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Bending transition in the penetration of a flexible intruder in a two-dimensional dense granular medium

Nicolas Algarra1, Panagiotis G. Karagiannopoulos1, Arnaud Lazarus2, Damien Vandembroucq1, and Evelyne Kolb1,*

  • 1Laboratoire PMMH, UMR 7636 CNRS/ESPCI Paris/PSL Research University/Sorbonne Universités, UPMC Univ Paris 06,/Univ Paris Diderot, 10 rue Vauquelin, 75231 Paris cedex 05, France
  • 2Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005, Paris, France

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Phys. Rev. E 97, 022901 – Published 5 February, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.022901

Abstract

We study the quasistatic penetration of a flexible beam into a two-dimensional dense granular medium lying on a horizontal plate. Rather than a buckling-like behavior we observe a transition between a regime of crack-like penetration in which the fiber only shows small fluctuations around a stable straight geometry and a bending regime in which the fiber fully bends and advances through series of loading and unloading steps. We show that the shape reconfiguration of the fiber is controlled by a single nondimensional parameter L/Lc, which is the ratio of the length of the flexible beam L to Lc, a bending elastogranular length scale that depends on the rigidity of the fiber and on the departure from the jamming packing fraction of the granular medium. We show, moreover, that the dynamics of the bending transition in the course of the penetration experiment is gradual and is accompanied by a symmetry breaking of the granular packing fraction in the vicinity of the fiber. Together with the progressive bending of the fiber, a cavity grows downstream of the fiber and the accumulation of grains upstream of the fiber leads to the development of a jammed cluster of grains. We discuss our experimental results in the framework of a simple model of bending-induced compaction and we show that the rate of the bending transition only depends on the control parameter L/Lc.

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References (50)

  1. B. Audoly and Y. Pomeau, Elasticity and Geometry: From Hair Curls to the Nonlinear Response of Shells (Oxford University Press Inc., New York, 2010).
  2. Z. Bazant and L. Cedolin, Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories (World Scientific Publishing Co. Pte. Ltd., Singapore, 2010).
  3. B. Roman and J. Bico, J. Phys.: Condens. Matter 22, 493101 (2010).
  4. M. J. Shelley and J. Zhang, Annu. Rev. Fluid Mech. 43, 449 (2011).
  5. A. Lindner and M. Shelley, Fluid-Structure Interactions in Low-Reynolds-Number Flows (Royal Society of Chemistry, 2015), pp. 168–192.
  6. S. Ramananarivo, R. Godoy-Diana, and B. Thiria, Proc. Natl. Acad. Sci. USA 108, 5964 (2011).
  7. F. Gosselin, E. de Langre, and B. A. Machado-Almeida, J. Fluid Mech. 650, 319 (2010).
  8. L. Schouveiler and A. Boudaoud, J. Fluid Mech. 563, 71 (2006).
  9. S. Alben, M. Shelley, and J. Zhang, Nature (London) 420, 479 (2002).
  10. S. Vogel, Life in Moving Fluids: The Physical Biology of Flow (Princeton University Press, 1994).
  11. N. Coq, O. du Roure, J. Marthelot, D. Bartolo, and M. Fermigier, Phys. Fluids 20, 051703 (2008).
  12. J. Xiao and X. Chen, J. R. Soc., Interface 10, 0399 (2013).
  13. M. K. Jawed, N. K. Khouri, F. Da, E. Grinspun, and P. M. Reis, Phys. Rev. Lett. 115, 168101 (2015).
  14. E. de Langre, A. Gutierrez, and J. Cosse, C. R. Mec. 340, 35 (2012).
  15. M. Luhar and H. M. Nepf, Limnol. Oceanogr. 56, 2003 (2011).
  16. S. Barsu, D. Doppler, J. J. S. Jerome, N. Rivière, and M. Lance, Phys. Fluids 28, 107101 (2016).
  17. G. C. Buster, M. R. Laufer, and P. F. Peterson, Nucl. Eng. Des. 303, 153 (2016).
  18. E. Kolb, C. Hartmann, and P. Genet, Plant Soil 360, 19 (2012).
  19. D. M. Wendell, K. Luginbuhl, J. Guerrero, and A. E. Hosoi, Exp. Mech. 52, 945 (2012).
  20. A. E. Hosoi and D. I. Goldman, Ann. Rev. Fluid Mech. 47, 431 (2015).
  21. R. Albert, M. A. Pfeifer, A. L. Barabási, and P. Schiffer, Phys. Rev. Lett. 82, 205 (1999).
  22. I. Albert, J. G. Sample, A. J. Morss, S. Rajagopalan, A.-L. Barabási, and P. Schiffer, Phys. Rev. E 64, 061303 (2001).
  23. M. B. Stone, R. Barry, D. P. Bernstein, M. D. Pelc, Y. K. Tsui, and P. Schiffer, Phys. Rev. E 70, 041301 (2004).
  24. R. Candelier and O. Dauchot, Phys. Rev. Lett. 103, 128001 (2009).
  25. R. Candelier and O. Dauchot, Phys. Rev. E 81, 011304 (2010).
  26. A. Fiege, M. Grob, and A. Zippelius, Granular Matter 14, 247 (2012).
  27. E. Kolb, P. Cixous, N. Gaudouen, and T. Darnige, Phys. Rev. E 87, 032207 (2013).
  28. E. Kolb, P. Cixous, and J. C. Charmet, Granular Matter 16, 223 (2014).
  29. A. Seguin, Y. Bertho, F. Martinez, J. Crassous, and P. Gondret, Phys. Rev. E 87, 012201 (2013).
  30. A. Seguin, C. Coulais, F. Martinez, Y. Bertho, and P. Gondret, Phys. Rev. E 93, 012904 (2016).
  31. A. H. Clark, L. Kondic, and R. P. Behringer, Phys. Rev. E 93, 050901(R) (2016).
  32. R. A. L. de la Cruz and G. A. Caballero-Robledo, J. Fluid Mech. 800, 248 (2016).
  33. A. Merceron, A. Sauret, and P. Jop, Phys. Rev. E 93, 062904 (2016).
  34. A. R. Mojdehi, B. Tavakol, W. Royston, D. A. Dillard, and D. P. Holmes, Extreme Mech. Lett. 9, 237 (2016).
  35. D. J. Schunter Jr., M. Brandenbourger, S. Perriseau, and D. P. Holmes, arXiv:1706.07849.
  36. N. Algarra, M. Leang, A. Lazarus, D. Vandembroucq, and E. Kolb, EPJ Web Conf. 140, 14002 (2017).
  37. M. Bouzid, A. Izzet, M. Trulsson, E. Clément, P. Claudin, and B. Andreotti, Eur. Phys. J. E: Soft Matter Biol. Phys. 38, 125 (2015).
  38. F. Radjai and S. Roux, Phys. Rev. Lett. 89, 064302 (2002).
  39. G. Combe, V. Richefeu, G. Viggiani, S. A. Hall, A. Tengattini, and A. Atman, AIP Conf. Proc. 1542, 453 (2013).
  40. K. Saitoh and H. Mizuno, Soft Matter 12, 1360 (2016).
  41. P. Cixous, Ph.D. thesis, Université Pierre et Marie Curie - Paris VI, 2009, https://pastel.archives-ouvertes.fr/pastel-00622262/file/pierre_cixous_final.pdf.
  42. A. Boudaoud, P. Patricio, Y. Couder, and M. Ben Amar, Nature (London) 407, 718 (2000).
  43. P. Mills, P. G. Rognon, and F. Chevoir, Europhys. Lett. 81 64005 (2008).
  44. P. G. Rognon, T. Miller, B. Metzger, and I. Einav, J. Fluid Mech. 764, 171 (2015).
  45. D. Bi, J. Zhang, B. Chakraborty, and R. P. Behringer, Nature (London) 480, 355 (2011).
  46. C. Goldenberg, A. Tanguy, and J.-L. Barrat, Europhys. Lett. 80, 16003 (2007).
  47. K. W. Desmond and E. R. Weeks, Phys. Rev. E 80, 051305 (2009).
  48. S. R. Waitukaitis, L. K. Roth, V. Vitelli, and H. M. Jaeger, Europhys. Lett. 102, 44001 (2013).
  49. K. A. Reddy, Y. Forterre, and O. Pouliquen, Phys. Rev. Lett. 106, 108301 (2011).
  50. A. Lazarus, J. T. Miller, and P. M. Reis, J. Mech. Phys. Solids 61, 1712 (2013).

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Phys. Rev. E 97, 022901– Published 5 February, 2018
  • Received 4 August 2017
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