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Applying GSH to a wide range of experiments in granular media

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Abstract

Granular solid hydrodynamics (GSH) is a continuum-mechanical theory for granular media, whose wide range of applicability is shown in this paper. Simple, frequently analytic solutions are related to classic observations at different shear rates, including: i) static stress distribution, clogging; ii) elasto-plastic motion: loading and unloading, approach to the critical state, angle of stability and repose; iii) rapid dense flow: the μ-rheology, Bagnold scaling and the stress minimum; iv) elastic waves, compaction, wide and narrow shear band. Less conventional experiments have also been considered: shear jamming, creep flow, visco-elastic behavior and non-local fluidization. With all these phenomena ordered, related, explained and accounted for, though frequently qualitatively, we believe that GSH may be taken as a unifying framework, providing the appropriate macroscopic vocabulary and mindset that help one coming to terms with the breadth of granular physics.

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References

  1. P. Wroth, A. Schofield, Critical State Soil Mechanics (McGraw-Hill, London, 1968).

  2. R.M. Nedderman, Statics and Kinematics of Granular Materials (Cambridge University Press, 1992).

  3. D.M. Wood, Soil Behaviour and Critical State Soil Mechanics (Cambridge University Press, 1990).

  4. D. Kolymbas, Introduction to Hypoplasticity (Balkema, Rotterdam, 2000).

  5. W. Wu, D. Kolymbas, Constitutive Modelling of Granular Materials (Springer, Berlin, 2000).

  6. G. Gudehus, Physical Soil Mechanics (Springer SPIN, 2010).

  7. S.P. Pudasaini, K. Hutter, Avalanche Dynamics (Springer, 2007).

  8. L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Butter-worth-Heinemann, 1987).

  9. I.M. Khalatnikov, Introduction to the Theory of Superfluidity (Benjamin, New York, 1965).

  10. P.G. de Gennes, J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993).

  11. F. Nicot, F. Darve, Mech. Mater. 37, 980 (2005) and Second International Symposium on Computational Geomechanics (ComGeo II).

    Google Scholar 

  12. S.R. de Groot, P. Masur, Non-Equilibrium Thermodynamics (Dover, New York, 1984).

  13. D. Forster, Hydrodynamic Fluctuations, Broken Symmetry and Correlation Functions (Benjamin, New York, 1975).

  14. P.G. de Gennes, J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993).

  15. P.C. Martin, O. Parodi, P.S. Pershan, Phys. Rev. A 6, 2401 (1972).

    ADS  Google Scholar 

  16. T.C. Lubensky, Phys. Rev. A 6, 452 (1972).

    ADS  Google Scholar 

  17. M. Liu, Phys. Rev. A 19, 2090 (1979).

    ADS  Google Scholar 

  18. M. Liu, Phys. Rev. A 24, 2720 (1981).

    ADS  Google Scholar 

  19. M. Liu, Phys. Rev. E 50, 2925 (1994).

    ADS  Google Scholar 

  20. H. Pleiner, H.R. Brand, in Pattern Formation in Liquid Crystals, edited by A. Buka, L. Kramer (Springer, New York, 1996).

  21. R. Graham, Phys. Rev. Lett. 33, 1431 (1974).

    ADS  Google Scholar 

  22. R. Graham, H. Pleiner, Phys. Rev. Lett. 34, 792 (1975).

    ADS  Google Scholar 

  23. M. Liu, Phys. Rev. Lett. 35, 1577 (1975).

    ADS  Google Scholar 

  24. M. Liu, M.C. Cross, Phys. Rev. Lett. 41, 250 (1978).

    ADS  Google Scholar 

  25. M. Liu, M.C. Cross, Phys. Rev. Lett. 43, 296 (1979).

    ADS  Google Scholar 

  26. M. Liu, Phys. Rev. Lett. 43, 1740 (1979).

    ADS  Google Scholar 

  27. M. Liu, Phys. Rev. Lett. 81, 3223 (1998).

    ADS  Google Scholar 

  28. Y.M. Jiang, M. Liu, Phys. Rev. B 6, 184506 (2001).

    ADS  Google Scholar 

  29. M. Liu, J. Low Temp. Phys. 126, 911 (2002).

    ADS  Google Scholar 

  30. K. Henjes, M. Liu, Ann. Phys. 223, 243 (1993).

    ADS  MATH  MathSciNet  Google Scholar 

  31. M. Liu, Phys. Rev. Lett. 70, 3580 (1993).

    ADS  Google Scholar 

  32. Mario Liu, Phys. Rev. Lett. 74, 1884 (1995).

    ADS  Google Scholar 

  33. Y.M. Jiang, M. Liu, Phys. Rev. Lett. 77, 1043 (1996).

    ADS  Google Scholar 

  34. M.I. Shliomis, Sov. Phys. Usp. 17, 153 (1974).

    ADS  Google Scholar 

  35. R.E. Rosensweig, Ferrohydrodynamics (Dover, New York, 1997).

  36. M. Liu, Phys. Rev. Lett. 74, 4535 (1995).

    ADS  Google Scholar 

  37. M. Liu, Phys. Rev. Lett. 80, 2937 (1998).

    ADS  Google Scholar 

  38. M. Liu, Phys. Rev. E 59, 3669 (1999).

    ADS  Google Scholar 

  39. H.W. Müller, M. Liu, Phys. Rev. E 64, 061405 (2001).

    ADS  Google Scholar 

  40. H.W. Müller, M. Liu, Phys. Rev. Lett. 89, 67201 (2002).

    ADS  Google Scholar 

  41. O. Müller, D. Hahn, M. Liu, J. Phys.: Condens. Matter 18, 2623 (2006).

    Google Scholar 

  42. S. Mahle, P. Ilg, M. Liu, Phys. Rev. E 77, 016305 (2008).

    ADS  Google Scholar 

  43. M. Liu, K. Stierstadt, Thermodynamics, Electrodynamics, and Ferrofluid Dynamics, in Colloidal Magnetic Fluids: Basics, Development and Application of Ferrofluids, edited by S. Odenbach, Lect. Notes Phys., Vol. 763 (Springer, Berlin, Heidelberg, 2009) DOI:10.1007/978-3-540-85387-9.

  44. H. Temmen, H. Pleiner, M. Liu, H.R. Brand, Phys. Rev. Lett. 84, 3228 (2000).

    ADS  Google Scholar 

  45. H. Temmen, H. Pleiner, M. Liu, H.R. Brand, Phys. Rev. Lett. 86, 745 (2001).

    ADS  Google Scholar 

  46. H. Pleiner, M. Liu, H.R. Brand, Rheol. Acta 43, 502 (2004).

    Google Scholar 

  47. O. Müller, Die Hydrodynamische Theorie Polymerer Fluide, PhD Thesis, University Tübingen (2006).

  48. Y.M. Jiang, M. Liu, Granular Matter 11, 139 (2009) free download available online at http://www.dx.doi.org/10.1007/s10035-009-0137-3.

    MATH  Google Scholar 

  49. Y.M. Jiang, M. Liu, The physics of granular mechanics, in Mechanics of Natural Solids, edited by D. Kolymbas, G. Viggiani (Springer, 2009) pp. 27--46.

  50. G. Gudehus, Y.M. Jiang, M. Liu, Granular Matter 1304, 319 (2011).

    Google Scholar 

  51. Y.M. Jiang, M. Liu, Acta Mech. 225, 2363 (2014).

    MATH  MathSciNet  Google Scholar 

  52. Y.P. Chen, M.Y. Hou, Y.M. Jiang, M. Liu, Phys. Rev. E 88, 052204 (2013).

    ADS  Google Scholar 

  53. V. Magnanimo, S. Luding, Granular Matter 13, 225 (2011).

    Google Scholar 

  54. M. Mayer, M. Liu, Phys. Rev. E 82, 042301 (2010).

    ADS  Google Scholar 

  55. Stefan Luding, Nonlinearity 22, 101 (2009).

    MathSciNet  Google Scholar 

  56. Y.M. Jiang, M. Liu, Phys. Rev. Lett. 99, 105501 (2007).

    ADS  Google Scholar 

  57. G.T. Houlsby, A.M. Puzrin, Principles of Hyperplasticity (Springer, 2006).

  58. I.F. Collins, G.T. Houlsby, Proc. R. Soc. London A 453, 1975 (1997).

    ADS  MATH  Google Scholar 

  59. M.B. Rubin, Arch. Mech. 53, 519 (2001).

    MATH  Google Scholar 

  60. L. Bocquet, W. Losert, D. Schalk, T.C. Lubensky, J.P. Gollub, Phys. Rev. E 65, 011307 (2001).

    ADS  Google Scholar 

  61. D.O. Krimer, M. Pfitzner, K. Bräuer, Y.M. Jiang, M. Liu, Phys. Rev. E 74, 061310 (2006).

    ADS  Google Scholar 

  62. K. Bräuer, M. Pfitzner, D.O. Krimer, M. Mayer, Y.M. Jiang, M. Liu, Phys. Rev. E 74, 061311 (2006).

    ADS  Google Scholar 

  63. Y.M. Jiang, M. Liu. Eur., Phys. J. E 22, 255 (2007).

    Google Scholar 

  64. R. Kuwano, R.J. Jardine, Geotechnique 52, 727 (2002).

    Google Scholar 

  65. Y.M. Jiang, M. Liu, Phys. Rev. E 77, 021306 (2008).

    ADS  Google Scholar 

  66. Y. Khidas, X. Jia, Phys. Rev. E 81, 021303 (2010).

    ADS  Google Scholar 

  67. Y.M. Jiang, H.P. Zheng, Z. Peng, L.P. Fu, S.X. Song, Q.C. Sun, M. Mayer, M. Liu, Phys. Rev. E 85, 051304 (2012).

    ADS  Google Scholar 

  68. B.O. Hardin, F.E. Richart, J. Soil Mech. Found. Div. ASCE 89, 33 (1963).

    Google Scholar 

  69. Stefan Mahle, Yimin Jiang, Mario Liu, Granular solid hydrodynamics: Dense flow, fluidization and jamming, arXiv:1010.5350v1 [cond-mat.soft], 2010.

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

    Google Scholar 

  71. Stefan Mahle, Yimin Jiang, Mario Liu, The critical state and the steady-state solution in granular solid hydrodynamics, arXiv:1006.5131v3 [physics.geo-ph], 2010.

  72. Yimin Jiang, Mario Liu, Granular Matter 15, 237 (2013).

    Google Scholar 

  73. Kolymbas D. Barodesy, Geotech. Lett. 2, 17 (2012) http://dx.doi.org/10.1680/geolett.12.00004.

    Google Scholar 

  74. D. Kolymbas, Int. J. Numer. Anal. Methods Geomech. 36, 1220 (2012) DOI:10.1002/nag.1051.

    Google Scholar 

  75. D. Kolymbas, Sand as an archetypical natural solid, in Mechanics of Natural Solids, edited by D. Kolymbas, G. Viggiani (Springer, Berlin, 2009) pp. 1--26.

  76. T. Wichtmann, Schriftreihe Inst. Grundbau u. Bodenmechanik, Univ. Bochum, Heft 38 (2005) fig. 4.17.

  77. C. Thornton, S.J. Antony, Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 356, 2763 (1998).

    ADS  MATH  Google Scholar 

  78. D.P. Bi, J. Chang, B. Chakraborty, R.P. Behringer, Nature 480, 355 (2011).

    ADS  Google Scholar 

  79. N. Kumar, Stefan Luding, arXiv:1407.6167v1 [cond-mat.soft].

  80. J.A. Dijksman, G.H. Wortel, L.T.H. van Dellen, O. Dauchot, M. van Hecke, Phys. Rev. Lett. 107, 108303 (2011).

    ADS  Google Scholar 

  81. D. Krimer, S. Mahle, M. Liu, Phys. Rev. E 86, 061312 (2012).

    ADS  Google Scholar 

  82. J.-N. Roux, AIP Conf. Proc. 1227, 260 (2010) DOI:10.1063/1.3435396.

    ADS  Google Scholar 

  83. J.-N. Roux, AIP Conf. Proc. 1542, 46 (2013) DOI:10.1063/1.4811865.

    ADS  Google Scholar 

  84. I. Einav, Int. J. Solid Struct. 49, 1305 (2012).

    Google Scholar 

  85. Y.M. Jiang, M. Liu, AIP Conf. Proc. 1145, 1096 (2009).

    ADS  Google Scholar 

  86. Van Bau Nguyen, Thierry Darnige, Ary Bruand, Eric Clement, Phys. Rev. Lett. 107, 138303 (2011).

    Google Scholar 

  87. I.S. Aranson, L.S. Tsimring, Phys. Rev. E 65, 061303 (2002).

    ADS  MathSciNet  Google Scholar 

  88. I.S. Aranson, L.S. Tsimring, Rev. Mod. Phys. 78, 641 (2006).

    ADS  Google Scholar 

  89. T.S. Komatsu, S. Inagaki, N. Nakagawa, S. Nasuno, Phys. Rev. Lett. 86, 1757 (2001).

    ADS  Google Scholar 

  90. J. Crassous, J.-F. Metayer, P. Richard, C. Laroche, J. Stat. Mech. 2008, P03009 (2008).

    Google Scholar 

  91. D.L. Henann, K. Kamrin, Proc. Natl. Acad. Sci. U.S.A. 110, 6730 (2012) DOI:10.1073/pnas.1219153110.

    ADS  MathSciNet  Google Scholar 

  92. K. Kamrin, G. Koval, Phys. Rev. Lett. 108, 178301 (2012).

    ADS  Google Scholar 

  93. D. Fenistein, J.W. van de Meent, M. van Hecke, Nature 425, 695 (2003).

    Google Scholar 

  94. D. Fenistein, J.W. van de Meent, M. van Hecke, Phys. Rev. Lett. 96, 118001 (2006).

    ADS  Google Scholar 

  95. D. Fenistein, J.W. van de Meent, M. van Hecke, Phys. Rev. Lett. 96, 038001 (2006).

    Google Scholar 

  96. Kiri Nichol, Alexey Zanin, Renaud Bastien, Elie Wandersman, Martin van Hecke, Phys. Rev. Lett. 104, 078302 (2010).

    ADS  Google Scholar 

  97. K.A. Reddy, Y. Forterre, O. Pouliquen, Phys. Rev. Lett. 106, 108301 (2011).

    ADS  Google Scholar 

  98. D.A. Huerta, Victor Sosa, M.C. Vargas, J.C. Ruiz-Surez, Phys. Rev. E 72, 031307 (2005).

    ADS  Google Scholar 

  99. G.A. Caballero-Robledo, E. Clement, Eur. Phys. J. E 30, 395 (2009).

    Google Scholar 

  100. Wei Wu, J. Eng. Math. 56, 23 (2006).

    MATH  Google Scholar 

  101. J. Tejchman, W. Wu, Granular Matter 12, 399 (2010).

    MATH  Google Scholar 

  102. R.A. Bagnold, Proc. R. Soc. London Ser A. Math. Phys. Sci. 225, 49 (1954).

    ADS  Google Scholar 

  103. Y.M. Jiang, M. Liu, AIP Conf. Proc. 1542, 52 (2013) DOI:10.1063/1.4811867.

    ADS  Google Scholar 

  104. J.T. Jenkins, S.B. Savage, J. Fluid Mech. 130, 187 (1983).

    ADS  MATH  Google Scholar 

  105. S.B. Savage, Adv. Appl. Mech. 24, 289 (1984).

    MATH  Google Scholar 

  106. C.S. Campbell, Annu. Rev. Fluid Mech. 22, 57 (1990).

    ADS  Google Scholar 

  107. I. Goldhirsch, Chaos 9, 659 (1999).

    ADS  MATH  Google Scholar 

  108. I. Goldhirsch, Annu. Rev. Fluid Mech. 35, 267 (2003).

    ADS  MathSciNet  Google Scholar 

  109. P.C. Johnson, R. Jackson, J. Fluid Mech. 176, 67 (1987).

    ADS  Google Scholar 

  110. M.Y. Louge, Phys. Rev. E 67, 061303 (2003).

    ADS  Google Scholar 

  111. C. Josserand, P.Y. Lagre, D. Lhuillier, Europhys. Lett. 73, 363 (2006).

    ADS  MathSciNet  Google Scholar 

  112. D. Berzi, C.G. di Prisco, D. Vescovi, Phys. Rev. E 84, 031301 (2011).

    ADS  Google Scholar 

  113. Pierre Jop, Yoël Forterre, Olivier Pouliquen, Nature 441, 727 (2006).

    ADS  Google Scholar 

  114. Yoël Forterre, Olivier Pouliquen, Annu. Rev. Fluid Mech. 40, 1 (2008).

    ADS  Google Scholar 

  115. F. Boyer, E. Guazzelli, O. Pouliquen, Phys. Rev. Lett. 107, 188301 (2011).

    ADS  Google Scholar 

  116. G. Lois, A. Lemaitre, J. Carlson, Phys. Rev. E 72, 051303 (2005).

    ADS  Google Scholar 

  117. C.S. Campbell, J. Fluid Mech. 465, 261 (2002).

    ADS  MATH  MathSciNet  Google Scholar 

  118. K. Lu, E.E. Brodsky, H.P. Kavehpour, J. Fluid. Mech. 587, 347 (2007).

    ADS  MATH  Google Scholar 

  119. K. Lu, E.E. Brodsky, H.P. Kavehpour, Nature Lett. 4, 404 (2008).

    ADS  Google Scholar 

  120. F. da Cruz, S. Emam, M. Prochnow, J.N. Roux, F. Chevoir, Phys. Rev. E 72, 021309 (2005).

    ADS  Google Scholar 

  121. O. Pouliquen, Phys. Fluids 11, 542 (1999).

    ADS  MATH  MathSciNet  Google Scholar 

  122. X. Jia, C. Caroli, B. Velicky, Phys. Rev. Lett. 82, 1863 (1999).

    ADS  Google Scholar 

  123. X. Jia, Phys. Rev. Lett. 93, 154303 (2004).

    ADS  Google Scholar 

  124. Q. Zhang, Y.C. Li, M.Y. Hou, Y.M. Jiang, M. Liu, Phys. Rev. E 85, 031306 (2012).

    ADS  Google Scholar 

  125. C. Josserand, A.V. Tkachenko, D.M. Mueth, H.M. Jaeger, Phys. Rev. Lett. 85, 3632 (2000).

    ADS  Google Scholar 

  126. P. Richard, M. Nicodemi, R. Delannay, P. Ribiere, D. Bideau, Nature 4, 121 (2005).

    Google Scholar 

  127. S.F. Edwards, R.B.S. Oakeshott, Physica A 157, 1080 (1989).

    ADS  MathSciNet  Google Scholar 

  128. S.F. Edwards, D.V. Grinev, Granular Matter 4, 147 (2003).

    MATH  Google Scholar 

  129. Yimin Jiang, Mario Liu, The critical state and the steady-state solution in granular solid hydrodynamics, arXiv:0911.2199v2 [cond-mat.soft] (2010).

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  1. Central South University, 410083, Changsha, China

    Yimin Jiang

  2. Theoretische Physik, Universität Tübingen, 72076, Tübingen, Germany

    Mario Liu

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  1. Yimin Jiang
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Jiang, Y., Liu, M. Applying GSH to a wide range of experiments in granular media. Eur. Phys. J. E 38, 15 (2015). https://doi.org/10.1140/epje/i2015-15015-6

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