Skip to main content
SpringerLink
Log in

Multiscale mechanical behaviors in discrete materials: A review

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

The discrete material, which belongs to the category of soft materials, is one of the most prevalent forms of matter in nature and engineering fields. These materials often exhibit abundant and complex mechanical properties which are still far from being perfectly understood. From the view of multi-scale framework concentrated on the ‘bridge’ role in the macro-micro relation, this review mainly introduces some theoretical investigations of mechanical behaviors in discrete materials, including the continuum constitutive model based on the macroscopic phenomenological approach and coupled micro-macro approach, the statistical analysis of some microscopic physical quantities involved contacted forces between particles and its transmission within the whole system, and the statistical analysis for some microscopic processes in aeolian landform systems involving the grain-bed impact, the transportation and sedimentation of wind-blown sand flux, et al. Finally, some further worthwhile challenges in these fields are suggested.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bai, Y.L., Wang, H.Y., Xia, M.F. and Ke, F.J., Statistical mesomechanics of solid, linking coupled multiple space and time scales. Applied Mechanics Reviews, 2005, 58: 372–388.

    Article  Google Scholar 

  2. Landau, L.D. and Lifshitz, E.M., Statistical Physics. Translated by Peierls, E. and Peierls, R.F., London: Pergamon Press, 1958.

    MATH  Google Scholar 

  3. Liao, C.C. and Hsiau, S.S., Influence of interstitial fluid viscosity on transport phenomenon in sheared granular materials. Chemical Engineering Science, 2009, 64: 2562–2569.

    Article  Google Scholar 

  4. Li, Y.C., Zhang, Z.B., Tu, H.E., Liu, R., Hu, H.Y. and Hou, M.Y., The flux profile of granular gas in compartmentalized system. Acta Physica Sinica, 2009, 58(8): 5857–5863 (in Chinese).

    Google Scholar 

  5. Hou, M., Chen, W., Zhang, T. and Lu, K., Global nature of dilute-to-dense transition of granular flows in a 2D Channel. Physical Review Letters, 2003, 91: 204301.

    Article  Google Scholar 

  6. Börzsöny, T., Halsey, T.C. and Ecke, R.E., Avalanche dynamics on a rough inclined plane. Physical Review E, 2008, 78: 011306.

    Article  Google Scholar 

  7. Peters, J.F., Muthuswamy, M., Wibowo, J. and Tordesillas, A., Characterization of force chains in granular material. Physical Review E, 2005, 72: 041307.

    Article  Google Scholar 

  8. Sun, Q.C., Jin, F., Wang, G.Q. and Zhang, G.H., Force chains in a uniaxially compressed static granular matter. Acta Physica Sinica, 2010, 29(1): 30–37 (in Chinese).

    Google Scholar 

  9. Tsimring, L.S., Patterns and collective behavior in granular media: theoretical concepts. Reviews of Modern Physics, 2006, 78: 641–687.

    Article  Google Scholar 

  10. Bizon, C., Shattuck, M.D., Swift, J.B., McCormick. W.D. and Swinney, H.L., Patterns in 3D vertically oscillated granular layers: simulation and experiment. Physical Review Letters, 1998, 80(1): 57–60.

    Article  Google Scholar 

  11. Wu, Q.S. and Hu, M.B., Advances on dynamic modeling and experimental studies for granular flow. Advances in Mechanics, 2002 32(2): 250–258 (in Chinese).

    Google Scholar 

  12. Campbell, C.S., Granular material flows—An overview. Powder Technology, 2006, 162: 208–229.

    Article  Google Scholar 

  13. Ji, S.Y. and Shen, H.H., Characteristics of temporalspatial in quasi solid-fluid phase transition of granular materials. Chinese Science Bulletin, 2006, 51(3): 255–262 (in Chinese).

    Google Scholar 

  14. Li, S.H., Li, X. And Liu, X.Y., Some issues in engineering geomechanics and its applications. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(6): 1125–1140 (in Chinese).

    MathSciNet  Google Scholar 

  15. Wang, G.Q. and Ni, J.R., Basic equation for debris flow. Chinese Science Bulletin, 1994, 39(18): 1700–1710 (in Chinese).

    Google Scholar 

  16. Cui, P., Experimental study of starting conditions and mechanics in debris flow. Chinese Science Bulletin, 1991, 36(21): 1650–1660 (in Chinese).

    MathSciNet  Google Scholar 

  17. Xu, X.Z., Zhang, H.W., Zhang. L. and Li, Z.M., Study of sediment yield in soil and water conservation model. Soil and Water Conservation, 2007, 1: 35–37 (in Chinese).

    Google Scholar 

  18. Jiang, M.J., Main features of future constitutive models for granular materials in penetration analysis. Chinese Journal of Geotechnical Engineering, 2007, 29(9): 1281–1288 (in Chinese).

    Google Scholar 

  19. Zhang, H.W., Wang, K.P. and Chen, Z., Material point method for dynamic analysis of saturated porous media. Chinese Journal of Geotechnical Engineering, 2009, 31(10): 1505–1511 (in Chinese).

    Google Scholar 

  20. Zhou, J., Wang, J.Q., Kong, X.L. and Jia, M.C., Mesoscopic study of the interface between sandy soil and geosynthetics. Chinese Journal of Geotechnical Engineering, 2010, 32(1): 61–67 (in Chinese).

    Google Scholar 

  21. Zhang, Y.F., Zhu, T., Feng, Y.C., Han, S.Q., Li, X. and Liu, C.X., Evaluation model for the effectiveness of air pollution control and its application. China Environmental Science, 2009, 29(3): 225–230 (in Chinese).

    Google Scholar 

  22. Jin, X.C. and Wang, G.L., Sediment effects about adsorption of heavy metal. Environmental Science and Technology, 1984, 2: 6–11 (in Chinese).

    Google Scholar 

  23. Zheng, X.J., He, L.H. and Wu, J.J., Vertical profiles of mass flux for windblown sand movement at steady state. Journal of Geophysical Research, 2004, 109: B01106.

    Google Scholar 

  24. Zheng, X.J., Mechanics of Wind-blown Sand Movement. German: Springer-Verlag, 2009.

    Book  Google Scholar 

  25. Daouadji, A., Hicher, P.Y. and Rahma, A., An elastoplastic model for granular materials taking into account grain breakage. European Journal of Mechanics-A/Solid, 2001, 20: 113–137.

    Article  Google Scholar 

  26. Cundall, P.A. and Strack, O.D.L., A discrete numerical model for granular assemblies. Geotechnique, 1979, 299(1): 47–65.

    Article  Google Scholar 

  27. Kuhn, M.R. Micro-mechanics of fabric and failure in granular materials. Mechanics of Materials, 2010, 42: 827–840.

    Article  Google Scholar 

  28. Shen, C.W., Ji, S.Y. and Lei, J.P., Granular material and hypoelastic constitutive model. Journal of Wuhan Tansportation University, 1997, 21(6): 622–627 (in Chinese).

    Google Scholar 

  29. Wu, W. and Bauer, E., Hypoplastic constitutive model with critical state for granular materials. Mechanics of Materials, 1996, 23: 45–49.

    Article  Google Scholar 

  30. Chu, X.H., Xu, Y.J., Zhang, M.L. and Yu, C., Numerical implementations and discussion on hypoplastic model for granular materials based on ABAQUS. Rock and Soil Mechanics, 2009, 30: 215–224 (in Chinese).

    Google Scholar 

  31. Anand, L. and Gu, C., Granular materials: constitutive equations and strain localization. Journal of the Mechanics and Physics of Solids, 2000, 48: 1701–1733.

    Article  MathSciNet  Google Scholar 

  32. Darve, F., Flavigny, E. and Meghachou, M., Yield surfaces and principle of superposition revisited by incrementally non-linear constitutive relations. International Journal of Plasticity, 1995, 11(8): 927–948.

    Article  Google Scholar 

  33. Roscoe, K.H., Schofield, A.N. and Wroth, C.P., On the yielding of soils. Geotechnique, 1958, 8: 22–52.

    Article  Google Scholar 

  34. Jiang, P.N., Constitutive Models in Soils. Beijing: Science Press, 1982 (in Chinese).

    Google Scholar 

  35. Hueckel, T., Chemo-plasticity of clays subjected to stress and flow of a single contaminant. International Journal for Numerical and Analytical Methods in Geomechanics, 1997, 21: 43–72.

    Article  Google Scholar 

  36. Loret, B., Hueckel, T. and Gajo, A., Chemo-mechanical coupling in saturated porous media: elastic-plastic behaviour of homoionic expansive clays. International Journal of Solids and Structures, 2002, 39: 2773–2806.

    Article  Google Scholar 

  37. Ni, J.R. and Wang, G.Q., Conceptual two phase flow model of debris flow—I. theory. Acta Geographica Sinaca, 1998, 53(1): 66–76 (in Chinese).

    Google Scholar 

  38. Huttcr, K., Svendsen, B. and Rickenmann, D., Debris flow modeling: a review. Continuum Mechanics and Thermodynamics, 1996, 8: 1–35.

    Article  MathSciNet  Google Scholar 

  39. Nubel, K. and Huang, W.X., A study of localized deformation pattern in granular media. Computer Methods in Applied Mechanics and Engineering, 2004, 193: 2719–2743.

    Article  MathSciNet  Google Scholar 

  40. Li, X.K., Liu, Q.P. and Zhang, J.B., A micro-macro homogenization approach for discrete particle assembly—cosserat continuum modeling of granular materials. International Journal of Solids and Structures, 2010, 47: 291–303.

    Article  Google Scholar 

  41. Nemat-Nasser, S., A micromechanically-based constitutive model for firctional deformation of granular materials. Journal of the Mechanics and Physics of Solids, 2000, 48: 1541–1563.

    Article  MathSciNet  Google Scholar 

  42. Nemat-Nasser, S. and Zhang, J.H., Constitutive relations for cohesionless frictional granular materials. International Journal of Plasticity, 2002, 18: 531–547.

    Article  Google Scholar 

  43. Borja, R.I., Condition for liquefaction instability in fluid-saturated granular soils. Acta Geotechnica, 2006, 1: 211–224.

    Article  Google Scholar 

  44. Oda, M., Takemura, T. and Takahashi, M., Microstructure in shear band observed by microfocus X-ray computed tomography. Géotechnique, 2004, 54: 539–542.

    Article  Google Scholar 

  45. Nicot, F. and Darve, F., A multi-scale approach to granular materials. Mechanics of Materials, 2005, 37: 980–1006.

    MATH  Google Scholar 

  46. Liu, S.H., Yao, Y.P., Sun, Q.C., Li, T.J. and Liu, M.Z., Microscopic study on stress-strain relation of granular materials. Chinese Science Bulletin, 2009, 54(11): 1496–1503 (in Chinese).

    Article  Google Scholar 

  47. Li, X., Yu, H.S. and Li, X.S., Macro-micro relations in granular mechanics. International Journal of Solids and Structures, 2009, 46: 4331–4341.

    Article  Google Scholar 

  48. Stroeven, M., Askes, H. and Sluys, L.J., Numerical determination of representative volumes for granular materials. Computer Methods in Applied Mechanics and Engineering, 2004, 193: 3221–3238.

    Article  Google Scholar 

  49. Lätzel, M., Luding, S. and Herrmann, H.J., Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell. Granular Matter, 2000, 2(3): 1–12.

    Article  Google Scholar 

  50. Hu, N. and Molinari, J.F., Shear bands in dense metallic granular materials. Journal of the Mechanics and Physics of Solids, 2004, 52: 499–531.

    Article  Google Scholar 

  51. Wang, D.M. and Zhou, Y.H., Shear profiles and velocity distribution in dense shear granular flow. Chinese Physics Letter, 2009, 26(2): 024501.

    Article  Google Scholar 

  52. Gladwell, G.M.L., Classical Contact Problem of Elasticity Theory. Translated by Fan, T.Y. Beijing: Beijing Institute of Technology Press, 1991 (in Chinese).

    Google Scholar 

  53. Johnson, K.L., Kendall, K. and Roberts, A.D., Surface energy and the contact of elastic solids. Proceeding of the Royal Society A, 1971, 324: 301–313.

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  55. Thornton, C. and Ning, Z.M., A theoretical model for the stick/bounce behaviour of adhesive elastic-plastic spheres. Powder Technology, 1998, 99: 154–162.

    Article  Google Scholar 

  56. Vu-Quoc, L. and Zhang, X., A normal force-displacement model for contacting spheres accounting for plastic deformation: force-driven formulation. Journal of Applied Mechanics, 2000, 67: 363–371.

    Article  Google Scholar 

  57. Zhang, H.W. and Qin, J.M., Simulation of mechanical behaviors of granular materials by discrete element method based on mesoscale nonlinear contact law. Chinese Journal of Geotechnical Engineering, 2006, 28(11): 1964–1969 (in Chinese).

    Google Scholar 

  58. Claudin, P. and Bouchaud, J.P., Static avalanches and giant stress fluctuations in silos. Physical Review Letters, 1997, 78: 231.

    Article  Google Scholar 

  59. Blair, D.L., Mueggenburg, N.W., Marshall, A.H., Jaeger, H.M. and Nagel, S.R., Force distributions in three-dimensional granular assemblies: effects of packing order and interparticle friction. Physical Review E, 2001, 63: 041304.

    Article  Google Scholar 

  60. Makse, H.A., Johnson, D.L and Schwartz, L.M., Packing of compressible granular materials. Physical Review Letters, 2002, 84: 4160.

    Article  Google Scholar 

  61. Geng, J.F., Howell, D., Longhi.E. and Behringer, R.P., Footprints in sand: the response of a granular material to local perturbations. Physical Review Letters, 2001, 87: 035506.

    Article  Google Scholar 

  62. Corwin, E.I., Jaeger, H.M. and Nagel, S.R., Structural signature of jamming in granular media. Nature (London), 2005, 435: 1075–1078.

    Article  Google Scholar 

  63. Wang, D.M. and Zhou, Y.H., Particle dynamics in dense sheared granular flow. Acta Mechanica Sinica, 2010, 26(1): 91–100.

    Article  MathSciNet  Google Scholar 

  64. Schulz, M. and Schulz, B.M., Shear-induced solid-fluid transition in a wet granular medium. Physical Review E, 2005, 67: 052301.

    Article  Google Scholar 

  65. Aumaître, S., Schnautz, T., Kruelle, C.A. and Rehberg, I., Granular phase transition as a precondition for segregation. Physical Review Letters, 2003, 90: 114302.

    Article  Google Scholar 

  66. D’Anna, G. and Gremaud, G., The jamming route to the glass state in weakly perturbed granular media. Nature (London), 2001, 413: 407–409.

    Article  Google Scholar 

  67. Schröter, M., Goldman, D.I. and Swinney, H.L., Stationary state volume fluctuations in a granular medium. Physical Review E, 2005, 71: 030301(R).

    Article  Google Scholar 

  68. Bocquet, L., Errami, J. and Lubensky, T.C., Hydrodynamic model for a dynamical jammed-to-flowing transition in gGravity driven granular media. Physical Review Letters, 2002, 89: 184301.

    Article  Google Scholar 

  69. Orpe, A.V. and Khakhar, D.V., Solid-fluid transition in agranular shear flow. Physical Review Letters, 2004, 93: 068001.

    Article  Google Scholar 

  70. Zheng, X.J., Bo, T.L. and Xie, L., DPTM simulation of aeolian sand ripple, Science in China (Series G), 2008 51(3): 328–336.

    Google Scholar 

  71. Zheng, X.J., Bo, T.L. and Zhu, W., A scale-coupled method for simulation of the formation and evolution of aeolian dune field. International Journal of Nonlinear Sciences and Numerical Simulation, 2009, 10: 387–395.

    Google Scholar 

  72. Yue, G.W. and Zheng, X.J., Electric field in wind-blown sand flux with thermal diffusion. Journal of Geophysical Research, 2006, 111: D16106.

    Article  Google Scholar 

  73. Zheng, X.J., Xie, L. and Zou, X.Y., Theoretical prediction of liftoff angular velocity distributions of sand particles in wind-blown sand flux. Journal of Geophysical Research, 2006, 111: D11109.

    Article  Google Scholar 

  74. Xie, L., Ling, Y.Q. and Zheng, X.J., Laboratory measurement of saltating sand particles’ angular velocities and simulation of its effect on saltation trajectory, Journal of Geophysical Research, 2007, 112: D12116.

    Article  Google Scholar 

  75. Zhou, Y.H., Li, W.Q. and Zheng, X.J., Particle dynamics method simulations of stochastic collisions of sandy grain bed with mixed size in aeolian sand saltation. Journal of Geophysical Research, 2006, 111: D15108.

    Article  Google Scholar 

  76. Zheng, X.J., Zhu, W. and Xie, L., A probability density function of liftoff velocities in mixed-size wind sand flux. Science in China (Series G), 2008, 51(8): 976–985.

    Article  Google Scholar 

  77. Zheng, X.J. and Zhang, J.H., Characteristics of near-surface turbulence during a dust storm passing Minqin on March 19, 2010, Chinese Science Bulletin, 2010, 55(3): 1–7.

    Google Scholar 

  78. Uehara, J.S., Ambroso, M.A., Ojha, R.P. and Durian, D.J., Low-speed impact craters in loose granular media, Physical Review Letters, 2003, 90: 194301.

    Article  Google Scholar 

  79. Ambroso, M.A., Santore, C.R., Abate, A.R. and Durian, D.J., Penetration depth for shallow impact cratering. Physical Review E, 2005, 71: 051305.

    Article  Google Scholar 

  80. Walsh, A.M., Holloway, K.E., Habdas, P. and Bruyn, J.R., Morphology and scalling of impact craters in granular media. Physical Review E, 2003, 91: 104301.

    Google Scholar 

  81. Zheng, X.J., Wang, Z.T. and Qiu, Z.G., Impact craters in loose granular media. The European Physical Journal E, 2004, 13: 321–324.

    Article  Google Scholar 

  82. Nishida, M., Okumura, M. and Tanaka, K., Effects of density ratio and diameter ratio on critical incident angles of projectiles impacting granular media. Granular Matter, 2010, 12(4): 337–344.

    Article  Google Scholar 

  83. Kadanoff, L.P., Statistical Physics (Staics, Dynamics and Renormalization). Singapore: Word Scientific, 2000.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Mechanics on Western Disaster and Environment, the Ministry of Education of China, Lanzhou University, Lanzhou, 730000, China

    Xiaojing Zheng & Dengming Wang

Authors
  1. Xiaojing Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dengming Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaojing Zheng.

Additional information

Project supported by the Ministry of Science and Technology of China (No. 2009CB421304), National Natural Science Foundation of China (Nos. 10872082 and 11002064), Ministry of Education, Science and Technology Research Project (No. 308022).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zheng, X., Wang, D. Multiscale mechanical behaviors in discrete materials: A review. Acta Mech. Solida Sin. 23, 579–591 (2010). https://doi.org/10.1016/S0894-9166(11)60005-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S0894-9166(11)60005-0

Key words

Search

Navigation