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Hysteresis of the drag force of an intruder moving into a granular medium

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Abstract.

We numerically investigate the force-displacement relation of a moving intruder initially at rest into a granular medium. Our model granular medium is composed of one layer of coplanar polydisperse spheres subjected to a gravity field. The interactions between the grains are modelled by Hertzian contacts to which a viscous damping is applied. Moving it horizontally and with alternating positive and negative velocity, we recover a hysteresis of the force-displacement curve. Considering that the flow is plastic as the yield strength has been reached, we describe the transient part of the flow around the intruder. We show that the drag stress increases as its distance to an ultimate drag stress \( \sigma_{u}\) with a typical deformation \( \varepsilon_{c}\): the drag stress-strains curve appears to exponentially decay as it saturates to this ultimate drag stress. This protocol of deformation highlights that the deformation of the grains is negligible compared to the deformation of the packing, i.e. related to the irreversible displacements of grains allowing the intruder to pass through. Simultaneously, the lift force is constant on average during the displacement of the intruder. We then give the different scaling laws of the yield strength, this ultimate drag stress, the characteristic deformation of the packing and the lift stress. Finally, we recover the complete hysteresis cycle of the drag force around the intruder.

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References

  1. M.P. O’Reilly, S.F. Brown, Cyclic Loading of Soils (Blackie, 1991)

  2. D. Howell, R. Behringer, C. Veje, Phys. Rev. Lett. 82, 5241 (1999)

    Article  ADS  Google Scholar 

  3. GDR MiDi, Eur. Phys. J. E 14, 341 (2004)

    Article  Google Scholar 

  4. S.C. du Pont, R. Fischer, P. Gondret, B. Perrin, M. Rabaud, Phys. Rev. Lett. 94, 048003 (2005)

    Article  ADS  Google Scholar 

  5. P. Jop, Y. Forterre, O. Pouliquen, Nature 441, 727 (2006)

    Article  ADS  Google Scholar 

  6. C.S. Chang, A. Misra, S.S. Sundaram, Soil Dyn. Earthq. Eng. 10, 201 (1991)

    Article  Google Scholar 

  7. J. Sun, S. Sundaresan, J. Fluid Mech. 682, 590 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  8. N. Khalili, M. Habte, S. Valliappan, Int. J. Numer. Methods Eng. 63, 1939 (2005)

    Article  Google Scholar 

  9. M. Nicolas, P. Duru, O. Pouliquen, Eur. Phys. J. E 3, 309 (2000)

    Article  Google Scholar 

  10. J. Zhang, T. Majmudar, A. Tordesillas, R. Behringer, Granular Matter 12, 159 (2010)

    Article  Google Scholar 

  11. M. Bouzid, M. Trulsson, P. Claudin, E. Clément, B. Andréotti, Phys. Rev. Lett. 111, 238301 (2013)

    Article  ADS  Google Scholar 

  12. M. Bouzid, A. Izzet, M. Trulsson, E. Clément, P. Claudin, B. Andreotti, Eur. Phys. J. E 38, 125 (2015)

    Article  Google Scholar 

  13. A. Seguin, Y. Bertho, P. Gondret, J. Crassous, EPL 88, 44002 (2009)

    Article  ADS  Google Scholar 

  14. A. Seguin, Y. Bertho, P. Gondret, Phys. Rev. E 78, 010301 (2008)

    Article  ADS  Google Scholar 

  15. C.S. O’Hern, S.A. Langer, A.J. Liu, S.R. Nagel, Phys. Rev. Lett. 88, 075507 (2002)

    Article  ADS  Google Scholar 

  16. C.S. O’Hern, L.E. Silbert, A.J. Liu, S.R. Nagel, Phys. Rev. E 68, 011306 (2003)

    Article  ADS  Google Scholar 

  17. Y. Ding, N. Gravish, D.I. Goldman, Phys. Rev. Lett. 106, 028001 (2011)

    Article  ADS  Google Scholar 

  18. A. Seguin, A. Lefebvre-Lepot, S. Faure, P. Gondret, Eur. Phys. J. E 39, 63 (2016)

    Article  Google Scholar 

  19. Y. Takehara, S. Fujimoto, K. Okumura, EPL 92, 44003 (2010)

    Article  ADS  Google Scholar 

  20. J.E. Hilton, A. Tordesillas, Phys. Rev. E 88, 062203 (2013)

    Article  ADS  Google Scholar 

  21. Y. Takehara, K. Okumura, Phys. Rev. Lett. 112, 148001 (2014)

    Article  ADS  Google Scholar 

  22. T. Faug, Eur. Phys. J. E 38, 34 (2015)

    Article  Google Scholar 

  23. A. Seguin, C. Coulais, F. Martinez, Y. Bertho, P. Gondret, Phys. Rev. E 93, 012904 (2016)

    Article  ADS  Google Scholar 

  24. F. Guillard, Y. Forterre, O. Pouliquen, Phys. Rev. Lett. 110, 138303 (2013)

    Article  ADS  Google Scholar 

  25. F.Q. Potiguar, Y. Ding, Phys. Rev. E 88, 012204 (2013)

    Article  ADS  Google Scholar 

  26. I. Albert, J.G. Sample, A.J. Morss, S. Rajagopalan, A.L. Barabási, P. Schiffer, Phys. Rev. E 64, 061303 (2001)

    Article  ADS  Google Scholar 

  27. Z. Peng, X. Xu, K. Lu, M. Hou, Phys. Rev. E 80, 021301 (2009)

    Article  ADS  Google Scholar 

  28. A. Seguin, Y. Bertho, P. Gondret, J. Crassous, Phys. Rev. Lett. 107, 048001 (2011)

    Article  ADS  Google Scholar 

  29. D.J. Costantino, J. Bartell, K. Scheidler, P. Schiffer, Phys. Rev. E 83, 011305 (2011)

    Article  ADS  Google Scholar 

  30. A. Seguin, Y. Bertho, F. Martinez, J. Crassous, P. Gondret, Phys. Rev. E 87, 012201 (2013)

    Article  ADS  Google Scholar 

  31. M.B. Stone, R. Barry, D.P. Bernstein, M.D. Pelc, Y.K. Tsui, P. Schiffer, Phys. Rev. E 70, 041301 (2004)

    Article  ADS  Google Scholar 

  32. R. Candelier, O. Dauchot, Phys. Rev. Lett. 103, 128001 (2009)

    Article  ADS  Google Scholar 

  33. R. Candelier, O. Dauchot, Phys. Rev. E 81, 011304 (2010)

    Article  ADS  Google Scholar 

  34. A. Fiege, M. Grob, A. Zippelius, Granular Matter 14, 247 (2012)

    Article  Google Scholar 

  35. A. Le Bouil, A. Amon, J.C. Sangleboeuf, H. Orain, P. Bésuelle, G. Viggiani, P. Chasle, J. Crassous, Granular Matter 16, 1 (2014)

    Article  Google Scholar 

  36. J.R. de Bruyn, A.M. Walsh, Can. J. Phys. 82, 439 (2004)

    Article  ADS  Google Scholar 

  37. R. Albert, M.A. Pfeifer, A.L. Barabási, P. Schiffer, Phys. Rev. Lett. 82, 205 (1999)

    Article  ADS  Google Scholar 

  38. D.L. Henann, K. Kamrin, Phys. Rev. Lett. 113, 178001 (2014)

    Article  ADS  Google Scholar 

  39. D. Berzi, J.T. Jenkins, Soft Matter 11, 4799 (2015)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Laboratoire FAST, Université Paris-Sud, CNRS, Université Paris-Saclay, F-91405, Orsay, France

    A. Seguin

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  1. A. Seguin
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Seguin, A. Hysteresis of the drag force of an intruder moving into a granular medium. Eur. Phys. J. E 42, 13 (2019). https://doi.org/10.1140/epje/i2019-11772-4

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  • DOI: https://doi.org/10.1140/epje/i2019-11772-4

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