Hu Zheng for fruitful discussions and Stephen Teitel and Scott Franklin for a critical review of this manuscript. Y.Z., J.B. and R.P.B. are funded by National Science Foundation (NSF grant DMR-1206351) and W. M. Keck Foundation. K.D. has benefitted from support of ITASCA Educational Partnership Program.

References

  1. 1.
    Miskin, M.Z., Jaeger, H.M.: Evolving design rules for the inverse granular packing problem. Soft Matter 10(21), 3708–3715 (2014)ADSCrossRefGoogle Scholar
  2. 2.
    Athanassiadis, A.G., Miskin, M.Z., Kaplan, P., Rodenberg, N., Lee, S.H., Merritt, J., Brown, E., Amend, J., Lipson, H., Jaeger, H.M.: Particle shape effects on the stress response of granular packings. Soft Matter 10(1), 48–59 (2014)ADSCrossRefGoogle Scholar
  3. 3.
    Smith, K.C., Alam, M., Fisher, T.S.: Athermal jamming of soft frictionless platonic solids. Phys. Rev. E 82, 051304 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    Franklin, S.V.: Extensional rheology of entangled granular materials. Europhys. Lett. 106(5), 58004 (2014)ADSCrossRefGoogle Scholar
  5. 5.
    Miskin, M.Z., Jaeger, H.M.: Adapting granular materials through artificial evolution. Nat. Mater. 12(4), 326–331 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    Saint-Cyr, B., Delenne, J.-Y., Voivret, C., Radjai, F., Sornay, P.: Rheology of granular materials composed of nonconvex particles. Phys. Rev. E 84, 041302 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    Brown, E., Nasto, A., Athanassiadis, A.G., Jaeger, H.M.: Strain stiffening in random packings of entangled granular chains. Phys. Rev. Lett. 108, 108302 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    Dierichs, K., Menges, A.: Granular morphologies: programming material behaviour with designed aggregates. Arch. Des. 85(5), 86–91 (2015)Google Scholar
  9. 9.
    Gravish, N., Franklin, S.V., Hu, D.L., Goldman, D.I.: Entangled granular media. Phys. Rev. Lett. 108, 208001 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    Franklin, S.V.: Geometric cohesion in granular materials. Phys. Today 65(9), 70 (2012)CrossRefGoogle Scholar
  11. 11.
    Miszta, K., de Graaf, J., Bertoni, G., Dorfs, D., Brescia, R., Marras, S., Ceseracciu, L., Cingolani, R., van Roij, R., Dijkstra, M.: Hierarchical self-assembly of suspended branched colloidal nanocrystals into superlattice structures. Nat. Mater. 10(11), 872–876 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    de Graaf, J., van Roij, R., Dijkstra, M.: Dense regular packings of irregular nonconvex particles. Phys. Rev. Lett. 107, 155501 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    Jiao, Y., Stillinger, F.H., Torquato, S.: Optimal packings of superballs. Phys. Rev. E 79, 041309 (2009)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Lajeunesse, E., Mangeney-Castelnau, A., Vilotte, J.-P.: Spreading of a granular mass on a horizontal plane. Phys. Fluids 16(7), 2371–2381 (2004)ADSCrossRefMATHGoogle Scholar
  15. 15.
    Lube, G., Huppert, H.E., Sparks, R.S.J., Freundt, A.: Collapses of two-dimensional granular columns. Phys. Rev. E 72, 041301 (2005)Google Scholar
  16. 16.
    Trepanier, M., Franklin, S.V.: Column collapse of granular rods. Phys. Rev. E 82, 011308 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    Desmond, K., Franklin, S.V.: Jamming of three-dimensional prolate granular materials. Phys. Rev. E 73, 031306 (2006)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Yuchen Zhao
    • 1
  • Kevin Liu
    • 2
  • Matthew Zheng
    • 3
  • Jonathan Barés
    • 1
  • Karola Dierichs
    • 4
  • Achim Menges
    • 4
  • Robert P. Behringer
    • 1
  1. 1.Department of Physics and Center for Nonlinear and Complex SystemsDuke UniversityDurhamUSA
  2. 2.Julia R. Masterman Laboratory and Demonstration SchoolPhiladelphiaUSA
  3. 3.North Carolina School of Science and MathematicsDurhamUSA
  4. 4.Institute for Computational DesignUniversity of StuttgartStuttgartGermany

Personalised recommendations