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Introduction to Computational Granular Mechanics

  • Conference paper
Book cover Behaviour of Granular Materials

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 385))

Abstract

The first discrete modeling of soils can be traced to Hertz [90] who formulated a contact law between spheres, and Reynolds [167] who proposed a dilatancy theory. Dantu [55] and Schneebli [180] idealized real soils as assemblies of rigid rods, and noticed some striking similarities between the mechanical responses of these mechanical analogs and real soils. Duffy and Mindlin [70], Deresiewicz [59, 60], and Thurston and Deresiewicz [204] examined the response of soil models made of spheres. Biarez [21] used glass beads and duralumium rods to examine the elastic and limit response of soils, and applied his observations to analyze practical problems in geotechnical engineering. These pioneer works were later followed by photoelastic investigations [e.g., 67, 68] to visualize stresses within granular media.

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References

  1. Aizawa, T., S. Tamura, Y. Shibata, J. Okuno, and J. Kihara, 1993, Powder granular modeling and simulation for agglomeration, Proceedings of the 6 th international symposium on agglomeration, Nagoya, Japan, 70–75.

    Google Scholar 

  2. Anandarajah, A., 1994, Micromechanics of clays evaluated by the discrete element methods, Proceedings of the 8th International Conference on Computer Methods and Advances in Geomechanics, Morgantown, VA, H. J. Siriwardane, and M. M. Zaman, Balkema, Rotterdam, The Netherlands, 797–802.

    Google Scholar 

  3. Azarkhin, A., 1988, Some history dependent problems for dissimilar cylinders with finite friction, Journal of Applied Mechanics, ASME, 55; 81–86.

    Google Scholar 

  4. Bardet, J. P., 1994, Numerical simulations of the incremental responses of idealized granular materials, International Journal of Plasticity, 10 (8), 879–980.

    MATH  Google Scholar 

  5. Bardet, J. P., 1994, Observations on the effects of particle rotations on the failure of idealized granular materials, Mechanics of Materials, 18, 159–182.

    Google Scholar 

  6. Bardet, J. P., 1997, Experimental Soil Mechanics, Prentice-Hall, Upper Saddle River, NJ.

    Google Scholar 

  7. Bardet, J. P., and J. Proubet, 1989, JP2, a program to simulate the behavior of two-dimensional granular materials, Civil Engineering Department, University of Southern California, Los Angeles, CA.

    Google Scholar 

  8. Bardet, J. P., and J. Proubet, 1991, A numerical investigation of the structure of persistent shear bands in granular materials, Géotechnique, 41 (4), 599–613.

    Google Scholar 

  9. Bardet, J. P., and J. Proubet, 1991, Adaptative relaxation technique for the statics of granular materials, Computers and Structures, 39 (3/4), 221–229.

    Google Scholar 

  10. Bardet, J. P., and J. Proubet, 1992, A shear band analysis in idealized granular materials, Journal of Engineering Mechanics, ASCE, 118 (2), 397–415.

    Google Scholar 

  11. Bardet, J. P., and Q. Huang, 1992, Numerical modeling of micropolar effects in idealized granular materials, in Mechanics of granular materials and powder systems, M. M. Mehrabadi, ed., ASME, 37, 85–92.

    Google Scholar 

  12. Bardet, J. P., and Q. Huang, 1993, Rotational stiffness of cylindrical particle contacts, Proceedings of the 2n d International Conference on Micromechanics of Granular Media, Birmingham, UK, C. Thornton, ed., 39–44.

    Google Scholar 

  13. Bardet, J. P., and R. F. Scott, 1985, Seismic stability of fractured rock masses with the distinct element method, Proceedings of the 26 th Us Symposium on Rock Mechanics, Rapid City, SD, E. Ashworth, ed., 139–149.

    Google Scholar 

  14. Bashir, Y. M. and J. D. Goddard, 1991, A novel simulation method for the quasistatic mechanics of granular assemblages, J. Rheology, 35 (5), 849–885.

    Google Scholar 

  15. Bathe, K. J., 1996, Finite element procedures, Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  16. Bathurst, R. J., and L. Rothenburg, 1988, Micromechanical aspects of isotropic granular assemblies with linear contact interactions, Journal of Applied Mechanics, ASME, 55, 17–23.

    Google Scholar 

  17. Bathurst, R. J., and L. Rothenburg, 1988, Note on a random isotropic granular material with negative Poisson’s ratio, International Journal of Engineering Sciences, 26 (4), 373–383.

    MATH  Google Scholar 

  18. Bathurst, R. J., and L. Rothenburg, 1990, Observations on stress-force-fabricrelationships in idealized granular materials, Mechanics of Materials, 9, 65–80.

    Google Scholar 

  19. Behringer, R. P., and J. T. Jenkins, Eds., 1997, Proceedings of the 3.d International Conference on Powders and Grains, Durham, NC, Balkema, Rotterdam, the Netherlands.

    Google Scholar 

  20. Bentall, R. H., and K. L. Johnson, 1967 Slip in the rolling contact of two dissimilar elastic rollers, Int. J. Mech. Sci., 9 (55), 389–404.

    Google Scholar 

  21. Biarez, J., 1962, Contribution à l’ étude des propriétés mécaniques des sols et des materiaux pulvérulents, Ph.D. Thesis, University of Grenoble, France.

    Google Scholar 

  22. Biarez, J., and R. Gourves, Eds., 1989, Proceedings of the l’ s ` International Conference on Powders and Grains, Clermont-Ferrand, France, Balkema, Rotterdam, the Netherlands.

    Google Scholar 

  23. Bishop, A. W., 1954, Correspondence on shear characteristics of a saturated silt measured in triaxial compression, Géotechnique, 4 (1), 43–45.

    Google Scholar 

  24. Bogdanova-Bontcheva, N., and H. Lippmann, 1975, Rotationssymmetrisches ebenes Fließen eines granularen Modellmaterials, Acta Mechanica, 21, in German, 93–113.

    Google Scholar 

  25. Borja, R. L and J. R. Wren, 1995a, Micromechanics of granular media, Part I: Generation of overall constitutive equation for assemblies of circular disks, Comput. Methods Appli. Mech. Engrg., 127, 13–36.

    MATH  MathSciNet  Google Scholar 

  26. Borja, R. I. and J. R. Wren, 1995b, Micromechanics of continuum models for granular materials, Proc. 10th Conf Engineering Mechanics, ASCE, S. Sture, ed., 11, 497–500.

    Google Scholar 

  27. Brogliato, B., 1996, Nonsmooth Impact Mechanics. Models, Dynamics and Control,Lecture Notes in Control and Information Sciences, 220, Springer-Verlag

    Google Scholar 

  28. Bromwell, L. W., 1966, The friction of quartz in high vacuum, M.I.T. Department of Civil Engineering, Research Report B66–18.

    Google Scholar 

  29. Campbell, C. S., and C. E. Brennen, 1985, Computer simulation of granular shear flow, Journal of Fluid Mechanics, 151, 167–188.

    Google Scholar 

  30. Carter, F.W, 1926, On the action of a locomotive driving wheel, Proc. Royal Society, A112, 151–157.

    MATH  Google Scholar 

  31. Chang, C. S., 1993, Micromechanical modeling of deformation and failure for granulates with frictional contacts, Mechanics of Materials, 16, 13–24.

    Google Scholar 

  32. Chang, C. S., A. Misra, and K. Acheampong, 1992, Elastoplastic deformation for particulates with frictional contacts, Journal of Engineering Mechanics, ASCE, 118 (8), 1692–1707.

    Google Scholar 

  33. Chang, C. S., A. Misra, and S. Sundararam, 1990, Micromechanical modeling of cemented sands under low amplitude oscillations, Géotechnique, 40 (2), 251–263.

    Google Scholar 

  34. Chang, C. S., and A. Misra, 1989, Computer simulation and modeling of mechanical properties of particulates, Computers and Geotechnics, 7 (4), 269–287.

    Google Scholar 

  35. Chang, C. S., and A. Misra, 1990, Packing structure and mechanical properties of granulates, Journal of Engineering Mechanics, ASCE, 116 (5), 1077–1093.

    Google Scholar 

  36. Chang, C. S., and C. S. Liao, 1990, Constitutive relation for a particulate medium with the effect of particle rotation, Int. J. Solids and Structures, 26 (4), 437–455.

    MATH  Google Scholar 

  37. Chang, C. S., and J. Gao, 1995, Second-gradient constitutive theory for granular material with random packing structure, Int. J. Solids and Structures, 32 (16), 22792293.

    Google Scholar 

  38. Chang, C. S., and L. Ma, 1991, A micromechanical-based micropolar theory for deformation of granular solids, Int. J. Solids and Structures, 28 (1), 67–86.

    MATH  Google Scholar 

  39. Chang, C. S., M. G. Kabir, and Y. Chang, 1992b, Micromechanical modeling for tress-strain behavior of granular soils. II: Evaluation Journal of Geotechnical Engineering, ASCE, 118 (12), 1975–1992.

    Google Scholar 

  40. Chang, C. S., S. J. Chao, and Y. Chang, 1995, Estimates of elastic moduli for granular material with anisotropic random packing structure, Int. J. Solids and Structures, 32 (14), 1989–2008.

    MATH  Google Scholar 

  41. Chang, C. S., Y. Chang, and M. G. Kabir, 1992, Micromechanical modeling for stress-strain behavior of granular soils. I: Theory, Journal of Geotechnical Engineering, ASCE, 118 (12), 1959–1974.

    Google Scholar 

  42. Chichili, D. R., D. E. Mouton, and M. M. Mehrabadi, 1993, Simulation of the mechanical behavior of two-dimensional granular assemblies utilizing linear programming, Mechanics of Materials, submitted.

    Google Scholar 

  43. Christoffersen, J., M. M. Mehrabadi, and S. Nemat-Nasser, 1981, A micromechanical description of granular material behavior, Journal of Applied Mechanics, ASME, 48, 339–344.

    MATH  Google Scholar 

  44. Clément, E., J. Duran and J. Rajchenbach, 1992, Experimental study of heaping in a two-dimensional sandpile, Physics Review Letters, 69, 1189–1192.

    Google Scholar 

  45. Cosserat, E., and F. Cosserat, 1909, Théorie des corps déformables, Hermann, Paris.

    Google Scholar 

  46. Cundall, P. A, 1982, Adaptative density-scaling for time-explicit calculations, Proceedings of the 4 112 International Conference on Numerical methods in geomechanics, Edmonton, 23–26.

    Google Scholar 

  47. Cundall, P. A., 1971, A computer model for simulating progressive large scale movements of blocky rock systems, Proceedings of the Symposium of the International Society of Rock Mechanics, Nancy, France, 1, 132–150.

    Google Scholar 

  48. Cundall, P. A., 1980, UDEC - A generalized distinct element program for modeling jointed rock, Final Technical Report to European Research Office, US Army, Contract No. DMA 37–79-C-0548, NTIS order No. AD-A087 610 /2.

    Google Scholar 

  49. Cundall, P. A., 1988, Formulation of a three-dimensional distinct element model–Part I: A scheme to detect and represent contacts in a system composed of many polyhedral blocks, International Journal of Rock Mechanics, 25, 107–116.

    Google Scholar 

  50. Cundall, P. A., 1989, Numerical experiments on localization in frictional materials, Ingenieur-Archiv, 59, 148–159.

    Google Scholar 

  51. Cundall, P. A., 1989, Numerical modeling of discontinua, Proceedings of the l’ s` US Conference on Discrete Element Methods (DEM), G. G. W. Mustoe, M. Henriksen,. and H. -P. Huttelmaier, Eds., Colorado School of Mines Press, Golden, CO, 1–17.

    Google Scholar 

  52. Cundall, P. A., and O. D. L. Strack, 1978–1979, The distinct element method as a tool for research in granular media, Parts I and II, Report to National Science Foundation, Eng. 76–20711,Department of Civil and Mineral Engineering, University of Minnesota, Minneapolis, MN.

    Google Scholar 

  53. Cundall, P. A., and O. D. L. Strack, 1979, A discrete numerical model for granular assemblies, Géotechnique, 29, 47–65.

    Google Scholar 

  54. Cundall, P.A., A. Drescher, and O.D.L. Strack, 1982, Numerical experiments on granular assemblies; Measurement and observations, Proceedings of the IUTAM symposium on deformation and failure of granular materials, Delft, Balkema Publishers, P.A. Vermeer and H.J. Luger Eds., 355–370.

    Google Scholar 

  55. Dantu, P., 1957, Contribution à l’ étude mécanique et géometrique des milieux pulvérulents, Proceedings of the el m International Conference of Soil Mechanics and Foundation Engineering, London, UK.

    Google Scholar 

  56. Daudon, D., J. Lanier, and M. Jean, 1997, A micromechanical comparison between experimental results and numerical simulation of a biaxial test on 2D granular materials, Proceedings of the 3’ d International Conference on Powders and Grains, Durham, NC, R. P. Behringer and J. T. Jenkins, Eds., Balkema, Rotterdam, the Netherlands, 219–222.

    Google Scholar 

  57. de Josselin de Jong, G., 1959, Statics and kinematics of the failable zone of a granular material, Vitgeverij Waltman, Delft.

    Google Scholar 

  58. Delassus, E., 1917, Mémoire sur la théorie des liaisons finies unilatérales, Ann. Sci. Ecole Norm. Sup., 34, 95–179.

    MATH  MathSciNet  Google Scholar 

  59. Deresiewicz, H., 1958, Mechanics of granular material, Advd. Appl. Mech., 5, 233306.

    Google Scholar 

  60. Deresiewicz, H., 1958, Stress-strain relations for a simple model of a granular medium, Journal of Applied Mechanics, ASME, 403–406.

    Google Scholar 

  61. Desrues, J., 1984, Localization de la déformation plastique dans les matériaux granulaires, Thèse d’état, Université de Grenoble..

    Google Scholar 

  62. Desrues, J., and B. Duthilleul, 1984, Stereophotogrametric method applied to the determination of plane strain fields, Journal de Mécanique théorique et appliquée, 3 (1), 79–103.

    Google Scholar 

  63. Desrues, J., J. Lanier, and P. Stutz, 1985, Localization of the deformation in tests on sand samples, Engineering Fracture Mechanics, 21, 909–921.

    Google Scholar 

  64. Diepolder, W., V. Mannl, and H. Lippman, 1991, The Cosserat continuum, a model for grain rotations in metals?, International journal of plasticity, 7, 313–328.

    Google Scholar 

  65. Dobry, R., and T.-T. Ng, 1992, Discrete modeling of stress-strain behavior of granular media at small and large strain, Engineering Computations, 9, 129–143.

    Google Scholar 

  66. Doménech, A., T. Doménech, and J. Cebriân, 1987, Introduction to the study of rolling friction, American Journal of Physics, 55 (3), 231–235.

    Google Scholar 

  67. Drescher, A. 1976, An experimental investigation of flow rules for granular materials using optically sensitive glasss particles, Géotechnique, 26 (4), 591–601.

    Google Scholar 

  68. Drescher, A. and G. De Josselin de Jong, 1972, Photoelastic verification of a material model for the flow of a granular material. J. Mech. Phys. Solids, 20, 337–351.

    Google Scholar 

  69. Dubujet, P., B. Cambou, F. Dedecker, and F. Emeriault, 1997, Statistical homogenization for granular media–Application to non linear elastic modeling, Proceedings of the 3’ International Conference on Powders and Grains, Durham, NC, R. P. Behringer and J. T. Jenkins, Eds., Balkema, Rotterdam, the Netherlands, 199–202.

    Google Scholar 

  70. Duffy, J., and Mindlin, R.D., 1957, Stress-strain relations and vibrations of a granular medium, J. of Applied Mech., ASME, 79, 585–593.

    MathSciNet  Google Scholar 

  71. El-Sohby, A. A. K., 1969, Deformation of sand under constant stress ratio, Proceedings of the 7` h international conference in Soil Mechanics and Foundation Engineering, Mexico, 1, 111–119.

    Google Scholar 

  72. Eringen, A.C., 1966, Linear theory of micropolar elasticity, Journal of Mathematics and Mechanics, 15 (6, 909–923.

    Google Scholar 

  73. Eringen, A.C., 1967, Mechanics of Continua, John Wiley, New York, NY.

    Google Scholar 

  74. Fabrikant, V. I., 1986, Inclined flat punch of arbitrary shape on an elastic half-space, Journal of Applied Mechanics, ASME, 53, 798–806.

    MATH  Google Scholar 

  75. Fabrikant, V. I., 1988, Elastic field around a circular punch, Journal of Applied Mechanics, ASME, 55, 604–605.

    MATH  Google Scholar 

  76. Foerster, S., M. Louge, H. Chang and K. Allia, 1994, Measurements of the collision properties of small spheres, Phys. Fluids, 6, 1108–1115.

    Google Scholar 

  77. Frankel, S. P., 1950, Convergences rates of iterative treatments of partial differential equations, Mathl. Tabl. Natn. Res. Coun., Washington DC, 4, 65–75.

    MathSciNet  Google Scholar 

  78. Germain, P., 1973, La méthode des puissances virtuelles en mécanique des milieux continus. Théories due second gradient, Journal de Mécanique, 12 (2), 235–274.

    MATH  MathSciNet  Google Scholar 

  79. Germain, P., 1973, The method of virtual power in continuum mechanics. Part 2: Microstructures, J. of Applied Mathematics, SIAM, 25 (3), 556–575.

    MATH  MathSciNet  Google Scholar 

  80. Ghaboussi, J., and R. Barbosa, 1990, Three-dimensional discrete element method for granular materials, International Journal for Numerical and Analytical Methods in Geomechanics, 14, 451–472.

    Google Scholar 

  81. Goddard, J. D., 1977, An elastohydrodymanic theory for the rheology of concentrated suspensions of deformable particles, Journal of Non-Newtonian Fluid mechanics, 2, 169–189.

    MATH  Google Scholar 

  82. Goddard, J. D., 1986, Microstructural origins of continuum stress fields–A brief history and some unresolved issues, Chapter 6 in Recent developments in structured continua, D. DeKee and P. N. Kaloni, Eds., Pitman research notes in mathematics (143, Longman/J. Wiley, p. 179–208.

    Google Scholar 

  83. Goddard, J. D., X. Zhueng, and A. K. Didwania, 1993, Microcell methods and the adjacency matrix in the simulation of the mechanics of granular media, Proceedings of the 2 nd international conference on discrete element methods, Massachusetts Institute of Technology, J. R. Williams and G. W. Mustoe, Eds., March, 3–14.

    Google Scholar 

  84. Goodman, E. L., 1962, Contact stress analysis of normally loaded rough spheres, J. of Applied Mech., ASME, 515–522.

    Google Scholar 

  85. Gray, J. E., 1960, The relationship between principal stress dilatancy and friction angle of a granular materials, M. Sc. Thesis, University of Manchester, UK.

    Google Scholar 

  86. Greening, D. R., G. G. W. Mustoe, and G. L. DePorter, 1997, Discrete element modeling of fabrication flaw precursors in the compaction of agglomerated ceramic powders, Proceedings of the 3rd International Conference on Powders and Grains, Durham, NC, R. P. Behringer and J. T. Jenkins, Eds., Balkema, Rotterdam, the Netherlands, 113–116.

    Google Scholar 

  87. Hafiz, M. S., 1950, Strength characteristics of sands and gravels in direct shear, PhD thesis, University of London, UK.

    Google Scholar 

  88. Hahn, J. K., 1988, Realistic animation of rigid bodies, Computer graphics, 22. (4), 299–308.

    Google Scholar 

  89. Hart, R. D., P. A. Cundall, and J. Lemos, 1988, Formulation of a three-dimensional distinct element model–Part II: Mechanical calculations for motion and interaction of a system composed of many polyhedral blocks, International Journal of Rock Mechanics, 25, 117–126.

    Google Scholar 

  90. Hertz, H., 1882, Über die Berührung fester elastische Körper and über die Harte (On the contact of rigid elastic solids and on hardness), Verhandlungen des Vereins zur Befôrderung des Gewerbefleisses, Leipzig.

    Google Scholar 

  91. Hill, R., 1962, Acceleration waves in solids, J. Mech. Phys. Solids, 10, 1–16.

    MATH  MathSciNet  Google Scholar 

  92. Hill, R., 1967, The essential structure of constitutive laws for metal composite and polycrystals, J. Mech. Physics Solids, 11, 357–372.

    Google Scholar 

  93. Hocking, G., G. G. W. Mustoe, and J. R. Williams, 1985, CICE discrete element analysis code - theoretical manual, Applied Mechanics Inc., Lakewood, CO.

    Google Scholar 

  94. Hong, C.-W., 1997, Process modeling and design for colloidal powder forming, Proceedings of the 3rd International Conference on Powders and Grains, Durham, NC, R. P. Behringer and J. T. Jenkins, Eds., Balkema, Rotterdam, the Netherlands, 41–44.

    Google Scholar 

  95. Horn, H. M., and D. V. Deere, 1962, Frictional characteristics of minerals, Géotechnique, 12 (4), 319–335.

    Google Scholar 

  96. Horne, M. R., 1965, The behavior of an assembly of rotund, rigid, cohesionless particles (I and II), Proc. Roy. Soc. London, A286, 62.

    Google Scholar 

  97. Home, M. R., 1969, The behavior of an assembly of rotund, rigid, cohesionless particles (III), Proc. Roy. Soc. London, A310, 21.

    Google Scholar 

  98. Houlfsly, G.T., 1981, A study of plasticity theory and their applicability to soils, Ph.D. thesis, University of Cambridge.

    Google Scholar 

  99. Hughes, T. J. R., 1983, Analysis of transient algorithms with particular reference to stability behavior, Computational methods for transient analysis, T. Belitschko, and T.J.R. Hughes, Eds., North Holland, Amsterdam, Holland, 67–156.

    Google Scholar 

  100. Hughes, T. J. R., 1987, The finite element method, Prentice-Hall, Englewoods Cliffs, NJ.

    Google Scholar 

  101. Hughes, T. J. R., and T. Belytschko, 1993, Nonlinear finite element analysis, Short course notes, Stanford, CA.

    Google Scholar 

  102. Jagota, A., C. Argento, and S. Mazur, 1997, Viscoelastic coalescence of spherical particles, Proceedings of the 3rd International Conference on Powders and Grains, Durham, NC, R. P. Behringer and J. T. Jenkins, Eds., Balkema, Rotterdam, the Netherlands, 31–36.

    Google Scholar 

  103. Jean, M., 1995, Frictional contact in collections of rigid or deformable bodies: numerical simulation of geomaterials, in Mechanics of Geomaterial Interfaces, Eds. A. P. S. Salvadurai and M. J. Boulon, Elsevier Science Publisher, Amsterdam, 463–486.

    Google Scholar 

  104. Jean, M., and J. J. Moreau, 1996, Numerical treatment of contact and friction: the Contact Dynamics method, Proc.1996 Engineering Systems Design and Analysis Conference,Eds. A. Lagarde and M. Raous, ASCE, New York, 4, 201–208.

    Google Scholar 

  105. Johnson, D. L., L. M. Schwartz, D. Elata, J. G. Berryman, B. Hornby, and A. N. Norris, 1997, Linear and nonlinear elasticity of granular media: Stress-induced anisotropy of a random sphere pack, Proceedings of the 3rd International Conference on Powders and Grains, Durham, NC, R. P. Behringer and J. T. Jenkins, Eds., Balkema, Rotterdam, the Netherlands, 243–246.

    Google Scholar 

  106. Johnson, K. L., 1958, The effect of spin upon the rolling motion of an elastic sphere on a plane, Journal of Applied Mechanics, September, 332–338.

    Google Scholar 

  107. Johnson,. K. L., 1958, The effect of tangential contact force upon the rolling motion of an elastic sphere on a plane, Journal of Applied Mechanics, September, 339–346.

    Google Scholar 

  108. Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.

    Google Scholar 

  109. Kalker, J. J., 1970, Transient phenomena in two elastic cylinders rolling over each other with dry friction, J. of Applied Mech., ASME, 677–688.

    Google Scholar 

  110. Kalker, J. J., 1990, Three-dimensional elastic bodies in rolling contact, Kluwer Academic Publishers, Dordrecht, The Netherlands, 59–97.

    Google Scholar 

  111. Kanatani, K., 1979, A micro-polar continuum theory for the flow of granular materials, Int. Journal of Engineering Science, 17 (4), 419–432.

    MATH  Google Scholar 

  112. Kawaguchi, T., Y. Yamamoto, T. Tanaka, and Y. Sudji, 1995, Numerical simulation of a single rising bubble in a two–dimensional fluidized bed, Proceedings of the 2nd International Conference on Multiphase Flows, Kyoto, Japan, FB2–17–22.

    Google Scholar 

  113. Ke, T.-C., and J. Bray, 1995, Modeling of particulate media using discontinuous deformation analysis, Journal of Engineering Mechanics, ASCE, 121 (11), 12341243.

    Google Scholar 

  114. Kishino, Y., 1988, Disc model analysis of granular media, in Micromechanics of Granular Materials, M. Satake and J. T. Jenkins, Eds., Elsevier Science Publishers, Amsterdam, The Netherlands, 143–152.

    Google Scholar 

  115. Knight, J. B., H. M. Jaeger and S. R. Nagel, 1993, Vibration-induced size separation in granular media: the convection connection, Physics Review Letters, 70, 37283731.

    Google Scholar 

  116. Koenders, M. A., 1987, The incremental stiffness of an assembly of particles, Acta Mechanica, 70, 31–49.

    MATH  Google Scholar 

  117. Krawietz, A., 1982, Some features of the gross behavior of granular media from micromechanics, Proceedings of the IUTAM conference on deformation and failure of granular materials, Delft, Balkema, Rotterdam, The Netherlands, 29–36.

    Google Scholar 

  118. Laalai, K. Sab, and N. Guérin, 1995, Micromechanical modelling of ballasted tracks, in Contact Mechanics, Eds. M. Raous et al., Plenum Press, New York, 363368.

    Google Scholar 

  119. LaBudde, R. A., and D. Greenspan, 1976, Energy and momentum conserving methods of arbitrary order for the numerical integration of equation of motion, I. Motion of a single particle, II. Motion of a system of particles, Numerical Mathematics, 25, 323–346; 26, 1–16.

    MathSciNet  Google Scholar 

  120. Lambe, T. W. and R. V. Whitman, 1979, Soil Mechanics, John Wiley and Sons, New York, N.Y.

    Google Scholar 

  121. Lecornu, L., 1905, Sur la loi de Coulomb, Comptes Rendus Acad. Sci. Paris, 140, 847–848.

    MATH  Google Scholar 

  122. Lee, I. K., 1966, Stress dilatancy performance of feldspar, Journal of the Soil Mechanics and Foundations Division, ASCE, 92, SM2, 79–103.

    Google Scholar 

  123. Lesburg, L., X. Zhang, L. Vu-Quoc, and O. R. Walton, 1997, Simplified tangential force-displacement models for a discrete element particle flow code, Proceedings of the 3rd International Conference on Powders and Grains, Durham, NC, R. P. Behringer and J. T. Jenkins, Eds., Balkema, Rotterdam, the Netherlands, 243–246.

    Google Scholar 

  124. Lian, G., C. Thornton, and M. J. Adams, 1997, A microscopic simulation of oblique collision of wet agglomerates, Proceedings of the 3rd International Conference on Powders and Grains, Durham, NC, R. P. Behringer and J. T. Jenkins, Eds., Balkema, Rotterdam, the Netherlands, 159–162.

    Google Scholar 

  125. Lun, C. K. K., and A. A. Bent, 1993, Computer simulation of simple shear flow of inelastic frictional spheres, Proceedings of the 2nd International Conference on Micromechanics of Granular Media, Birmingham, UK, C. Thornton, ed., Balkema, Rotterdam, 301–306.

    Google Scholar 

  126. Manna, S. S., and H. J. Herrmann, 1991, Precise determination of the fractal dimensions of Appolonian packing and space-filling bearings, Journal of Physics, A: Math. Gen., 24, 481–490.

    MathSciNet  Google Scholar 

  127. Matsuoka, H., and S. Yamamoto, 1994, A microscopic studdy on shear mechanism of granular materials by DEM, Journal of Geotechnical Engineering, JSCE, In Japanese, 487, 167–175.

    Google Scholar 

  128. Meakin P., and A. T. Skeltorp, 1993, Application of experimental and numerical methods to the physics of multiparticle systems, Advances in Physics, 42 (1), 1–127.

    Google Scholar 

  129. Meftah, W. P. Evesque, J. Biarez, D. Sornette, and N. E. Abriak, 1993, Evidence of local ‘seisms’ of microscopic and macroscopic stress fluctuations during the deformation of packings of grains, in Powders and Grains, C. Thornton, ed., Balkema, Rotterdam, 173–178.

    Google Scholar 

  130. Mehrabadi, M. M., B. Loret, and S. Nemat-Nasser, 1993, Incremental constitutive relations for granular materials based on micromechanics, Proceedings of the Royal Society, London, A 441, 443–463.

    Google Scholar 

  131. Mehrabadi, M. M., S. Nemat-Nasser, and M. Oda, 1982, On statistical description of stress and fabric in granular materials, Int. Journal for Numerical and Analytical Methods in Geomechanics, 6, 95–108.

    MATH  MathSciNet  Google Scholar 

  132. Mindlin, R. D., 1949, Compliance of elastic bodies in contact, Journal of Applied Mechanics, ASME, 71, 259–268.

    MathSciNet  Google Scholar 

  133. Mindlin, R. D., and H. Deresiewicz, 1953, Elastic spheres in contact under varying oblique forces, Journal of Applied Mechanics, ASME, 20, 327–344.

    MATH  MathSciNet  Google Scholar 

  134. Misra, A., 1995, Interfaces in particulate materials, Mechanics of geomaterial interfaces, A. P. S. Selvadurai and M. Boulon, Eds., Elsevier.

    Google Scholar 

  135. Monteiro Marques, M. D. P., 1993, Differential Inclusions, in Nonsmooth Mechanical Problems: Shocks and Dry Friction, Berlin, Germany.

    Google Scholar 

  136. Moreau, J. J., 1966, Quadratic programming in mechanics• dynamics of one-sided constraints, SIAM J. Control, 4, 153–158.

    MathSciNet  Google Scholar 

  137. Moreau, J. J., 1988, Bounded variation in time, in Topics in Nonsmooth Mechanics, J. J. Moreau, P. D. Panagiotopoulos and G. Strang, Eds., Berlin, Germany, 1–74.

    Google Scholar 

  138. Moreau, J. J., 1988, Unilateral contact and dry friction in finite freedom dynamics, in Nonsmooth Mechanics and Applications, J. J. Moreau and P. D. Panagiotopoulos, Eds., CISM Courses and Lectures, 302, Springer-Verlag, Wien, New York, 1–82.

    Google Scholar 

  139. Moreau, J. J., 1993, New computation methods in granular dynamics, Proceedings of the 2nd International Conference on Micromechanics of Granular Media, Birmingham, C. Thornton, ed., Balkema, Rotterdam, The Netherlands, 227–232.

    Google Scholar 

  140. Moreau, J. J., 1994, Some numerical methods in multibody dynamics: application to granular materials, Eur. J. Mech. Solids, 13, 93–114.

    MATH  MathSciNet  Google Scholar 

  141. Moreau, J. J., 1995, Numerical experiments in granular dynamics: vibration-induced size segregation, in Contact Mechanics, M. Raous et al., Eds., Plenum Press, New York, 347–358.

    Google Scholar 

  142. Moreau, J. J., 1996, Numerical investigation, of shear zones in granular materials, Proceedings of the HLRZ-workshop on Friction, Arching and contact Dynamics, Jülich, Germany, October.

    Google Scholar 

  143. Mühlhaus, H. B., and I. Vardoulakis, 1987, The thickness of shear bands in granular materials, Géotechnique, 37, 271–283.

    Google Scholar 

  144. Mujinza, A., N. Bicanic, and D. R. J. Owen, 1993, BSD contact detection algorithm for discrete elements in 2D, Proceedings of the 2n d international conference on discrete element methods, Massachusetts Institute of Technology, J. R. Williams and G. W. Mustoe, Eds., March, 39–52.

    Google Scholar 

  145. Mustoe, G. G. W., M. Henriksen, and H. -P. Huttelmaier, Eds., 1989, Proceedings of the I rs` US Conference on Discrete Element Methods (DEM), Colorado School of Mines Press, Golden, CO.

    Google Scholar 

  146. Nakase, H., T. Annaka, F. Katahira, and T. Kyono, 1992, An application study of the distinct element method to plane strain compression tests, Soils and Foundations, in Japanese, 454, 55–64.

    Google Scholar 

  147. Nemat-Nasser, S., and M. M. Mehrabadi, 1983, Micromechanically based rate constitutive description for granular materials, Proceedings of International Conference on Constitutive Laws for Engineering Materials; Theory and Applications, Tucson, A2.

    Google Scholar 

  148. Nemat-Nasser, S., and M. M. Mehrabadi, 1984, Micromechanically based rate constitutive descriptions for granular materials, Mechanics of Engineering Materials, C.S. Desai and R.H. Gallagher, Eds, John Wiley and Sons, New York, 451–463.

    Google Scholar 

  149. Ng, T. -T. and R. Dobry, R., 1994, Numerical simulation of monotonic and cyclic loading of granular soil, Journal of Geotechnical Engineering, ASCE, 120 (2), 388403.

    Google Scholar 

  150. Ng, T. -T., 1992, A non-linear numerical model for soil mechanics, International Journal for Numerical and Analytical Methods in Geomechanics, 16, 247–263.

    Google Scholar 

  151. O’connor, R., J. Gill, and J. R. Williams, 1993, A linear complexity contact detection algorithm for multi-body analysis, Proceedings of the 2 “d international conference on discrete element methods, Massachusetts Institute of Technology, J. R. Williams and G. W. Mustoe, Eds., 53–64.

    Google Scholar 

  152. Oda, M., 1972, Deformation mechanism of sand in triaxial compression tests, Soils and Foundations, Japanese Society of Soil Mechanics and Foundation Engineering, 12, 45–63.

    Google Scholar 

  153. Oda, M., 1972, Initial fabrics and their relations to mechanical properties of granular material, Soils and Foundations, Japanese Society of Soil Mechanics and Foundation Engineering, 12, 18–36.

    Google Scholar 

  154. Oda, M., 1972, The mechanism of fabric changes during compressional deformation of sand, Soils and Foundations, Japanese Society of Soil Mechanics and Foundation Engineering, 12, 1–17.

    Google Scholar 

  155. Oda, M., 1993, Micro-fabric and couple-stress in shear bands of granular materials, Proceedings of the 2 “d International Conference on Micromechanics of Granular Media, Birmingham, UK, C. Thornton, ed., 161–166.

    Google Scholar 

  156. Oda, M., and J. Konishi, 1974, Microscopic deformation mechanism of granular material in simple shear, Soils and Foundations, Japanese Society of Soil Mechanics and Foundation Engineering, 14, 25–38.

    Google Scholar 

  157. Oda, M., J. Konishi, and S. Nemat-Nasser, 1980. Some experimentally based fundamental results on the mechanical behavior of granular materials, Géotechnique, 30, 479–495.

    Google Scholar 

  158. Oda, M., K. Iwashita, and T. Kakiuchi, 1997, Importance of particle rotation in the mechanics of granular materials, Proceedings of the 3` d International Conference on Powders and Grains, Durham, NC, R. P. Behringer and J. T. Jenkins, Eds., Balkema, Rotterdam, the Netherlands, 207–210.

    Google Scholar 

  159. Oda, M., Konishi, J, and S. Nemat-Nasser, 1982. Experimental micromechanical evaluation of strength of granular materials: effects of particle rolling, Mechanics of Materials, 1, 269–283.

    Google Scholar 

  160. Papadrakakis, M., 1981, A method for the automatic evaluation of the dynamic relaxation parameters, Computer methods in applied mechanics and engineering, 25, 35–48.

    MATH  MathSciNet  Google Scholar 

  161. Parikh, P. V., 1967, The shearing behavior of sand under axisymmetric loading, PhD thesis, University of Manchester, UK.

    Google Scholar 

  162. Park, K. C., and P. Underwood, 1980, A variable-step central difference method for structural dynamic analysis–Part 1. Theoretical aspects, Computer methods in applied mechanics and engineering, 22, 241–258.

    MATH  MathSciNet  Google Scholar 

  163. Penman, A. D. M., 1953, Shear characteristics of saturated silts measured in triaxial compression, Géotechnique, 3 (4), 312–328.

    Google Scholar 

  164. Pfeiffer, F., and C. Glocker, 1966, Multibody Dynamics with Unilateral Contacts, John Wiley Sons, New York.

    Google Scholar 

  165. Procter, D. C., and R. R. Barton, 1974, Measurement of the angle of interparticle friction, Géotechnique, 24 (4), 581–604.

    Google Scholar 

  166. Radjai, F., M. Jean, J. J. Moreau and S. Roux, 1996, Force distributions in dense two-dimensional granular systems, Physics Review Letters, 77, 274.

    Google Scholar 

  167. Reynolds, O., 1885, On the dilatancy of media composed of rigid particles in contact, with experimental illustration, Philosophical Magazine, Series 5, 20, 469–481.

    Google Scholar 

  168. Reynolds, O., 1895, On rolling friction, Phil. Trans. Royal Society, 166, 155.

    Google Scholar 

  169. Rice, J. R., 1976, The localization of plastic deformation, Theoretical and Applied Mechanics, Proceedings of the 14th IUTAM Congress, W.T. Koiter, ed., North Holland, New York, 207–220.

    Google Scholar 

  170. Roscoe, K.H. and A.N. Schofield, 1964. Discussion on P.W. Rowe’s paper, Stressdilatancy, earth pressures and slopes (Proc Paper 3507, May 1963), J. Soil mechanics and Foundation Engineering, ASCE, 90 (1), 136.

    Google Scholar 

  171. Rosenberg, L., and A. P. S. Selvadurai, 1981, Micromechanical definition of the cauchy stress tensor for particulate media, In Mechanics of Structured Media, A. P. S. Selvadurai, ed., Elsevier, Amsterdam, The Netherlands, 469–486.

    Google Scholar 

  172. Rothenburg, L., and R. J. Bathurst, 1989, Analytical study of induced anisotropy in idealized granular materials, Géotechnique, 39, 601–614.

    Google Scholar 

  173. Rothenburg, L., and R. J. Bathurst, 1991, Numerical simulation of idealized granular assemblies with plane elliptical particles, Computers and Geotechnics, 11, 315–329.

    Google Scholar 

  174. Rothenburg, L., and R. J. Bathurst, 1992, Micromechanical features of granular assemblies with planar elliptical particles, Géotechnique, 42, 79–95.

    Google Scholar 

  175. Rowe, P.W., 1962, The stress-dilatancy relation for static equilibrium of an assembly of particles in contact, Proc. Roy. Soc. London, A269, 500.

    Google Scholar 

  176. Rudnicki, J.W., and J. R. Rice, 1975, Conditions for the localization of deformation in pressure-sensitive dilatant materials, J. Mech. Phys. Solids, 23, 371–394.

    Google Scholar 

  177. Satake, M., 1978, Constitution of mechanics of granular materials through graph representation, in Theoretical and Applied Mechanics 26, University of Tokyo Press, 257.

    Google Scholar 

  178. Satake, M., 1982, Fabric tensor in granular materials, Proceedings of the IUTAM symposium on deformation and failure of granular materials, Delft, Balkema Publishers, P.A. Vermeer H.J, Luger Eds., 63–68.

    Google Scholar 

  179. Savage, S. B., and D. J. Jeffrey, 1981, The stress tensor in a granular flow at high shear rate, J. Fluid Mech., 110, 255–272.

    MATH  Google Scholar 

  180. Schneebli, G., 1955, Une analogie mécanique pour les terres sans cohésion, Proceedings of the Academy of Sciences, Paris, France, 243, p. 256.

    Google Scholar 

  181. Schofield, A. N., and C. P. Wroth., 1968, Critical State Soil Mechanics. Mc GrawHill, London, UK.

    Google Scholar 

  182. Shi, G. -H, 1993, Block system modeling by discontinuous deformation analysis, Topics in engineering Volume 11, C. A. Brebbia and J. J. Connor, Eds., Computational mechanics Publication, Southampton, UK.

    Google Scholar 

  183. Shi, G.-H., and R. E. Goodman, 1988, Discontinuous deformation analysis–a new method for computing stress, strain and sliding of block systems, in Key questions in rock mechanics, Cundall et al., Eds., Balkema, Rotterdam, the Netherlands, 381–393.

    Google Scholar 

  184. Shi, G.-H., and R. E. Goodman, 1989, Generalization of two-dimensional discontinuous deformation analysis for forward modeling, International Journal for Numerical and Analytical Methods in Geomechanics, 13 (4), 359–380.

    MATH  Google Scholar 

  185. Singer I. L., and H. M. Pollock, 1992, Fundamentals of friction: Macroscopic and microscopic processes, Kluwer Academic, Dordrecht, the Netherlands.

    Google Scholar 

  186. Skinner, A. E., 1969, A note on the influence of interparticle friction on the shearing strength of a random assembly of spherical particles, Géotechnique, 19 (1) 150–157.

    Google Scholar 

  187. Southwell, R. V. 1940, Relaxation methods in engineering sciences, Oxford University Press, Oxford, UK.

    Google Scholar 

  188. Sternberg, E., 1968, Couple stress and singular stress concentrations in elastic solid, in Mechanics of generalized continua, Proceedings of the IUTAM Symposium on the Generalized Cosserat Continuum and the Continuum Theory of Dislocation with Applications, Edited by E. Kroner, Springer, New York.

    Google Scholar 

  189. Subbash, S. Nemat-Nasser, M. M. Mehrabadi, and H. M. Shodja, 1991. Experimental investigation of fabric-stress relations in granular materials, Mechanics of Materials, 11, 87–106.

    Google Scholar 

  190. Sudji, Y., T. Kawaguchi, and T. Tanaka, 1993, Discrete particle simulation of two-dimensional fluidized bed, Powder Technology, 77, 79–87.

    Google Scholar 

  191. Sudji, Y., T. Tanaka, and T. Ishida, 1992, Lagrangian numerical simulation of plug flow of cohesionless particles in an horizontal pipe, Powder Technology, 71, 239250.

    Google Scholar 

  192. Sukla, A., and H. P. Rossmanith, 1982, A photoelastic investigation of dynamic load transfer in granular media, Acta Mechanica, 42, 211–225.

    Google Scholar 

  193. Sun, G., and C. Thornton, 1994, Computer simulation of 3D quasi-static shear deformation of particulate media, Proceedings of I rst International Particle technology Forum, American Institute of Chemical Engineers, Denver, CO, 24–29.

    Google Scholar 

  194. Supel, J. A., 1985, Local destruction of granular media caused by crushing a single grain, Archives of Mechanics, 37 (4–5), 535–548.

    Google Scholar 

  195. Tabor, D., 1955, The mechanism of rolling friction: the elastic range, Proc. Royal Society, A251, 198–220.

    Google Scholar 

  196. Tamura, S., and T. Aizawa, 1993, Mechanical behavior of powder particle on the applied vibration, International journal of modern physics, 7 (9–10), 1829–1838.

    Google Scholar 

  197. Tatsuoka, F., S. Nakamura, C., Huang, and K. Tani, 1990, Strength anisotropy and shear band direction in plane strain tests on sand, Soils and Foundations, 30, 3554.

    Google Scholar 

  198. Taylor, R. L., 1977, Computer procedures for finite element analysis. Ch. 24, in: O.C. Zienkiewicz, The finite element method, 3rd ed., McGraw-Hill Book Co., London, England.

    Google Scholar 

  199. Thornton, C., 1979, The conditions of failure of a face-centered cubic array of uniform rigid spheres, Géotechnique, 29, 441–459.

    Google Scholar 

  200. Thornton, C., 1994, Micromechanics of elastic sphere assemblies during 3D shear, Proceedings of Mechanics and Statistical Physics of Particulate Materials, Institute for Mechanics and Materials, La Jolla, CA, June, 64–67.

    Google Scholar 

  201. Thornton, C., and C. W. Randall, 1988, Applications of theoretical contact mechanics to solid particle system simulation, in Micromechanics of Granular Materials, M. Satake and J. T. Jenkins, Eds., Elsevier Science Publishers, Amsterdam, Netherlands, 133–142.

    Google Scholar 

  202. Thornton, C., and G. Sun, 1994, Numerical simulation of general 3D quasi-static shear deformation of granular media, Proceedings of Numerical Methods in Geotechnical Engineering, I. M. Smith, ed., Balkema, Rotterdam, Netherlands, 143–148.

    Google Scholar 

  203. Thornton, C., ed., 1993, Proceedings of the 2“ d International Conference on Powders and Grains, Birmingham, UK, Balkema, Rotterdam, the Netherlands.

    Google Scholar 

  204. Thurston, C. W., and H. Deresiewicz, 1959, Analysis of a compression test of a model of a granular medium, Journal of Applied Mechanics, ASME, 251–258.

    Google Scholar 

  205. Timoshenko, S., and J. N. Goodier, 1951, Theory of elasticity, 3’d edition, McGraw-Hill, New York, NY.

    Google Scholar 

  206. Ting, J. M., 1992, A robust algorithm for ellipse-based discrete element modeling of granular materials, Computers and Geotechnics.

    Google Scholar 

  207. Ting, J. M., and B. T. Corkum, 1992, A computational laboratory for discrete element geomechanics, Journal of Computers in Civil Engineering, ASCE, 6, 129–146.

    Google Scholar 

  208. Ting, J. M., B. T. Corkum, C. R. Kauffman, and C. Greco, 1989, Discrete numerical model for soil mechanics, Journal of Geotechnical Engineering, ASCE, 115, 379–398.

    Google Scholar 

  209. Ting, J. M., M. Khawaja, L. M. Meachum, and J. D. Rowell, 1993, An ellipse-based discrete element model for granular materials, International Journal for Numerical and Analytical Methods in Geomechanics, 17, 603–623.

    MATH  Google Scholar 

  210. Tong, P. Y. L., 1970, Plane strain deformation of sands, PhD thesis, University of Manchester, UK.

    Google Scholar 

  211. Trent, B. C. and L. G. Margolin, 1992, A numerical laboratory for granular solids, Engineering Computations, 9, 191–197.

    Google Scholar 

  212. Truesdell, C., 1985, The Elements of Continuum Mechanics, Springer-Verlag, Berlin, Germany.

    Google Scholar 

  213. Tschebotarioff, G. P., and J. D. Welch, 1948, lateral earth pressures and friction between soil minerals, Proceedings of the 2 “d International Conference on Soil Mechanics and Foundations, Rotterdam, VII, 135–138.

    Google Scholar 

  214. Tsuji, Y., 1997, Discrete particle simulation of dispersed gas-solid flows, Proceedings of the 3 ’d International Conference on Powders and Grains, Durham, NC, R. P. Behringer and J. T. Jenkins, Eds., Balkema, Rotterdam, the Netherlands, 25–30.

    Google Scholar 

  215. Underwood, P., 1983, Dynamic relaxation, in Computational methods for transient analysis, T. Belitschko and T.J.R. Hughes, Eds., North Holland, Amsterdam, Holland, 245–265.

    Google Scholar 

  216. Underwood, P., and K. C. Park, 1980, A variable-step central difference method for structural dynamic analysis, Part 2. Implementation and performance evaluation, Computer methods in applied mechanics and engineering, 23, 259–279.

    MATH  MathSciNet  Google Scholar 

  217. Vardoulakis, I. and B. Graf, 1985, Calibration of constitutive models for granular materials using data from biaxial experiments, Géotechnique, 35, 299–317.

    Google Scholar 

  218. Vardoulakis, I., 1988, Theoretical and experimental bounds for shear-band bifurcation strain in biaxial tests on dry sand, Res Mechanica, 23, 239–259.

    Google Scholar 

  219. Vermeulen, P. J., and K. L. Johnson, 1964, Contact of nonspherical elastic bodies transmitting tangential forces, Journal of Applied Mechanics, June, 338–340.

    Google Scholar 

  220. Walton, O. R., 1980, Particle dynamics modeling of geological materials, Lawrence Livermore National Laboratory, Report UCRL-52915.

    Google Scholar 

  221. Walton, O. R., 1993, Numerical simulation of inelastic, frictional particle-particle interactions, in Particulate two-phase flow, M. C. Roco, ed., Butterworth Heinemann, Boston, 884–910.

    Google Scholar 

  222. Walton, O. R., and R. L. Braun, 1986, Stress calculations for assemblies of inelastic spheres in uniform shear, Acta Mechanica, 63, 73–86.

    Google Scholar 

  223. Walton, O. R., and R. L. Braun, 1986, Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks, Journal of Rheology, 30, 949–980.

    Google Scholar 

  224. Walton, O. R., R. L. Braun, R. G. Mallon, and D. M. Cervelli, 1988, Particle-dynamics calculations of gravity flows of inelastic, frictional sphere, Micromechanics of granular materials, M. Satake and J. T. Jenkins, Eds., Elsevier Science Publishers, Amsterdam, 153–161.

    Google Scholar 

  225. Weber, J., 1996, Recherches concernant les contraintes intergranulaires dans les milieux pulverulents, Cahiers du Groupe Français de Rhéologie, 2, 161–170 (see also Bulletin de Liaison des Ponts et Chaussées 20, 3–1 to 3–20).

    Google Scholar 

  226. Wells, J. C., 1997, Contact of rough elastic spheres: a simplified analysis, Proceedings of the 3rd International Conference on Powders and Grains, Durham, NC, R. P. Behringer and J. T. Jenkins, Eds., Balkema, Rotterdam, the Netherlands, 311–314.

    Google Scholar 

  227. Williams, J. R., and G. G. W. Mustoe, 1987, Modal methods for the analysis of discrete systems, Computers and Geotechnics, 4, 1–19.

    Google Scholar 

  228. Williams, J. R., and G. G. W. Mustoe, Eds., 1993, Proceedings of the 2 nd International Conference on Discrete Element Methods (DEM), The Massachusetts Institute of Technology, Intelligent Engineering System Laboratory Publication, Cambridge, MA.

    Google Scholar 

  229. Witters, J., and D. Duymelinck, 1986, Rolling and sliding resistive forces on balls moving on a flat surface, American Journal of Physics, 54 (1), 80–83.

    Google Scholar 

  230. Zhuang, X. and J. D. Goddard, 1993, Computer simulation and experiments on the quasi-static mechanics and transport properties of granular materials, Res. Rep. GR 93–01, University of California, San Diego, CA, October.

    Google Scholar 

  231. Zhuang, X., K. Didwania, and J. D. Goddard, 1995, Simulation of the quasi-static mechanics and scalar transport properties of ideal granular assemblages, Journal of computational physics, 121, 331–346.

    MATH  Google Scholar 

  232. Zienkiewicz, O. C., and R. L. Taylor, 1991, The finite element method, Vol. 2, McGraw-Hill, London, UK.

    Google Scholar 

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    J. P. Bardet

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    Bernard Cambou

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Bardet, J.P. (1998). Introduction to Computational Granular Mechanics. In: Cambou, B. (eds) Behaviour of Granular Materials. International Centre for Mechanical Sciences, vol 385. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2526-7_2

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