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Contact Force Models for Granular Materials

  • Shunying JiEmail author
  • Lu Liu
Chapter
  • 41 Downloads
Part of the Springer Tracts in Mechanical Engineering book series (STME)

Abstract

In the discrete element method (DEM), each particle in the bulk material is considered to be an independent discrete element which has its own physical parameters (shape, density, size and et al.) and mechanical properties (elastic modulus, Poisson’s ratio and et al.). The interconnection and constraints between discrete particles are activated by contacts, which can fully reflect the discontinuity of granular materials. In DEM simulations, particles’ attributes, such as the position, velocity and angular velocity, are computed and stored at each time step. In sum, this method has the advantage of taking full account of the unique properties of each particle.

References

  1. Azevedo N, Candeias M, Gouveia F (2015) A rigid particle model for rock fracture following the Voronoi tessellation of the grain structure: formulation and validation. Rock Mech Rock Eng 48(2):535–557CrossRefGoogle Scholar
  2. Babic M, Shen HH, Shen HT (1990) The stress tensor in granular shear flows of uniform, deformable disks at high solids concentrations. J Fluid Mech 219:81–118CrossRefGoogle Scholar
  3. Bahrami M, Yovanovich MM, Culham JR (2005) A compact model for spherical rough contacts. J Tribol 127(4):884–889CrossRefGoogle Scholar
  4. Bala K, Pradhan PR, Saxena NS et al (1989) Effective thermal conductivity of copper powders. J Phys D Appl Phys 22(8):1068CrossRefGoogle Scholar
  5. Batchelor GK, O’Brien RW (1977) Thermal or electrical conduction through a granular material. Proc R Soc A Math Phys Eng Sci 355(355):313–333Google Scholar
  6. Behraftar S, Galindo-Torres SA, Scheuermann A et al (2017) Validation of a novel discrete-based model for fracturing of brittle materials. Comput Geotech 81:274–283CrossRefGoogle Scholar
  7. Bergman TL, Lavine A, Incropera FP et al (2007) Fundamentals of heat and mass transfer. WileyGoogle Scholar
  8. Bradley RS (1932) The cohesive force between solid surfaces and the surface energy of solids. Phil Mag 13(86):853–862zbMATHCrossRefGoogle Scholar
  9. Briscoe BJ, Adams MJ (1987) Tribology in particulate technology. Adam HiglerGoogle Scholar
  10. Brizmer V, Zait Y, Kligerman Y et al (2006) The effect of contact conditions and material properties on elastic–plastic spherical contact. J Mech Mater Struct 5:865–879CrossRefGoogle Scholar
  11. Bardet JP, Huang Q (1992) Numerical modeling of micro-polar effects in idealized granular materials. Am Soc Mech Eng Mater Div (Publication) MD 37:85–92Google Scholar
  12. Campbell C (2002) Granular shear flows at the elastic limit. J Fluid Mech 465:261–291MathSciNetzbMATHCrossRefGoogle Scholar
  13. Chen K, Cole J, Conger C et al (2012) Packing grains by thermally cycling. Physics 442(7100):257Google Scholar
  14. Chen K, Harris A, Draskovic J et al (2009) Granular fragility under thermal cycles. Granul Matter 11(4):237–242CrossRefGoogle Scholar
  15. Chang L, Zhang H (2007) A mathematical model for frictional elastic-plastic sphere-on-flat contacts at sliding incipient. J Appl Mech 74(1):100–106zbMATHCrossRefGoogle Scholar
  16. Derjaguin BV, Muller VM, Toporov YP (1975) Effect of contact deformations on the adhesion of particles. J Colloid Interface Sci 53(2):314–326CrossRefGoogle Scholar
  17. Di Renzo A, Di Maio FP (2004) Comparison of contact-force models for the simulation of collisions in dem-based granular flow codes. Chem Eng Sci 59(3):525–541CrossRefGoogle Scholar
  18. Feng YT, Han K, Owen DRJ (2012) Energy-conserving contact interaction models for arbitrarily shaped discrete elements. Comput Methods Appl Mech Eng 205–208(1):169–177MathSciNetzbMATHCrossRefGoogle Scholar
  19. Hadley GR (1986) Thermal conductivity of packed metal powders. Int J Heat Mass Transf 29(6):909–920CrossRefGoogle Scholar
  20. Iwashita K, Oda M (2000) Micro-deformation mechanism of shear banding process based on modified distinct element method. Powder Technol 109(1–3):192–205CrossRefGoogle Scholar
  21. Ji SY, Di SC, Long X (2017) DEM simulation of uniaxial compressive and flexural strength of sea ice: parametric study of inter-particle bonding strength. ASCE J Eng Mech 143(1):C4016010CrossRefGoogle Scholar
  22. Ji SY, Shen HH (2006) Effect of contact force models on granular flow dynamics. ASCE J Eng Mech 132(11):1252–1259CrossRefGoogle Scholar
  23. Ji S, Shen HH (2008) Internal parameters and regime map for soft poly-dispersed granular materials. J Rheol 52(1):87–103CrossRefGoogle Scholar
  24. Jiang MJ, Yu HS, Harris D (2005) A novel discrete model for granular material incorporating rolling resistance. Comput Geotech 32(5):340–357CrossRefGoogle Scholar
  25. Jiang M, Yu HS, Harris D (2006) Kinematic variables bridging discrete and continuum granular mechanics. Mech Res Commun 33(5):651–666MathSciNetzbMATHCrossRefGoogle Scholar
  26. Jiang S, Ye Y, Li X et al (2019) DEM modeling of crack coalescence between two parallel flaws in SiC ceramics. Ceram Int 45(12):14997–15014CrossRefGoogle Scholar
  27. Johnson KL, Greenwood JA (1997) An adhesion map for the contact of elastic spheres. J Colloid Interface Sci 192(2):326–333CrossRefGoogle Scholar
  28. Johnson KL, Kendall K, Roberts AD (1971) Surface energy and the contact of elastic solids. Proc R Soc Lond Math Phys Eng Sci 324(1558):301–313Google Scholar
  29. Kogut L, Etsion I (2003) A semi-analytical solution for the sliding inception of a spherical contact. ASME J Tribol 125:499–506CrossRefGoogle Scholar
  30. Kremmer M, Favier JF (2001a) A method for representing boundaries in discrete element modelling-Part II: kinematics. Int J Numer Meth Eng 51:1423–1436zbMATHCrossRefGoogle Scholar
  31. Kremmer M, Favier JF (2001b) A method for representing boundaries in discrete element modelling-part I: geometry and contact detection. Int J Numer Meth Eng 51:1407–1421zbMATHCrossRefGoogle Scholar
  32. Lambert MA, Fletcher LS (1996) Thermal contact conductance of spherical rough metals. J Heat Transfer 119(4):684–690CrossRefGoogle Scholar
  33. Landau LD, Lifshit’S EM (1999) Theory of elasticity. World Publishing CorporationGoogle Scholar
  34. Lian G, Thornton C, Adams MJ (1993) A theoretical study of the liquid bridge forces between two rigid spherical bodies. J Colloid Interface Sci 161(1):138–147CrossRefGoogle Scholar
  35. Lian G, Thornton C, Adams MJ (1998) Discrete particle simulation of agglomerate impact coalescence. Chem Eng Sci 53(19):3381–3391CrossRefGoogle Scholar
  36. Long X, Ji S, Wang Y (2019) Validation of microparameters in discrete element modeling of sea ice failure process. Part Sci Technol 37(5):546–555CrossRefGoogle Scholar
  37. Liu L, Ji S (2019) Bond and fracture model in dilated polyhedral DEM and its application to simulate breakage of brittle materials. Granular Matter 21(3):41CrossRefGoogle Scholar
  38. Lian G, Xu Y, Huang W et al (2001) On the squeeze flow of a power-law fluid between rigid spheres. J Nonnewton Fluid Mech 100(1):151–164zbMATHCrossRefGoogle Scholar
  39. Mcdowell GR, Bolton MD, Robertson D (1996) The fractal crushing of granular materials. J Mech Phys Solids 44:2079–2102CrossRefGoogle Scholar
  40. Mesarovic SD, Johnson KL (2000) Adhesive contact of elastic–plastic spheres. J Mech Phys Solids 48(10):2009–2033zbMATHCrossRefGoogle Scholar
  41. Mindlin RD, Deresiewicz H (1953) Elastic spheres in contact under varying oblique forces. ASME J Appl Mech 20:327–344MathSciNetzbMATHGoogle Scholar
  42. Mindlin RD (1949) Compliance of elastic bodies in contact. ASME J Appl Mech 16(3):259–268MathSciNetzbMATHGoogle Scholar
  43. Nitka M, Tejchman J (2015) Modelling of concrete behaviour in uniaxial compression and tension with DEM. Granular Matter 17(1):145–164CrossRefGoogle Scholar
  44. Olsson E, Larsson PL (2016) A unified model for the contact behaviour between equal and dissimilar elastic–plastic spherical bodies. Int J Solids Struct 81:23–32CrossRefGoogle Scholar
  45. Oda M, Iwashita K (2000) Study on couple stress and shear band development in granular media based on numerical simulation analyses. Int J Eng Sci 38(15):1713–1740CrossRefGoogle Scholar
  46. Onate E, Rojek J (2004) Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems. Comput Methods Appl Mech Eng 193:3087–3128zbMATHCrossRefGoogle Scholar
  47. Popov VL (2010) Contact mechanics and friction: physical principles and applications. Springer, BerlinzbMATHCrossRefGoogle Scholar
  48. Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364CrossRefGoogle Scholar
  49. Richefeu V, Youssoufi MSE, Peyroux R et al (2008) A model of capillary cohesion for numerical simulations of 3D polydisperse granular media. Int J Numer Anal Meth Geomech 32(11):1365–1383zbMATHCrossRefGoogle Scholar
  50. Scholtes L, Donze FV (2012) Modelling progressive failure in fractured rock masses using a 3D discrete element method. Int J Rock Mech Min Sci 52:18–30CrossRefGoogle Scholar
  51. Shen HH, Sankaran B (2004) Internal length and time scales in a simple shear granular flow. Phys Rev E 70:051308CrossRefGoogle Scholar
  52. Soulié F, Cherblanc F, Youssoufi MSE et al (2010) Influence of liquid bridges on the mechanical behaviour of polydisperse granular materials. Int J Numer Anal Meth Geomech 30(3):213–228zbMATHCrossRefGoogle Scholar
  53. Sridhar MR, Yovanovich MM (1996) Empirical methods to predict Vickers microhardness. Wear 193(1):91–98CrossRefGoogle Scholar
  54. Tabor D (1959) Junction growth in metallic friction: the role of combined stresses and surface contamination. Proc R Soc Lond A 251:378–393CrossRefGoogle Scholar
  55. Tanner LH, Fahoum M (1976) A study of the surface parameters of ground and lapped metal surfaces, using specular and diffuse reflection of laser light. Wear 36(3):299–316CrossRefGoogle Scholar
  56. Tarokh A, Fakhimi A (2014) Discrete element simulation of the effect of particle size on the size of fracture process zone in quasi-brittle materials. Comput Geotech 62:51–60CrossRefGoogle Scholar
  57. Thornton C (1997) Coefficient of restitution for collinear collisions of elastic-perfectly plastic spheres. Trans ASME J Appl Mech 64:383–386zbMATHCrossRefGoogle Scholar
  58. Vu-Quoc L, Zhang X, Lesburg L (2001) Normal and tangential force-displacement relations for frictional elasto-plastic contact of spheres. Int J Solids Struct 38:6455–6489zbMATHCrossRefGoogle Scholar
  59. Wang S, Fan Y, Ji S (2018) Interaction between super-quadric particles and triangular elements and its application to hopper discharge. Powder Technol 339:534–549CrossRefGoogle Scholar
  60. Wang Y, Tonon F (2010) Calibration of a discrete element model for intact rock up to its peak strength. Int J Numer Anal Meth Geomech 34(5):447–469zbMATHCrossRefGoogle Scholar
  61. Wang Y, Tonon F (2009) Modeling Lac du Bonnet granite using a discrete element model. Int J Rock Mech Min Sci 46(7):1124–1135CrossRefGoogle Scholar
  62. Weerasekara NS (2013) The contribution of DEM to the science of comminution. Powder Technol 248:3–24CrossRefGoogle Scholar
  63. Weidenfeld G, Weiss Y, Kalman H (2003) The effect of compression and preconsolidation on the effective thermal conductivity of particulate beds. Powder Technol 133(1):15–22CrossRefGoogle Scholar
  64. Weidenfeld G, Weiss Y, Kalman H (2004) A theoretical model for effective thermal conductivity (ETC) of particulate beds under compression. Granular Matter 6(2–3):121–129zbMATHCrossRefGoogle Scholar
  65. Wensrich CM, Katterfeld A (2012) Rolling friction as a technique for modelling particle shape in DEM. Powder Technol 217(2):409–417CrossRefGoogle Scholar
  66. Wu CY, Li LY, Thornton C (2003) Rebound behaviour of spheres for plastic impacts. Int J Impact Eng 28(9):929–946CrossRefGoogle Scholar
  67. Zhang DZ, Rauenzahn RM (2000) Stress relaxation in dense and slow granular flows. J Rheol 44(5):1019–1041CrossRefGoogle Scholar
  68. Zhang HW, Zhou Q, Xing HL et al (2011) A DEM study on the effective thermal conductivity of granular assemblies. Powder Technol 205(1–3):172–183CrossRefGoogle Scholar
  69. Zheng QJ, Zhou ZY, Yu AB (2013) Contact forces between viscoelastic ellipsoidal particles. Powder Technol 248:25–33CrossRefGoogle Scholar
  70. Zhou Y, Zhou Y (2011) A theoretical model of collision between soft-spheres with Hertz elastic loading and nonlinear plastic unloading. Theor Appl Mech Lett 1(4):34–39CrossRefGoogle Scholar
  71. Zhu HP, Zhou ZY, Yang RY et al (2008) Discrete particle simulation of particulate systems: a review of major applications and findings. Chem Eng Sci 63(23):5728–5770CrossRefGoogle Scholar

Copyright information

© Science Press and Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of Engineering MechanicsDalian University of TechnologyDalianChina
  2. 2.Department of Engineering MechanicsDalian University of TechnologyDalianChina

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