Advertisement

Discovering Community Structures and Dynamical Networks from Grain-Scale Kinematics of Shear Bands in Sand

  • Antoinette TordesillasEmail author
  • David M. Walker
  • Amy L. Rechenmacher
  • Sara Abedi
Conference paper
Part of the Springer Series in Geomechanics and Geoengineering book series (SSGG, volume 11)

Abstract

The quest to understand the connections between the triumvirate of structure, dynamics and function continues to drive the forefront of research in Complex Systems. Crucial to these explorations is the development of graph-theoretic techniques that: (i) can detect communities and associated boundaries in the underlying network or graph, which represents the interactions of constituent units, and (ii) quantify shortest paths and related network measures within this graph. We report on a new study using data from high resolution digital image correlation (DIC) measurements of grain-scale kinematics in sand under shear. Preliminary results show that the nodes of the network in the shear band region exhibit high closeness centrality – a network measure of how efficient a given node is in spreading information to all the other nodes in the graph. It is thus reasonable to expect that the most efficient routes for spread of kinematical information within this network are those from nodes that correspond to the grid points that lie along the shear band. We believe these studies will ultimately lead to an improved understanding of self-organization, the nature of energy flow and dynamics in the critical state regime in the presence of persistent shear bands.

Keywords

Digital image correlation Localization band Grain-scale kinematics Networks Closeness centrality 

Notes

Acknowledgements

AT and DMW are funded by: US Army Research Office (W911NF-07-1-0370), Australian Research Council (DP0986876), VPAC. AR and SA are funded by the National Science Foundation, Grant CMMI-0748284.

References

  1. A. Clauset, Phys. Rev. E 72, 026132 (2005)CrossRefGoogle Scholar
  2. L. da F. Costa, F.A. Rodrigues, G. Travieso, P.R.V. Boas, Adv. Phys. 56, 167 (2007)Google Scholar
  3. M.E.J. Newman, SIAM Rev. 45, 167 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  4. M.E.J. Newman, Phys. Rev. E 74, 036104 (2006)MathSciNetCrossRefGoogle Scholar
  5. M. Oda, H. Kazama, Geotechnique 48, 465 (1998)CrossRefGoogle Scholar
  6. A.L. Rechenmacher, J. Mech. Phys. Solids 54, 22 (2006)zbMATHCrossRefGoogle Scholar
  7. A. Rechenmacher, Geotechnique 60(5), 343–351 (2010)CrossRefGoogle Scholar
  8. A. Tordesillas, Philos. Mag. 87, 4987 (2007)CrossRefGoogle Scholar
  9. A. Tordesillas, M. Muthuswamy, S.D.C. Walsh, ASCE J. Eng. Mech. 134, 1095 (2008)CrossRefGoogle Scholar
  10. A. Tordesillas, J. Zhang, R.P. Behringer, Geomech. Geoeng. 4, 3 (2009)CrossRefGoogle Scholar
  11. A. Tordesillas, S.D.C. Walsh, M. Muthuswamy, Math. Mech. Solids 15, 3 (2010a)zbMATHCrossRefGoogle Scholar
  12. A. Tordesillas, P. O’Sullivan, D.M. Walker, Paramitha, C. R. Mecanique 338, 556–569 (2010b)Google Scholar
  13. A. Tordesillas, D.M. Walker, Q. Lin, Phys. Rev. E 81, 011302 (2010c)CrossRefGoogle Scholar
  14. A. Tordesillas, Q. Lin, J. Zhang, R.P. Behringer, J. Shi, J. Mech. Phys. Solids 59(2), 265–296 (2011)CrossRefGoogle Scholar
  15. D.M. Walker, A. Tordesillas, Int. J. Solids Struct. 47, 624 (2010)zbMATHCrossRefGoogle Scholar
  16. X. Xu, J. Zhang, M. Small, Proc. Natl. Acad. Sci. U.S.A. 105, 19601 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  17. J. Zhang, T.S. Majmudar, A. Tordesillas, R.P. Behringer, Granul. Matter 12, 159 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Antoinette Tordesillas
    • 1
    Email author
  • David M. Walker
    • 1
  • Amy L. Rechenmacher
    • 2
  • Sara Abedi
    • 2
  1. 1.Department of Mathematics & StatisticsUniversity of MelbourneParkvilleAustralia
  2. 2.Department of Civil & Environmental EngineeringUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations