Kinematic flow patterns in slow deformation of a dense granular material

Abstract

The kinematic flow pattern in slow deformation of a model dense granular medium is studied at high resolution using in situ imaging, coupled with particle tracking. The deformation configuration is indentation by a flat punch under macroscopic plane-strain conditions. Using a general analysis method, velocity gradients and deformation fields are obtained from the disordered grain arrangement, enabling flow characteristics to be quantified. The key observations are the formation of a stagnation zone, as in dilute granular flow past obstacles; occurrence of vortices in the flow immediately underneath the punch; and formation of distinct shear bands adjoining the stagnation zone. The transient and steady state stagnation zone geometry, as well as the strength of the vortices and strain rates in the shear bands, are obtained from the experimental data. All of these results are well-reproduced in exact-scale non-smooth contact dynamics simulations. Full 3D numerical particle positions from the simulations allow extraction of flow features that are extremely difficult to obtain from experiments. Three examples of these, namely material free surface evolution, deformation of a grain column below the punch and resolution of velocities inside the primary shear band, are highlighted. The variety of flow features observed in this model problem also illustrates the difficulty involved in formulating a complete micromechanical analytical description of the deformation.

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References

  1. 1.

    Sarkar, S., Bi, D., Zhang, J., Behringer, R.P., Chakraborty, B.: Origin of rigidity in dry granular solids. Phys. Rev. Lett. 111(6), 068301 (2013)

    Article  ADS  Google Scholar 

  2. 2.

    Brilliantov, N.V., Pöschel, T.: Kinetic Theory of Granular Gases. Oxford University Press, Oxford (2010)

    Google Scholar 

  3. 3.

    Aranson, I.S., Tsimring, L.S.: Patterns and collective behavior in granular media: theoretical concepts. Rev. Mod. Phys. 78(2), 641 (2006)

    Article  ADS  Google Scholar 

  4. 4.

    Zhang, J., Majmudar, T.S., Tordesillas, A., Behringer, R.P.: Statistical properties of a 2D granular material subjected to cyclic shear. Granul. Matter 12(2), 159–172 (2010)

    Article  Google Scholar 

  5. 5.

    Nedderman, R.M.: Statics and Kinematics of Granular Materials. Cambridge University Press, Cambridge (2005)

    Google Scholar 

  6. 6.

    Rycroft, C.H., Kamrin, K., Bazant, M.Z.: Assessing continuum postulates in simulations of granular flow. J. Mech. Phys. Solids 57(5), 828–839 (2009)

    Article  ADS  Google Scholar 

  7. 7.

    Argon, A.S.: Plastic deformation in metallic glasses. Acta Metall. 27(1), 47–58 (1979)

    Article  Google Scholar 

  8. 8.

    Falk, M.L., Langer, J.S.: Dynamics of viscoplastic deformation in amorphous solids. Phys. Rev. E 57(6), 7192 (1998)

    Article  ADS  Google Scholar 

  9. 9.

    Kamrin, K., Bazant, M.Z.: Stochastic flow rule for granular materials. Phys. Rev. E 75(4), 041301 (2007)

    MathSciNet  Article  ADS  Google Scholar 

  10. 10.

    Duran, J.: Sands, Powders, and Grains. Springer, New York (2000)

    Google Scholar 

  11. 11.

    Fleck, N.A.: On the cold compaction of powders. J. Mech. Phys. Solids 43(9), 1409–1431 (1995)

    MATH  MathSciNet  Article  ADS  Google Scholar 

  12. 12.

    Spaepen, F.: A microscopic mechanism for steady state inhomogeneous flow in metallic glasses. Acta Metall. 25(4), 407–415 (1977)

    Article  Google Scholar 

  13. 13.

    Jiang, M.Q., Dai, L.H.: On the origin of shear banding instability in metallic glasses. J. Mech. Phys. Solids 57(8), 1267–1292 (2009)

    MATH  Article  ADS  Google Scholar 

  14. 14.

    Shimizu, F., Ogata, S., Li, J.: Theory of shear banding in metallic glasses and molecular dynamics calculations. Mater. Trans. 48(11), 2923–2927 (2007)

    Article  Google Scholar 

  15. 15.

    Bi, D., Zhang, J., Chakraborty, B., Behringer, R.P.: Jamming by shear. Nature 480(7377), 355–358 (2011)

    Article  ADS  Google Scholar 

  16. 16.

    Hill, R.: The Mathematical Theory of Plasticity, vol. 11. Oxford University Press, Oxford (1998)

    Google Scholar 

  17. 17.

    Tordesillas, A., Shi, J.: Frictional indentation of dilatant granular materials. Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci. 455(1981), 261–283 (1999)

    MATH  MathSciNet  Article  ADS  Google Scholar 

  18. 18.

    Peters, J.F., Muthuswamy, M., Wibowo, J., Tordesillas, A.: Characterization of force chains in granular material. Phys. Rev. E 72(4), 041307 (2005)

    Article  ADS  Google Scholar 

  19. 19.

    Kondic, L., Fang, X., Losert, W., O’Hern, C.S., Behringer, R.P.: Microstructure evolution during impact on granular matter. Phys. Rev. E 85(1), 011305 (2012)

    Article  ADS  Google Scholar 

  20. 20.

    Murthy, T.G., Saldana, C., Hudspeth, M., M’Saoubi, R.: Deformation field heterogeneity in punch indentation. Proc. R. Soc. A Math. Phys. Eng. Sci. 470(2166), 20130807 (2014)

    Article  ADS  Google Scholar 

  21. 21.

    Jean, M.: The non-smooth contact dynamics method. Comput. Methods Appl. Mech. Eng. 177(3), 235–257 (1999)

    MATH  MathSciNet  Article  ADS  Google Scholar 

  22. 22.

    Radjaï, F., Richefeu, V.: Contact dynamics as a nonsmooth discrete element method. Mech. Mater. 41(6), 715–728 (2009)

    Article  Google Scholar 

  23. 23.

    Pöschel, T., Schwager, T.: Computational Granular Dynamics. Springer, Berlin (2005)

    Google Scholar 

  24. 24.

    Weaire, D., Aste, T.: The Pursuit of Perfect Packing. CRC Press, Boca Raton (2008)

    Google Scholar 

  25. 25.

    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)

    Article  Google Scholar 

  26. 26.

    Cambou, B., Jean, M., Radjaï, F.: Micromechanics of Granular Materials. Wiley, New York (2009)

    Google Scholar 

  27. 27.

    Koziara, T., Bićanić, N.: A distributed memory parallel multibody contact dynamics code. Int. J. Numer. Meth. Eng. 87(1–5), 437–456 (2011)

    MATH  Article  Google Scholar 

  28. 28.

    Koziara, T.: Aspects of computational contact dynamics. Ph.D. thesis, University of Glasgow (2008)

  29. 29.

    Skoge, M., Donev, A., Stillinger, F.H., Torquato, S.: Packing hyperspheres in high-dimensional Euclidean spaces. Phys. Rev. E 74(4), 041127 (2006)

    MathSciNet  Article  ADS  Google Scholar 

  30. 30.

    Crocker, J.C., Grier, D.G.: Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179(1), 298–310 (1996)

    Article  Google Scholar 

  31. 31.

    Stukowski, A.: Visualization and analysis of atomistic simulation data with OVITO-the open visualization tool. Modell. Simul. Mater. Sci. Eng. 18(1), 015012 (2010)

    Article  ADS  Google Scholar 

  32. 32.

    De Berg, M., Van Kreveld, M., Overmars, M., Schwarzkopf, O.C.: Computational Geometry. Springer, Berlin (2000)

    Google Scholar 

  33. 33.

    See Supplemental Material at URL

  34. 34.

    Murthy, T.G., Gnanamanickam, E., Chandrasekar, S.: Deformation field in indentation of a granular ensemble. Phys. Rev. E 85(6), 061306 (2012)

    Article  ADS  Google Scholar 

  35. 35.

    Schall, P., van Hecke, M.: Shear bands in matter with granularity. Annu. Rev. Fluid Mech. 42(1), 67 (2009)

    Article  ADS  Google Scholar 

  36. 36.

    Samuels, L.E., Mulhearn, T.O.: An experimental investigation of the deformed zone associated with indentation hardness impressions. J. Mech. Phys. Solids 5(2), 125–134 (1957)

    Article  ADS  Google Scholar 

  37. 37.

    Amarouchene, Y., Boudet, J.F., Kellay, H.: Dynamic sand dunes. Phys. Rev. Lett. 86(19), 4286 (2001)

    Article  ADS  Google Scholar 

  38. 38.

    Tüzün, U., Nedderman, R.M.: Gravity flow of granular materials round obstaclesi: investigation of the effects of inserts on flow patterns inside a silo. Chem. Eng. Sci. 40(3), 325–336 (1985)

    Article  Google Scholar 

  39. 39.

    Chehata, D., Zenit, R., Wassgren, C.R.: Dense granular flow around an immersed cylinder. Phys. Fluids 15(6), 1622–1631 (2003)

    Article  ADS  Google Scholar 

  40. 40.

    Adams, M.J., Briscoe, B.J. (eds.): Tribology in Particulate Technology. Adam Hilger, London (1987)

    Google Scholar 

  41. 41.

    Radjaï, F., Roux, S.: Turbulentlike fluctuations in quasistatic flow of granular media. Phys. Rev. Lett. 89(6), 064302 (2002)

    Article  ADS  Google Scholar 

  42. 42.

    Miller, T., Rognon, P., Metzger, B., Einav, I.: Eddy viscosity in dense granular flows. Phys. Rev. Lett. 111(5), 058002 (2013)

    Article  ADS  Google Scholar 

  43. 43.

    Shojaaee, Z., Roux, J.N., Chevoir, F., Wolf, D.E.: Shear flow of dense granular materials near smooth walls. i. shear localization and constitutive laws in the boundary region. Phys. Rev. E 86(1), 011301 (2012)

    Article  ADS  Google Scholar 

  44. 44.

    Kabla, A.J., Senden, T.J.: Dilatancy in slow granular flows. Phys. Rev. Lett. 102(22), 228301 (2009)

    Article  ADS  Google Scholar 

  45. 45.

    Tordesillas, A., Hunt, G., Shi, J.: A characteristic length scale in confined elastic buckling of a force chain. Granul. Matter 13(3), 215–218 (2011)

    Article  Google Scholar 

  46. 46.

    Sundaram, N.K., Guo, Y., Chandrasekar, S.: Mesoscale folding, instability, and disruption of laminar flow in metal surfaces. Phys. Rev. Lett. 109(10), 106001 (2012)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work was supported in part by US Army Research Office Grant W911NF-12-1-0012 and NSF Grant CMMI 1234961 (Purdue); Department of Science and Technology (DST, India) Grant No. SR-CE-0057-2010 (to T.G.M., Indian Institute of Science); and a Bilsland Dissertation Fellowship (to K. V., Purdue). Use of codes made available by D. Blair (Georgetown U), E. Dufresne (Yale) and A. Donev (NYU) is gratefully acknowledged.

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Correspondence to Koushik Viswanathan.

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Viswanathan, K., Mahato, A., Murthy, T.G. et al. Kinematic flow patterns in slow deformation of a dense granular material. Granular Matter 17, 553–565 (2015). https://doi.org/10.1007/s10035-015-0576-y

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Keywords

  • Dense flow
  • Vortices
  • Stagnation
  • Shear bands
  • Pattern formation