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Granular Material Theories Revisited

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Geomorphological Fluid Mechanics

Part of the book series: Lecture Notes in Physics ((LNP,volume 582))

Abstract

A granular material is a collection of a large number of discrete solid particles with interstices filled with a fluid or a gas. If the interstitial fluid plays an insignificant role in the transportation of momentum, flows of such materials can be considered as dispersed single-phase flows. In other occasions, when the mass of the interstitial fluid is comparable to that of the solids the interactions between the fluid and solid phases are significant, the motion of the fluid can then provide the driving force for the flow of the solid phase. The dynamical behaviour of these materials can be very complex; its description involves aspects of traditional fluid mechanics, plasticity theory, soil mechanics and rheology.

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References

  1. G. Ahmadi: Int. J. Non-linear Mechanics 15, 251–262 (1980)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. G. Ahmadi: Acta Mech. 44, 299–317 (1982)

    Article  MATH  Google Scholar 

  3. M.P. Allen, D.J. Tildesley: Computer Simulation of Liquids (Oxford University Press, Oxford 1987)

    MATH  Google Scholar 

  4. C. Ancey, P. Coussot, P. Evesque: Mech. Cohesive-Frictional Mat. 1, 385–403 (1996)

    Article  Google Scholar 

  5. R.A. Bagnold: Proc. R. Soc. London A225, 49–63 (1954)

    ADS  Google Scholar 

  6. P.L. Bhatnagar, P. Gross, M. Krook: Physical Reviews 94, 5511–5536 (1954)

    Google Scholar 

  7. J. Bluhm, R. De Boer, K. Wilmanski: Mech. Res. Comm. 22, 171–180 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  8. R.M. Bowen: Int. J. Engng. Sci. 18, 1129–1148 (1980)

    Article  MATH  Google Scholar 

  9. E.J. Boyle, M. Massoudi: Kinetic theories of granular media with applications to fluided beds. U. S. Department of Energy, Technical Note, DOE/METC-89-4088 (1989)

    Google Scholar 

  10. V. Buchholtz, T. Pöschel: Physica A 202, 390 (1994)

    Article  ADS  Google Scholar 

  11. C.S. Campbell: Ann. Rev. Fluid Mech. 22, 57–92(1990)

    Article  ADS  Google Scholar 

  12. C.S. Campbell, C.E. Brennen: J. Fluid Mech. 151, 167–188 (1985)

    Article  ADS  Google Scholar 

  13. R.P. Chhabra, P.H.T. Uhlherr: ‘Static equilibrium and motion of spheres in viscoplastic liquids’. In: Encyclopedia of Fluid Mechanics, ed. by N.P. Cheremisino. (Gulf Publishing Coo., Houston 1988) Chapter 21, Vol. 7

    Google Scholar 

  14. C.L. Chen: Geol. Soc. Am. Rev. Eng. Geol. Vol. VII, 13–29 (1987)

    Google Scholar 

  15. C.L. Chen, C.H. Ling: J. Eng. Mech. 122, 469–480 (1996)

    Article  Google Scholar 

  16. B.D. Coleman, W. Noll: Arch. Rat. Mech. Anal. 13, 167–178 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  17. P. Coussot: J. Hydr. Res. 32(4), 535–559 (1994)

    Google Scholar 

  18. P. Coussot: Mud.ow Rheology and Dynamics. (Balkema, Rotterdam 1997)

    Google Scholar 

  19. P. Coussot, J.M. Piau: Rheol. Acta 33, 175–184 (1994)

    Article  Google Scholar 

  20. S.C. Cowin, M.A. Goodman: Zeitschrift für Angewandte Mathematik and Mechanik 56, 281–286 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  21. S.C. Cowin, J.W. Nunziato: Int. J. Engng. Sci. 19, 993–1008 (1981)

    Article  MATH  Google Scholar 

  22. W.O. Criminale, J.L. Ericksen, G.L. Filbey: Arch. Rational Mech. Anal. 1, 410–417 (1958)

    MATH  MathSciNet  ADS  Google Scholar 

  23. P.A. Cundall, O.D.L. Strack: Gèotechnique 29(1), 47–65 (1979)

    Article  Google Scholar 

  24. C.M. Dury, G.H. Ristow: J. Phys. I France 7, 737 (1997)

    Article  MathSciNet  Google Scholar 

  25. W. Ehlers: ‘Constitutive equations for granular materials in geomechanical context’. In: Continuum Mechanics in Environmental Sciences and Geophysics, ed. by K. Hutter (Springer Verlag, Heidelberg, New York 1993) pp. 313–402

    Google Scholar 

  26. S.H. Faria: Continuum Mech. Thermodyn. in press (2001)

    Google Scholar 

  27. A.G. Fredrickson: Principles and Applications of Rheology. (Prentice-Hall, Englewood Cliffs 1964)

    Google Scholar 

  28. J.A.C. Gallas, H.J. Herrmann, S. Sokolowski: J. Phys. II France 2, 1389 (1992)

    Article  Google Scholar 

  29. J.D. Goddard: Acta Mechanica 63, 3–13 (1986)

    Article  MATH  Google Scholar 

  30. M.A. Goodman, S.C. Cowin: J. Fluid Mech. 45, 321–339 (1971)

    Article  MATH  ADS  Google Scholar 

  31. M.A. Goodman, S.C. Cowin: Arch. Rat. Mech. and Anal. 44, 249–266 (1972)

    MATH  ADS  MathSciNet  Google Scholar 

  32. G.W. Govier, C.A. Shook, E.O. Lilge: Trans. Can. Insti. Mining and Met. 60, 147–154 (1957)

    Google Scholar 

  33. J.M.N.T. Gray, M. Wieland, K. Hutter: Proc. R. Soc. Lond. A455, 1841–1874 (1999)

    MATH  ADS  MathSciNet  Google Scholar 

  34. J.M.N.T. Gray, K. Hutter: Continuum Mech. Thermodyn 9, 341–345 (1997)

    Article  ADS  Google Scholar 

  35. R. Greve, K. Hutter: Phil. Trans. R. Soc. London A342, 573–604 (1993)

    Article  ADS  Google Scholar 

  36. R. Greve, T. Koch, K. Hutter: Proc. R. Soc. London A445, 399–413 (1994)

    MATH  ADS  Google Scholar 

  37. R. Gudhe, R.C. Yalamanchili, M. Massoudi: The flow of granular materials in a pipe: numerical solutions. Rec. Adv. Mech. Strcted. Continua, AMD-160/MD-41, 41–53 (1993)

    Google Scholar 

  38. G. Gudehus: Soils and Foundations 36, 1–12(1996)

    Google Scholar 

  39. P.K. Ha.: J. Fluid Mech. 134, 401–430 (1983)

    Article  ADS  Google Scholar 

  40. P.K. Ha., B.T. Werner: Powder Technol. 48, 239 (1987)

    Google Scholar 

  41. D.M. Hanes, D.L. Inman: J. Fluid Mech. 150, 357–380 (1985)

    Article  ADS  Google Scholar 

  42. H.J. Herrmann, S. Luding: Continuum Mech. Thermodyn. 10, 1–48 (1998)

    Article  MathSciNet  Google Scholar 

  43. H. Hertz: J. für die reine und angew. Math. 92, 136 (1882)

    Google Scholar 

  44. K. Hutter: Acta Mechanica (Suppl.) 1, 167–181 (1991)

    Google Scholar 

  45. K. Hutter: ‘Avalanche Dynamics’. In: Hydrology of Disasters, ed. by V.P. Singh (Kluwer Academic Publ., Dordrecht-Boston-London 1996) pp. 317–394

    Google Scholar 

  46. K. Hutter, R. Greve: J. Glaciology 39, 357–372(1993)

    ADS  Google Scholar 

  47. K. Hutter, L. Laloui, L. Vulliet: Mech. Cohesive-Frictional Mat. 4(4), 295–338 (1999)

    Article  Google Scholar 

  48. K. Hutter, K.R. Rajagopal: Continuum Mech. Thermodyn. 6, 81–139 (1994)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  49. K. Hutter, T. Koch: Phil. Trans. R. Soc. London, A334, 93–138 (1991)

    Article  ADS  Google Scholar 

  50. H. Hwang, K. Hutter: Continuum Mech. Thermodyn. 7, 357–384 (1995)

    MATH  ADS  MathSciNet  Google Scholar 

  51. J.T. Jenkins: ‘Balance laws and constitutive relations for rapid flows of granular materials‘. In: Proc. Army Research O.ce Workshop on Constitutive Relations, ed. by J. Chandra, R. Srivastava (Philadephia, 1987)

    Google Scholar 

  52. J.T. Jenkins, S.C. Cowin: ‘Theories for flowing granular materials’. In: The Joint ASME-CSME Appl. Mech. Fluid Engng. and Bioengng. Conf., AMD-Vol. 31, pp. 79–89 (1979)

    Google Scholar 

  53. J.T. Jenkins, M.W. Richman: Arch. Rat. Mech. Anal. 87, 355–377 (1985a)

    Article  MATH  MathSciNet  Google Scholar 

  54. J.T. Jenkins, M.W. Richman: Phys. Fluids 28, 3485–3494 (1985b)

    Article  MATH  ADS  Google Scholar 

  55. J.T. Jenkins, M.W. Richman: J. Fluid Mech. 171, 53–69 (1986)

    Article  MATH  ADS  Google Scholar 

  56. J.T. Jenkins, S.B. Savage: J. Fluid Mech. 130, 186–202 (1983)

    Article  ADS  Google Scholar 

  57. G. Johnson, M. Massoudi, K.R. Rajagopal: Chem. Engng. Sci. 46(7), 1713–1723 (1991)

    Article  Google Scholar 

  58. G. Johnson, M. Massoudi, K.R. Rajagopal: Int. J. Engng. Sci. 29, 649–661 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  59. G. Johnson, M. Massoudi, K.R. Rajagopal: Rec. Adv. Mech. Strctd. Cont. AMD 117, 97–105 (1991)

    Google Scholar 

  60. P.C. Johnson, R. Jackson: J. Fluid Mech. 130, 187–202 (1987)

    Google Scholar 

  61. P.C. Johnson, P. Nott, R. Jackson: J. Fluid Mech. 210, 501–535 (1990)

    Article  ADS  Google Scholar 

  62. P.Y. Julien, Y. Lan: J. Hydraulic Eng. 117(3), 346–353 (1991)

    Article  Google Scholar 

  63. N. Kirchner: Thermodynamics of Structured Granular Media. Ph.D. Thesis, Institute of Mechanics, Darmstadt University of Technology (2001)

    Google Scholar 

  64. N. Kirchner, K. Hutter: ‘Thermodynamic modelling of granular continua exhibiting quasi-static frictonal behaviour with abrasion’. In: Mathematical Models of granular and porous materials. ed. by G. Capriz, G. Ghionna, P. Giovine (Modelling and Simulation in Science, Engineering and Technology Series, Birkhaeuser 2001)

    Google Scholar 

  65. T. Koch, R. Greve, K. Hutter: Proc. R. Soc. London A445, 415–435 (1994)

    Article  MATH  ADS  Google Scholar 

  66. D. Kolymbas: Ing. Arch. 61, 143–151 (1991)

    MATH  Google Scholar 

  67. D. Kolymbas, W. Wu: ‘Introduction to hypoplasticity’. In: Modern Approaches to Plasticity, ed. by D. Kolymbas (Elsevier, 1993) pp. 213–223

    Google Scholar 

  68. L.D. Landau, E.M. Lifschitz: Elastizitätstheorie (Akademie-Verlag, Berlin 1989)

    MATH  Google Scholar 

  69. J. Lee, H.J. Herrmann: J. Phys. A: Math. Gen. 26, 373 (1993)

    Article  ADS  Google Scholar 

  70. I-Shih Liu: Arch. Rat. Mech. and Anal. 46, 131–148 (1972)

    MATH  ADS  Google Scholar 

  71. K.F. Liu, C.C. Mei: Physics of Fluids A6(8), 2577–2590 (1994)

    Article  ADS  Google Scholar 

  72. S. Luding: Die Physik kohäsionsloser granularere Medien. Habilitation (Logos Verlag, Berlin 1997) pp. 1–197

    Google Scholar 

  73. C.K.K. Lun, S.B. Savage, D.J. Jeffrey, N. Chepurniy: J. Fluid Mech. 140, 233–256 (1984)

    Article  ADS  Google Scholar 

  74. D.N. Ma, G. Ahmadi: Power Tech. 56, 191 (1988)

    Article  Google Scholar 

  75. M. Massoudi: Application of mixture theory to fluidized beds. Ph.D. Thesis, University of Pittsburgh (1986)

    Google Scholar 

  76. M. Massoudi, E.J. Boyle: A review of theories for flowing granular materials with applications to fluidized beds and solids transport. U.S. Department of energy Report, DOE/PETC/TR-91/8 (1991)

    Google Scholar 

  77. J.J. McCarthy, J.E. Wolf, T. Shinbrot, G. Metcalfe: AICHE 42, 3351–3363 (1996)

    Article  Google Scholar 

  78. D.F. McTigue: A nonlinear continuum theory for flowing granular materials. Ph.D. Thesis, Dept. of Geol., Stanford University (1979)

    Google Scholar 

  79. D.F. McTigue: J. Appl. Mech. 49, 291–296 (1982)

    Article  MATH  Google Scholar 

  80. S. Melin: Int. J. Mod. Phys. C 4, 1103 (1993)

    Article  ADS  Google Scholar 

  81. G. Metcalfe, T. Shinbrot, J.J. McCarthy, J.M. Ottino: Nature 374, 39–41 (1995)

    Article  ADS  Google Scholar 

  82. I. Müller: Arch. Rat. Mech. and Anal. 40 (1971)

    Google Scholar 

  83. I. Müller: Thermodynamics (Pitmann, Boston 1985)

    MATH  Google Scholar 

  84. Q.D. Nguyen, D.V. Boger: J. Rheol. 27, 321–349 (1983)

    Article  Google Scholar 

  85. H. Norem, F. Irgens, B.A. Schieldrop: ‘A continuum model for calculating snow avalanches’. In: Avalanche Formation, Movement and Effects, ed. by B. Salm, H. Gubler (IAHS publ. Noangemessen. 126, 1987) pp. 363–379

    Google Scholar 

  86. J.W. Nunziato, S.C. Cowin: Arch. Rotational Mech. Anal. 72, 175–201 (1979)

    MATH  ADS  MathSciNet  Google Scholar 

  87. J.W. Nunziato, S.L. Passman, J.P. Thomas: J. Rheol. 24, 395–420 (1980)

    Article  MATH  ADS  Google Scholar 

  88. S. Ogawa, A. Unemura, N. Oshima: J. Appl. Math. Phys. 31, 483–493 (1980)

    Article  MATH  Google Scholar 

  89. T. Ohtsuki, Y. Takemoto, T. Hata, S. Kawai, A. Hayashi: Int. J. Mod. Phys. B 7, 1865–1872(1993)

    Article  ADS  Google Scholar 

  90. S.L. Passman, J.W. Nunziato, P.B. Bailey: J. Rheol. 30, 167–192(1986)

    Article  MATH  ADS  Google Scholar 

  91. S.L. Passman, J.W. Nunziato, P.B. Bailey, J.P. Thomas: J. Eng. Mech. Division, ASCE 106, 773–783 (1980)

    Google Scholar 

  92. T. Pöschel: J. Phys. II France 3, 27 (1993)

    Article  Google Scholar 

  93. K.R. Rajagopal, M. Massoudi: A method for measuring material moduli of granular materials: flow in an orthogonal rheometer. Topical Report U, Department of Energy. DOE/PETC/TR-90/3 (1990)

    Google Scholar 

  94. K.R. Rajagopal, W.C. Troy, M. Massoudi: Eur. J. Mech., B/Fluids 11, 265–276 (1992)

    MATH  MathSciNet  Google Scholar 

  95. G.H. Ristow: Int. J. Mod. Phys. C 3, 1281–1293 (1992)

    Article  ADS  Google Scholar 

  96. G.H. Ristow: Europhys. Lett. 28, 97–101 (1994a)

    Article  ADS  Google Scholar 

  97. G.H. Ristow: Flow properties of granular materials in three-dimensional geometries. Habilitation, Philipps-Universität Marburg, pp. 1–111 (1998)

    Google Scholar 

  98. G.H. Ristow, H.J. Herrmann: Phys. Rev. E 50, R5–R8 (1994)

    Article  ADS  Google Scholar 

  99. R.S. Sampaio, W.O. Williams: J. de Mechanique 18, 19–45 (1979)

    ADS  MathSciNet  MATH  Google Scholar 

  100. S.B. Savage: J. Fluid Mech. 92, 53–96 (1979)

    Article  MATH  ADS  Google Scholar 

  101. S.B. Savage: ‘Granular flows down rough inclines-review and extension’. In: Mech. of Granular Materials: New Models and Constitutive Relations, ed. by J.T. Jenkins, M. Satake (Elsevier 1983) pp. 261–282

    Google Scholar 

  102. S.B. Savage, K. Hutter: J. Fluid Mech. 199, 177–215 (1989)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  103. S.B. Savage, K. Hutter: Acta Mech. 86, 201–223 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  104. S.B. Savage, D.J. Jeffrey: J. Fluid Mech. 110, 255–272 (1981)

    Article  MATH  ADS  Google Scholar 

  105. S.B. Savage, C.K.K. Lun: J. Fluid Mech. 189, 311–335 (1988)

    Article  ADS  Google Scholar 

  106. S.B. Savage, S. McKeown: J. Fluid Mech. 127, 453–472(1983)

    Article  ADS  Google Scholar 

  107. S.B. Savage, M. Sayed: J. Fluid Mech. 142, 391–430 (1984)

    Article  ADS  Google Scholar 

  108. T. Scheiwiller, K. Hutter: ‘Lawinendynamik, Übersicht über Experimente und theoretische Modelle von Fließ-und Staublawinen’. Mitteilung N0. 58 der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie an der ETH Zürich, pp. 166 (1982)

    Google Scholar 

  109. W.R. Schowalter: Mechanics of non-Newtonian fluids (Pergamon Press, Oxford 1978)

    Google Scholar 

  110. M. Shahinpoor, S.P. Lin: Acta Mechanica 42, 183–196 (1982)

    Article  MATH  Google Scholar 

  111. M. Shahinpoor, J.S.S. Siah: J. Non-Newt. Fluid Mech. 9, 147–156 (1981)

    Article  MATH  Google Scholar 

  112. H. Shen, N.L. Ackerman: J. Eng. Mech. Div. 108, 748–763 (1982)

    Google Scholar 

  113. S. Straub: Schnelles granular Fließen in subaerischen pyroklastischen Strömen. PhD thesis, Bayerische Julius-Maximilians-Universität Würzburg (1994)

    Google Scholar 

  114. B. Svendsen, K. Hutter: Int. J. Engng Sci. 33, 2021–2054 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  115. B. Svendsen, K. Hutter, L. Laloui: Continuum Mech. Thermodyn. 11, 263–275 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  116. Y.C. Tai: Dynamics of Granular Avalanches and their Simulations with Shock-Capturing and Front-Tracking Numerical Schemes. Ph.D. Thesis, DarmstadtUniversity of Technology, 146 p (2000)

    Google Scholar 

  117. P.A. Thompson, G.S. Grest: Phys. Rev. Lett. 67, 1751 (1991)

    Article  ADS  Google Scholar 

  118. Y. Tsuji, T. Tanaka, T. Ishida: Powder Technol. 71, 239 (1992)

    Article  Google Scholar 

  119. O.R. Walton, R.L. Braun: J. Rheology 30, 949–980 (1986)

    Article  ADS  Google Scholar 

  120. O.R. Walton, R.L. Braun, R.G. Mallon, D.M. Cervelli: ‘Particle-dynamics calculations of gravity flow of inelastic, frictional spheres’. In: Micromechanics of Granular Materials, ed. by M. Satake, J.T. Jenkins (Elsevier 1987) pp. 153–162

    Google Scholar 

  121. O.R. Walton, H. Kim, A. Rosato: ‘Micro-structure and stress difference in shearing flows of granular materials’. In: Proc. ASCE Eng. Mech. Div. Conf. (Columbus, Ohio, May 19–21, 1991)

    Google Scholar 

  122. Y. Wang, K. Hutter: Particulate Science and Technology 17, 97–124 (1999)

    Article  Google Scholar 

  123. Y. Wang, K. Hutter: Granular Matter 1(4), 163–181 (1999)

    Article  Google Scholar 

  124. Y. Wang, K. Hutter: Arch. Mech. 51(5), 605–632(1999c)

    MATH  MathSciNet  Google Scholar 

  125. K. Wilmanski: Arch. Mech. 48, 591–628 (1996)

    MATH  Google Scholar 

  126. K. Wilmanski: The thermodynamical model of compressible porous materials with the balance equation of porosity. Preprint No. 310, ed. by Weierstraß-Institute für Angewandte Analysis und Stochastik, Berlin (1997)

    Google Scholar 

  127. W. Wu, E. Bauer, D. Kolymbas: Mech. Mat. 24, 45–69 (1996)

    Article  Google Scholar 

  128. Y. Zhang, C.S. Campbell: J. Fluid Mech. 237, 541 (1992)

    Article  ADS  Google Scholar 

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  1. Institute of Mechanics, Darmstadt University of Technology, Hochschulstr. 1, 64289, Darmstadt, Germany

    Y. Wang & K. Hutter

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  1. School of Engineering, University of California at Santa Cruz, 1156 High St., 95064, Santa Cruz, CA, USA

    N. J. Balmforth

  2. Istituto di Scienze dell’Atmosfera e del Clima, CNR, Corso Fiume 4, 10133, Torino, Italy

    A. Provenzale

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Wang, Y., Hutter, K. (2001). Granular Material Theories Revisited. In: Balmforth, N.J., Provenzale, A. (eds) Geomorphological Fluid Mechanics. Lecture Notes in Physics, vol 582. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45670-8_4

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