Advertisement

Granular Matter

, Volume 14, Issue 6, pp 695–705 | Cite as

Vortex formation and dissolution in sheared sands

  • Sara Abedi
  • Amy L. RechenmacherEmail author
  • Andrés D. Orlando
Original Paper

Abstract

Using digital image correlation, we track the displacement fluctuations within a persistent shear band in a dense sand specimen bounded by glass walls undergoing plane strain compression. The data evidences a clear, systematic, temporally recurring pattern of vortex formation, dissolution, and reformation throughout macroscopic softening and critical state regimes. During softening, locally affine deformation zones are observed at various locations along the shear band, which we argue to be kinematic signatures of semi-stable force chains. Force chain collapse then occurs, inducing vortex formation. Local jamming at the conflux of opposing displacements between adjacent vortices arrests the vortices, providing an avenue for potential new force chains to form amidst these jammed regions. The process repeats itself temporally throughout the critical state. The pattern further correlates with fluctuations in macroscopic shear stress. We characterize the nature of the observed vortices, as they are different in our sands comprised of irregular shaped particles, as compared to previous observations from experiments and numerical simulations which involved circular or rounded particles. The results provide an interesting benchmark for behavior of non-circular/non-spherical particles undergoing shear.

Keywords

Sand Vortex Force chain Nonaffine deformation Meso-scale Shear band 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Drescher A., De-Josselin-de-Jong G.: Photoelastic verification of a mechanical model for the flow of a granular material. J. Mech. Phys. Solids. 20(5), 337–351 (1972)ADSCrossRefGoogle Scholar
  2. 2.
    Majmudar T.S., Behringer R.P.: Contact force measurements and stress-induced anisotropy in granular materials. Nature 435(7045), 1079–1082 (2005)ADSCrossRefGoogle Scholar
  3. 3.
    Tordesillas A., Muthuswamy M.: On the modeling of confined buckling of force chains. J. Mech. Phys. Solids. 57(4), 706–727 (2009)MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    Bardet J.P., Proubet J.: Numerical investigation of the structure of persistent shear bands in granular media. Geotechnique 41(4), 599–613 (1991)CrossRefGoogle Scholar
  5. 5.
    Veje C.T., Howell D.W., Behringer R.P.: Kinematics of a two-dimensional granular Couette experiment at the transition to shearing. Phys. Rev. E. 59(1), 739–745 (1999)ADSCrossRefGoogle Scholar
  6. 6.
    Oda M., Iwashita K.: Study on couple stress and shear band development in granular media based on numerical simulation analyses. Int. J. Eng. Sci. 38(15), 1713–1740 (2000)CrossRefGoogle Scholar
  7. 7.
    Rognon P., Einav I.: Thermal transients and convective particle motion in dense granular materials. Phys. Rev. Lett. 105(21), 218301 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    Alonso-Marroquín F., Vardoulakis I., Herrmann H.J.: Effect of rolling on dissipation in fault gouges. Phys. Rev. E. 74(3), 031306 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    Williams J.R., Rege N.: Coherent vortex structures in deforming granular materials. Mech. Coh. Fric. Mat. 2(3), 223–236 (1997)CrossRefGoogle Scholar
  10. 10.
    Williams J.R., Rege N.: The development of circulation cell structures in granular materials undergoing compression. Powder Technol. 90(3), 187–194 (1997)CrossRefGoogle Scholar
  11. 11.
    Kuhn M.R.: Structured deformation in granular materials. Mech. Mater. 31(6), 407–429 (1999)CrossRefGoogle Scholar
  12. 12.
    Radjai F., Roux S.: Turbulentlike fluctuations in quasistatic flow of granular media. Phys. Rev. Lett. 89(6), 064302 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    Thornton C., Zhang L.: A numerical examination of shear banding and simple shear non-coaxial flow rules. Philos. Mag. 86(21–22), 3425–3452 (2006)ADSCrossRefGoogle Scholar
  14. 14.
    Tordesillas A.: Force chain buckling, unjamming transitions and shear banding in dense granular assemblies. Philos. Mag. 87(32), 4987–5016 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    Tordesillas A., Muthuswamy M., Walsh S.D.C.: Mesoscale measures of nonaffine deformation in dense granular assemblies. J. Eng. Mech. 134(12), 1095–1113 (2008)CrossRefGoogle Scholar
  16. 16.
    Utter B., Behringer R.P.: Self-diffusion in dense granular shear. Flows. Phys. Rev. E. 69(3), 031308-1–031308-12 (2004)ADSGoogle Scholar
  17. 17.
    Rechenmacher A.L.: Grain-scale processes governing shear band initiation and evolution in sands. J. Mech. Phys. Solids. 54(1), 22–45 (2006)ADSzbMATHCrossRefGoogle Scholar
  18. 18.
    Rechenmacher A.L., Abedi S., Chupin O.: Evolution of force chains in shear bands in sands. Geotechnique 60(5), 343 (2010)CrossRefGoogle Scholar
  19. 19.
    Gudehus G., Nubel K.: Evolution of shear bands in sand. Geotechnique 54(3), 187–201 (2004)CrossRefGoogle Scholar
  20. 20.
    Borja R.I., Andrade J.E.: Critical state plasticity. Part VI: meso-scale finite element simulation of strain localization in discrete granular materials. Comput. Methods Appl. Mech. Eng. 195(37–40), 5115–5140 (2006)ADSzbMATHCrossRefGoogle Scholar
  21. 21.
    Desrues J., Viggiani G.: Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int. J. Numer. Anal. Methods Geomech. 28(4), 279–321 (2004)CrossRefGoogle Scholar
  22. 22.
    Head K.H.: Manual of Soil Laboratory Testing. Volume 3: Effective Stress Tests. Wiley, West Sussex (1998)Google Scholar
  23. 23.
    Finno R.J., Rechenmacher A.L.: Effects of consolidation history on critical state of sand. J. Geotech. Geoenv. Eng. 129(4), 350–360 (2003)CrossRefGoogle Scholar
  24. 24.
    Sutton M.D., McNeill S.R., Helm J.D., Chao Y.J.: Advances in two-dimensional and three-dimensional computer vision. In: Rastogi, P.K. (ed.) Photomechanics topics in applied physics, pp. 323–372. Springer, Berlin (2000)Google Scholar
  25. 25.
    Sutton M.A., Orteu J.-J., Schreier H.W.: Image Correlation for Shape, Motion and Deformation Measurements. Springer, New York (2009)Google Scholar
  26. 26.
    Rechenmacher A.L., Abedi S., Chupin O.: Characterization of mesoscale instabilities in localized granular shear using digital image correlation. Acta Geotech. 6(4), 205–217 (2011)CrossRefGoogle Scholar
  27. 27.
    Chupin, O., Rechenmacher, A.L., Abedi, S.: Finite strain analysis of nonuniform deformation inside shear bands in sands. Int. J. Numer. Anal. Methods Geomech. (2011). doi: 10.1002/nag.1071
  28. 28.
    Hu N., Molinari J.F.: Shear bands in dense metallic granular materials. J. Mech. Phys. Solids. 52(3), 499–531 (2004)ADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Sara Abedi
    • 1
  • Amy L. Rechenmacher
    • 2
    Email author
  • Andrés D. Orlando
    • 2
  1. 1.Department of Civil and Environmental EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of Civil and Environmental EngineeringUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations