1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Fluid Mechanics
  4. Volume 56, 2024
  5. Article

Annual Review of Fluid Mechanics

Volume 56, 2024

Advances in Modeling Dense Granular Media

Abstract

This review focuses on how the modeling of dense granular media has advanced over the last 15 years. The jumping-off point of our review is the μ() rheology for dry granular flow, which opened the door to generic flow field modeling but was primarily geared toward problems involving small monodisperse grains of simple shapes. Our review focuses on advances in modeling more material types and behaviors including new approaches for modeling finite-grain-size effects or nonlocality, polydispersity and unmixing, and nontrivial grain shapes. We also discuss growing application areas with tractable order-reduction strategies with a focus on intrusion and locomotion problems.

Keyword(s): discrete particle modeling, granular media, intrusion, particle segregation, polydispersity, rheology
Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-121021-022045
2024-01-19
2024-04-29
Loading full text...

Full text loading...

/deliver/fulltext/fluid/56/1/annurev-fluid-121021-022045.html?itemId=/content/journals/10.1146/annurev-fluid-121021-022045&mimeType=html&fmt=ahah

Literature Cited

  1. AAAS (Am. Assoc. Adv. Sci.). 2005. So much more to know…. Science 309:573178–102
     [Google Scholar]
  2. Agarwal S, Karsai A, Goldman DI, Kamrin K. 2021. Surprising simplicity in the modeling of dynamic granular intrusion. Sci. Adv. 7:17eabe0631
     [Google Scholar]
  3. Aguilar J, Goldman DI. 2016. Robophysical study of jumping dynamics on granular media. Nat. Phys. 12:3278–83
     [Google Scholar]
  4. Aguilar J, Zhang T, Qian F, Kingsbury M, McInroe B et al. 2016. A review on locomotion robophysics: the study of movement at the intersection of robotics, soft matter and dynamical systems. Rep. Prog. Phys. 79:11110001
     [Google Scholar]
  5. Albert I, Sample J, Morss A, Rajagopalan S, Barabási AL, Schiffer P. 2001. Granular drag on a discrete object: shape effects on jamming. Phys. Rev. E 64:6061303
     [Google Scholar]
  6. Albert R, Pfeifer M, Barabási AL, Schiffer P. 1999. Slow drag in a granular medium. Phys. Rev. Lett. 82:205
     [Google Scholar]
  7. Alonso-Marroquin F, Herrmann H. 2002. Calculation of the incremental stress-strain relation of a polygonal packing. Phys. Rev. E 66:2021301
     [Google Scholar]
  8. Andrade J, Lim KW, Avila C, Vlahinić I. 2012. Granular element method for computational particle mechanics. Comput. Methods Appl. Mech. Eng. 241:262–74
     [Google Scholar]
  9. Aranson IS, Tsimring LS. 2001. Continuum description of avalanches in granular media. Phys. Rev. E 64:020301
     [Google Scholar]
  10. Aranson IS, Tsimring LS. 2002. Continuum theory of partially fluidized granular flows. Phys. Rev. E 65:061303
     [Google Scholar]
  11. Aranson IS, Tsimring LS, Malloggi F, Clément E. 2008. Nonlocal rheological properties of granular flows near a jamming limit. Phys. Rev. E 78:3031303
     [Google Scholar]
  12. Askari H, Kamrin K. 2016. Intrusion rheology in grains and other flowable materials. Nat. Mater. 15:121274–79
     [Google Scholar]
  13. Astley HC, Gong C, Dai J, Travers M, Serrano MM et al. 2015. Modulation of orthogonal body waves enables high maneuverability in sidewinding locomotion. PNAS 112:196200–5
     [Google Scholar]
  14. Astley HC, Mendelson JR III, Dai J, Gong C, Chong B et al. 2020. Surprising simplicities and syntheses in limbless self-propulsion in sand. J. Exp. Biol. 223:5jeb103564
     [Google Scholar]
  15. Athanassiadis A, Miskin M, Kaplan P, Rodenberg N, Lee S et al. 2014. Particle shape effects on the stress response of granular packings. Soft Matter 10:148–59
     [Google Scholar]
  16. Aydin YO, Rieser JM, Hubicki CM, Savoie W, Goldman DI 2019. Physics approaches to natural locomotion: Every robot is an experiment. Robotic Systems and Autonomous Platforms SM Walsh, MS Strano 109–27. Duxford, UK: Woodhead
     [Google Scholar]
  17. Bardou E. 2002. Méthodologie de diagnostic des laves torrentielles sur un bassin versant alpin PhD Thesis Ec. Polytech. Féd. Lausanne Lausanne, Switz.:
  18. Barker G, Mehta A. 1993. Size segregation mechanisms. Nature 364:486–87
     [Google Scholar]
  19. Bazant MZ. 2006. The spot model for random-packing dynamics. Mech. Mater. 38:8717–31
     [Google Scholar]
  20. Berzi D. 2014. Extended kinetic theory applied to dense, granular, simple shear flows. Acta Mech. 225:82191–98
     [Google Scholar]
  21. Beverloo WA, Leniger HA, de Velde JV. 1961. The flow of granular solids through orifices. Chem. Eng. Sci. 15:3–4260–69
     [Google Scholar]
  22. Bocquet L, Colin A, Ajdari A. 2009. Kinetic theory of plastic flow in soft glassy materials. Phys. Rev. Lett. 103:3036001
     [Google Scholar]
  23. Bouzid M, Izzet A, Trulsson M, Clément E, Claudin P, Andreotti B. 2015. Non-local rheology in dense granular flows. Eur. Phys. J. E 38:11125
     [Google Scholar]
  24. Bouzid M, Trulsson M, Claudin P, Clément E, Andreotti B. 2013. Nonlocal rheology of granular flows across yield conditions. Phys. Rev. Lett. 111:23238301
     [Google Scholar]
  25. Brilliantov NV, Pöschel T. 2010. Kinetic Theory of Granular Gases Oxford, UK: Oxford Univ. Press
  26. Buscarnera G, Einav I. 2021. The mechanics of brittle granular materials with coevolving grain size and shape. Proc. R. Soc. A 477:224920201005
     [Google Scholar]
  27. Cho G, Dodds J, Santamarina C. 2006. Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. J. Geotech. Geoenviron. Eng. 132:5591–602
     [Google Scholar]
  28. Chong B, Aydin YO, Gong C, Sartoretti G, Wu Y et al. 2021. Coordination of lateral body bending and leg movements for sprawled posture quadrupedal locomotion. Int. J. Robot. Res. 40:4–5747–63
     [Google Scholar]
  29. Chong B, Aydin YO, Rieser JM, Sartoretti G, Wang T et al. 2022a. A general locomotion control framework for multi-legged locomotors. Bioinspir. Biomimet. 17:4046015
     [Google Scholar]
  30. Chong B, Wang T, Erickson E, Bergmann PJ, Goldman DI. 2022b. Coordinating tiny limbs and long bodies: geometric mechanics of lizard terrestrial swimming. PNAS 119:27e2118456119
     [Google Scholar]
  31. Christoffersen J, Mehrabadi MM, Nemat-Nasser S. 1981. A micromechanical description of granular material behavior. J. Appl. Mech. 48:339–44
     [Google Scholar]
  32. Conway SL, Liu X, Glasser BJ. 2006. Instability-induced clustering and segregation in high-shear Couette flows of model granular materials. Chem. Eng. Sci. 61:196404–23
     [Google Scholar]
  33. Cortez R, Fauci L, Medovikov A. 2005. The method of regularized Stokeslets in three dimensions: analysis, validation, and application to helical swimming. Phys. Fluids 17:3031504
     [Google Scholar]
  34. Cosserat E, Cosserat F. 1909. Théorie des corps déformables Paris: Hermann
  35. Cundall P. 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. Int. J. Rock Mech. Mining Sci. Abstracts 25:3107–16
     [Google Scholar]
  36. Cundall P, Strack O. 1979. A discrete numerical model for granular assemblies. Géotechnique 29:147–65
     [Google Scholar]
  37. da Cruz F, Emam S, Prochnow M, Roux JN, Chevoir F. 2005. Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72:2021309
     [Google Scholar]
  38. de Gennes PG. 1999. Granular matter: a tentative view. Rev. Mod. Phys. 71:2S374
     [Google Scholar]
  39. Depken M, van Saarloos W, van Hecke M. 2006. Continuum approach to wide shear zones in quasistatic granular matter. Phys. Rev. E 73:031302
     [Google Scholar]
  40. Ding Y, Li C, Goldman DI. 2013a. Swimming in the desert. Phys. Today 66:1168–69
     [Google Scholar]
  41. Ding Y, Sharpe SS, Wiesenfeld K, Goldman DI. 2013b. Emergence of the advancing neuromechanical phase in a resistive force dominated medium. PNAS 110:2510123–28
     [Google Scholar]
  42. Dunatunga S, Kamrin K. 2022. Modelling silo clogging with non-local granular rheology. J. Fluid Mech. 940:A14
     [Google Scholar]
  43. Einav I. 2007. Breakage mechanics—part I: Theory. J. Mech. Phys. Solids 55:61274–97
     [Google Scholar]
  44. Fan Y, Hill KM. 2011a. Theory for shear-induced segregation of dense granular mixtures. New J. Phys. 13:9095009
     [Google Scholar]
  45. Fan Y, Hill KM. 2011b. Phase transitions in shear-induced segregation of granular materials. Phys. Rev. Lett. 106:21218301
     [Google Scholar]
  46. Faroux D, Washino K, Tsuji T, Tanaka T. 2022. 3D implementation and validation of VOF-coupled non-local granular rheology. Granular Matter 24:252
     [Google Scholar]
  47. Félix G, Thomas N. 2004. Evidence of two effects in the size segregation process in dry granular media. Phys. Rev. E 70:5051307
     [Google Scholar]
  48. Fenistein D, van de Meent JW, van Hecke M. 2004. Universal and wide shear zones in granular bulk flow. Phys. Rev. Lett. 92:9094301
     [Google Scholar]
  49. Fenistein D, van Hecke M. 2003. Wide shear zones in granular bulk flow. Nature 425:256
     [Google Scholar]
  50. Forterre Y, Pouliquen O. 2008. Flows of dense granular media. Annu. Rev. Fluid Mech. 40:1–24
     [Google Scholar]
  51. Gans C. 1973. Locomotion and burrowing in limbless vertebrates. Nature 242:414–15
     [Google Scholar]
  52. Garcia X, Akanji L, Blunt M, Matthai S, Latham J. 2009a. Numerical study of the effects of particle shape and polydispersity on permeability. Phys. Rev. E 80:2021304
     [Google Scholar]
  53. Garcia X, Latham JP, Xiang JS, Harrison J. 2009b. A clustered overlapping sphere algorithm to represent real particles in discrete element modelling. Géotechnique 59:9779–84
     [Google Scholar]
  54. Garzó V. 2009. Segregation by thermal diffusion in moderately dense granular mixtures. Eur. Phys. J. E 29:261–74
     [Google Scholar]
  55. Garzó V, Dufty J. 1999. Dense fluid transport for inelastic hard spheres. Phys. Rev. E 59:55895
     [Google Scholar]
  56. Goldman DI, Umbanhowar P. 2008. Scaling and dynamics of sphere and disk impact into granular media. Phys. Rev. E 77:2021308
     [Google Scholar]
  57. Gray J, Chugunov V. 2006. Particle-size segregation and diffusive remixing in shallow granular avalanches. J. Fluid Mech. 569:365–98
     [Google Scholar]
  58. Gray J, Hancock G. 1955. The propulsion of sea-urchin spermatozoa. J. Exp. Biol. 32:4802–14
     [Google Scholar]
  59. Gray J, Thornton A. 2005. A theory for particle size segregation in shallow granular free-surface flows. Proc. R. Soc. A 461:20571447–73
     [Google Scholar]
  60. Gray JMNT. 2018. Particle segregation in dense granular flows. Annu. Rev. Fluid Mech. 50:407–33
     [Google Scholar]
  61. Guillard F, Forterre Y, Pouliquen O. 2014. Lift forces in granular media. Phys. Fluids 26:4043301
     [Google Scholar]
  62. Guo P, Su X. 2007. Shear strength, interparticle locking, and dilatancy of granular materials. Can. Geotech. J. 44:5579–91
     [Google Scholar]
  63. Gurtin M, Fried E, Anand L. 2010. The Mechanics and Thermodynamics of Continua Cambridge, UK: Cambridge Univ. Press
  64. Haff P. 1983. Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech. 134:401–30
     [Google Scholar]
  65. Henann DL, Kamrin K. 2013. A predictive, size-dependent continuum model for dense granular flows. PNAS 110:176730–35
     [Google Scholar]
  66. Henann DL, Kamrin K. 2014. Continuum modeling of secondary rheology in dense granular materials. Phys. Rev. Lett. 113:17178001
     [Google Scholar]
  67. Henann DL, Kamrin K. 2016. A finite element implementation of the nonlocal granular rheology. Int. J. Numer. Methods Eng. 108:4273–302
     [Google Scholar]
  68. Hernández-Delfin D, Tunuguntla D, Weinhart T, Hidalgo R, Thornton A. 2022. Shape matters: competing mechanisms of particle shape segregation. Phys. Rev. E 106:5054614
     [Google Scholar]
  69. Hill KM. 2016. Segregation in dense sheared systems. Handbook of Granular Materials SV Franklin, MD Shattuck 337–88. Boca Raton, FL: CRC
     [Google Scholar]
  70. Hill KM, Fan Y. 2016. Granular temperature and segregation in dense sheared particulate mixtures. KONA Powder Part. J. 33:150–68
     [Google Scholar]
  71. Hill KM, Gioia G, Amaravadi D. 2004. Radial segregation patterns in rotating granular mixtures: waviness selection. Phys. Rev. Lett. 93:22224301
     [Google Scholar]
  72. Hill KM, Khakhar DV, Gilchrist JF, McCarthy JJ, Ottino JM. 1999. Segregation-driven organization in chaotic granular flows. PNAS 96:2111701–6
     [Google Scholar]
  73. Hill KM, Tan DS. 2014. Segregation in dense sheared flows: gravity, temperature gradients, and stress partitioning. J. Fluid Mech. 756:54–88
     [Google Scholar]
  74. Hosoi A, Goldman DI. 2015. Beneath our feet: strategies for locomotion in granular media. Annu. Rev. Fluid Mech. 47:431–53
     [Google Scholar]
  75. Houlsby G. 2009. Potential particles: a method for modelling non-circular particles in DEM. Comput. Geotech. 36:6953–59
     [Google Scholar]
  76. Irschick DJ, Jayne BC. 1999. A field study of the effects of incline on the escape locomotion of a bipedal lizard, Callisaurus draconoides. Physiol. Biochem. Zool. 72:144–56
     [Google Scholar]
  77. Jenkins JT, Berzi D. 2010. Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory. Granul. Matter 12:2151–58
     [Google Scholar]
  78. Jenkins JT, Savage SB. 1983. A theory for the rapid flow of identical, smooth, nearly elastic particles. J. Fluid Mech. 130:187–202
     [Google Scholar]
  79. Johnson RE. 1980. An improved slender-body theory for Stokes flow. J. Fluid Mech. 99:2411–31
     [Google Scholar]
  80. Jop P, Forterre Y, Pouliquen O. 2006. A constitutive law for dense granular flows. Nature 441:7094727–30
     [Google Scholar]
  81. Kamrin K. 2010. Nonlinear elasto-plastic model for dense granular flow. Int. J. Plast. 26:2167–88
     [Google Scholar]
  82. Kamrin K, Henann DL. 2015. Nonlocal modeling of granular flows down inclines. Soft Matter 11:179–85
     [Google Scholar]
  83. Kamrin K, Koval G. 2012. Nonlocal constitutive relation for steady granular flow. Phys. Rev. Lett. 108:17178301
     [Google Scholar]
  84. Karapiperis K, Harmon J, Andò E, Viggiani G, Andrade J. 2020. Investigating the incremental behavior of granular materials with the level-set discrete element method. J. Mech. Phys. Solids 144:104103
     [Google Scholar]
  85. Katsuragi H, Durian DJ. 2007. Unified force law for granular impact cratering. Nat. Phys. 3:6420–23
     [Google Scholar]
  86. Kawamoto R, Andò E, Viggiani G, Andrade J. 2016. Level set discrete element method for three-dimensional computations with triaxial case study. J. Mech. Phys. Solids 91:1–13
     [Google Scholar]
  87. Kawamoto R, Andò E, Viggiani G, Andrade J. 2018. All you need is shape: predicting shear banding in sand with LS-DEM. J. Mech. Phys. Solids 111:375–92
     [Google Scholar]
  88. Khakhar D, McCarthy J, Ottino JM. 1997. Radial segregation of granular mixtures in rotating cylinders. Phys. Fluids 9:123600–14
     [Google Scholar]
  89. Kim S, Kamrin K. 2020. Power-law scaling in granular rheology across flow geometries. Phys. Rev. Lett. 125:8088002
     [Google Scholar]
  90. Kim S, Kamrin K. 2023. A second-order non-local model for granular flows. Front. Phys. 11:1092233
     [Google Scholar]
  91. Knight JB, Jaeger HM, Nagel SR. 1993. Vibration-induced size separation in granular media: the convection connection. Phys. Rev. Lett. 70:243728
     [Google Scholar]
  92. Komatsu TS, Inagaki S, Nakagawa N, Nasuno S. 2001. Creep motion in a granular pile exhibiting steady surface flow. Phys. Rev. Lett. 86:91757
     [Google Scholar]
  93. Koval G, Roux JN, Corfdir A, Chevoir F. 2009. Annular shear of cohesionless granular materials: from the inertial to quasistatic regime. Phys. Rev. E 79:2021306
     [Google Scholar]
  94. Lai Z, Zhao S, Zhao J, Huang L. 2022. Signed distance field framework for unified DEM modeling of granular media with arbitrary particle shapes. Comput. Mech. 70:4763–83
     [Google Scholar]
  95. Larcher M, Jenkins JT. 2019. The influence of granular segregation on gravity-driven particle-fluid flows. Adv. Water Resour. 129:365–72
     [Google Scholar]
  96. Li C, Hsieh ST, Goldman DI. 2012. Multi-functional foot use during running in the zebra-tailed lizard (Callisaurus draconoides). J. Exp. Biol. 215:183293–308
     [Google Scholar]
  97. Li C, Zhang T, Goldman DI. 2013. A terradynamics of legged locomotion on granular media. Science 339:61261408–12
     [Google Scholar]
  98. Li S, Henann DL. 2019. Material stability and instability in non-local continuum models for dense granular materials. J. Fluid Mech. 871:799–830
     [Google Scholar]
  99. Li S, Henann DL. 2020. Nonlocal continuum modeling of dense granular flow in a split-bottom cell with a vane-shaped intruder. Phys. Rev. E 102:2022908
     [Google Scholar]
  100. Lighthill J. 1976. Flagellar hydrodynamics. SIAM Rev. 18:2161–230
     [Google Scholar]
  101. Lim KW, Krabbenhoft K, Andrade J. 2014. On the contact treatment of non-convex particles in the granular element method. Comput. Part. Mech. 1:257–75
     [Google Scholar]
  102. Litwiniszyn J. 1963. The model of a random walk of particles adapted to researches on problems of mechanics of loose media. Bull. Acad. Pol. Sci. 11:10593–602
     [Google Scholar]
  103. Liu D, Henann DL. 2017. Non-local continuum modelling of steady, dense granular heap flows. J. Fluid Mech. 831:212–27
     [Google Scholar]
  104. Liu D, Henann DL. 2018. Size-dependence of the flow threshold in dense granular materials. Soft Matter 14:255294–305
     [Google Scholar]
  105. Lun C, Savage S, Jeffrey D, Chepurniy N. 1984. Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield. J. Fluid Mech. 140:223–56
     [Google Scholar]
  106. Maladen RD, Ding Y, Li C, Goldman DI. 2009. Undulatory swimming in sand: subsurface locomotion of the sandfish lizard. Science 325:5938314–18
     [Google Scholar]
  107. Maladen RD, Ding Y, Umbanhowar PB, Kamor A, Goldman DI. 2011a. Mechanical models of sandfish locomotion reveal principles of high performance subsurface sand-swimming. J. R. Soc. Interface 8:621332–45
     [Google Scholar]
  108. Maladen RD, Umbanhowar PB, Ding Y, Masse A, Goldman DI. 2011b. Granular lift forces predict vertical motion of a sand-swimming robot. 2011 IEEE International Conference on Robotics and Automation1398–403. New York: IEEE
     [Google Scholar]
  109. Marvi H, Gong C, Gravish N, Astley H, Travers M et al. 2014. Sidewinding with minimal slip: snake and robot ascent of sandy slopes. Science 346:6206224–29
     [Google Scholar]
  110. Maugin G. 2013. Continuum Mechanics Through the Twentieth Century Berlin: Springer
  111. Mazouchova N, Gravish N, Savu A, Goldman DI. 2010. Utilization of granular solidification during terrestrial locomotion of hatchling sea turtles. Biol. Lett. 6:3398–401
     [Google Scholar]
  112. Mazouchova N, Umbanhowar PB, Goldman DI. 2013. Flipper-driven terrestrial locomotion of a sea turtle-inspired robot. Bioinspir. Biomimet. 8:2026007
     [Google Scholar]
  113. MiDi GDR 2004. On dense granular flows. Eur. Phys. J. E 14:4341–65
     [Google Scholar]
  114. Miller T, Rognon P, Metzger B, Einav I. 2013. Eddy viscosity in dense granular flows. Phys. Rev. Lett. 111:5058002
     [Google Scholar]
  115. Misra A, Poorsolhjouy P. 2015. Identification of higher-order elastic constants for grain assemblies based upon granular micromechanics. Math. Mech. Complex Syst. 3:3285–308
     [Google Scholar]
  116. Mohan LS, Rao KK, Nott PR. 2002. A frictional Cosserat model for the slow shearing of granular materials. J. Fluid Mech. 457:377–409
     [Google Scholar]
  117. Mosauer W. 1932. Adaptive convergence in the sand reptiles of the Sahara and of California: a study in structure and behavior. Copeia 1932:272–78
     [Google Scholar]
  118. Mühlhaus HB, Vardoulakis I. 1987. The thickness of shear bands in granular materials. Géotechnique 37:3271–83
     [Google Scholar]
  119. Mullins WW. 1972. Stochastic theory of particle flow under gravity. J. Appl. Phys. 43:665–78
     [Google Scholar]
  120. Mullins WW. 1974. Experimental evidence for the stochastic theory of particle flow under gravity. Powder Technol. 9:29–37
     [Google Scholar]
  121. Munjiza A. 2004. The Combined Finite-Discrete Element Method Chichester, UK: John Wiley & Sons
  122. Murphy K, Dahmen K, Jaeger H. 2019. Transforming mesoscale granular plasticity through particle shape. Phys. Rev. X 9:1011014
     [Google Scholar]
  123. Nichol K, Zanin A, Bastien R, Wandersman E, van Hecke M. 2010. Flow-induced agitations create a granular fluid. Phys. Rev. Lett. 104:7078302
     [Google Scholar]
  124. Nicot F, Darve F. 2005. A multi-scale approach to granular materials. Mech. Mater. 37:9980–1006
     [Google Scholar]
  125. Nott PR. 2017. A non-local plasticity theory for slow granular flows. EPJ Web Conf. 140:11015
     [Google Scholar]
  126. Ottino J, Khakhar D. 2000. Mixing and segregation of granular materials. Annu. Rev. Fluid Mech. 32:55–91
     [Google Scholar]
  127. Pouliquen O. 1999. Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11:542–48
     [Google Scholar]
  128. Pouliquen O, Forterre Y. 2009. A non-local rheology for dense granular flows. Philos. Trans. R. Soc. Lond. A 367:19095091–107
     [Google Scholar]
  129. Pouliquen O, Vallance J. 1999. Segregation induced instabilities of granular fronts. Chaos Interdiscip. J. Nonlinear Sci. 9:3621–30
     [Google Scholar]
  130. Purcell EM. 1977. Life at low Reynolds number. Am. J. Phys. 45:13–11
     [Google Scholar]
  131. Reddy K, Forterre Y, Pouliquen O. 2011. Evidence of mechanically activated processes in slow granular flows. Phys. Rev. Lett. 106:10108301
     [Google Scholar]
  132. Rieser JM, Li TD, Tingle JL, Goldman DI, Mendelson JR 3rd 2021. Functional consequences of convergently evolved microscopic skin features on snake locomotion. PNAS 118:6e2018264118
     [Google Scholar]
  133. Rodenborn B, Chen CH, Swinney HL, Liu B, Zhang H. 2013. Propulsion of microorganisms by a helical flagellum. PNAS 110:5E338–47
     [Google Scholar]
  134. Sarkar S, Khakhar D. 2008. Experimental evidence for a description of granular segregation in terms of the effective temperature. Europhys. Lett. 83:554004
     [Google Scholar]
  135. Savage S. 1998. Analyses of slow high-concentration flows of granular materials. J. Fluid Mech. 377:1–26
     [Google Scholar]
  136. Savage S, Lun C. 1988. Particle size segregation in inclined chute flow of dry cohesionless granular solids. J. Fluid Mech. 189:311–35
     [Google Scholar]
  137. Schiebel PE, Astley HC, Rieser JM, Agarwal S, Hubicki C et al. 2020. Mitigating memory effects during undulatory locomotion on hysteretic materials. eLife 9:e51412
     [Google Scholar]
  138. Seguin A, Bertho Y, Gondret P, Crassous J. 2011. Dense granular flow around a penetrating object: experiment and hydrodynamic model. Phys. Rev. Lett. 107:4048001
     [Google Scholar]
  139. Sharpe SS, Ding Y, Goldman DI. 2013. Environmental interaction influences muscle activation strategy during sand-swimming in the sandfish lizard Scincus scincus. J. Exp. Biol. 216:2260–74
     [Google Scholar]
  140. Sharpe SS, Koehler SA, Kuckuk RM, Serrano M, Vela PA et al. 2015. Locomotor benefits of being a slender and slick sand swimmer. J. Exp. Biol. 218:3440–50
     [Google Scholar]
  141. Shrivastava S, Karsai A, Aydin YO, Pettinger R, Bluethmann W et al. 2020. Material remodeling and unconventional gaits facilitate locomotion of a robophysical rover over granular terrain. Sci. Robot. 5:42eaba3499
     [Google Scholar]
  142. Silbert LE, Ertas D, Grest GS, Halsey TC, Levine D, Plimpton SJ. 2001. Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64:051302
     [Google Scholar]
  143. Silbert LE, Landry JW, Grest GS. 2003. Granular flow down a rough inclined plane: transition between thin and thick piles. Phys. Fluids 15:1–10
     [Google Scholar]
  144. Staron L, Lagrée PY, Popinet S. 2012. The granular silo as a continuum plastic flow: the hour-glass versus the clepsydra. Phys. Fluids 24:10103301
     [Google Scholar]
  145. Sznitman J, Shen X, Sznitman R, Arratia PE. 2010. Propulsive force measurements and flow behavior of undulatory swimmers at low Reynolds number. Phys. Fluids 22:12121901
     [Google Scholar]
  146. Tang Z, Brzinski TA, Shearer M, Daniels KE. 2018. Nonlocal rheology of dense granular flow in annular shear experiments. Soft Matter 14:163040–48
     [Google Scholar]
  147. Tasora A, Anitescu M. 2010. A convex complementarity approach for simulating large granular flows. J. Comput. Nonlinear Dyn. 5:3031004
     [Google Scholar]
  148. Ting J, Khwaja M, Meachum L, Rowell J. 1993. An ellipse-based discrete element model for granular materials. Int. J. Numer. Anal. Methods Geomech. 17:9603–23
     [Google Scholar]
  149. Tripathi A, Khakhar D. 2013. Density difference-driven segregation in a dense granular flow. J. Fluid Mech. 717:643–69
     [Google Scholar]
  150. Tüzün U, Nedderman RM. 1979. Experimental evidence supporting the kinematic modelling of the flow of granular media in the absence of air drag. Powder Technol. 23:257–66
     [Google Scholar]
  151. Umbanhowar P, Goldman DI. 2010. Granular impact and the critical packing state. Phys. Rev. E 82:1010301
     [Google Scholar]
  152. Umbanhowar PB, Lueptow RM, Ottino JM. 2019. Modeling segregation in granular flows. Annu. Rev. Chem. Biomol. Eng. 10:129–53
     [Google Scholar]
  153. van der Vaart K, van Schrojenstein Lantman M, Weinhart T, Luding S, Ancey C, Thornton A. 2018. Segregation of large particles in dense granular flows suggests a granular Saffman effect. Phys. Rev. Fluids 3:7074303
     [Google Scholar]
  154. Vlahinić I, Andò E, Viggiani G, Andrade J. 2014. Towards a more accurate characterization of granular media: extracting quantitative descriptors from tomographic images. Granular Matter 16:9–21
     [Google Scholar]
  155. Wandersman E, Van Hecke M. 2014. Nonlocal granular rheology: role of pressure and anisotropy. EPL 105:224002
     [Google Scholar]
  156. Wang Y, Li L, Hofmann D, Andrade J, Daraio C. 2021. Structured fabrics with tunable mechanical properties. Nature 596:7871238–43
     [Google Scholar]
  157. Yoon DK, Jenkins JT. 2006. The influence of different species' granular temperatures on segregation in a binary mixture of dissipative grains. Phys. Fluids 18:7073303
     [Google Scholar]
  158. Zhang Q, Kamrin K. 2017. Microscopic description of the granular fluidity field in nonlocal flow modeling. Phys. Rev. Lett. 118:5058001
     [Google Scholar]
  159. Zhang T, Goldman DI. 2014. The effectiveness of resistive force theory in granular locomotion. Phys. Fluids 26:10101308
     [Google Scholar]
  160. Zhang T, Qian F, Li C, Masarati P, Hoover AM et al. 2013. Ground fluidization promotes rapid running of a lightweight robot. Int. J. Robot. Res. 32:7859–69
     [Google Scholar]
  161. Zuriguel I, Parisi DR, Hidalgo RC, Lozano C, Janda A et al. 2014. Clogging transition of many-particle systems flowing through bottlenecks. Sci. Rep. 4:7324
     [Google Scholar]
/content/journals/10.1146/annurev-fluid-121021-022045
Loading
Advances in Modeling Dense Granular Media
Annual Review of Fluid Mechanics 56, 215 (2024); https://doi.org/10.1146/annurev-fluid-121021-022045
/content/journals/10.1146/annurev-fluid-121021-022045
/content/journals/10.1146/annurev-fluid-121021-022045
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error