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Numerical simulations of shock-induced load transfer processes in granular media using the discrete element method

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Abstract

By the discrete element method (DEM), we perform numerical simulations of shock-induced load transfer processes in granular layers composed of spherical particles packed in vertical channels. In order to isolate the load transfer through the grains’ contact points from the complicated load transfer processes, we simulate the shock wave interactions with granular layers having no permeability for gas. The shock loading is achieved by applying a downward step force on the top of the granular layers. Complex, three-dimensional load transfer processes in the granular media, which are extremely difficult to understand from experiments, are visualized based on the results from the present DEM simulation. The numerical results show that highly concentrated load transfer paths, through which shock loads are transferred mainly, exist in the granular media, and that the dimensions of the container of the granular media considerably affect the shock-induced load transfer processes. From a coarse-grained representation of intergranular stress, wave-like load transfer processes are clearly observed. For relatively deep granular layers, however, the wave fronts became unclear as they propagated.

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References

  1. Jaeger H.M., Nagel S.R., Behringer R.P.: Granular solids, liquids, and gases. Rev. Mod. Phys. 68, 1259–1273 (1996)

    Article  Google Scholar 

  2. Britan A., Levy A.: Weak shock wave interaction with inert granular media. In: Ben-Dor, G., Igra, O., Elperin, T. (eds) Handbook of Shock Waves, vol. 2., pp. 597–666. Academic Press, San Diego (2001)

    Google Scholar 

  3. Suzuki, T., Adachi, T.: A basic study of the blast waves over a dust deposit. In: The Japan National Committee for Theoretical and Applied Mechanics (ed.) Theoretical and Applied Mechanics, vol. 31, pp. 439–446. University of Tokyo Press, Tokyo (1982)

  4. Adachi, T., Suzuki, T.: The singular pressure wave in a dust layer over which a shock wave is propagating. In: Archer, R.D., Milton, B.E. (eds.) Proceedings of the 14th International Symposium on Shock Tubes and Waves, pp. 497–504 (1983)

  5. Gelfand B.E., Medvedev S.P., Borisov A.A., Polenov A.N., Frolov S.M., Tsyganov S.A.: Shock loading of stratified dusty systems. Arch. Combust. 9, 153–165 (1989)

    Google Scholar 

  6. Sakakita, H., Hayashi, A.K.: Study on pressure profiles in a powder layer using a vertical shock tube. In: Proceedings of the Symposium on Shock Waves, Japan ’92, pp. 655–660 (1992)

  7. Ben-Dor G., Britan A., Elperin T., Igra O., Jiang J.P.: Experimental investigation of the interaction between weak shock waves and granular layers. Exp. Fluid 22, 432–443 (1997)

    Article  Google Scholar 

  8. Britan A., Ben-Dor G., Elperin T., Igra O., Jiang J.P.: Mechanism of compressive stress formation during weak shock wave impact with granular materials. Exp. Fluid 22, 507–518 (1997)

    Article  Google Scholar 

  9. Britan A., Ben-Dor G., Elperin T., Igra O., Jiang J.P.: Gas filtration during the impact of weak shock waves on granular layers. Int. J. Multiph. Flow 24, 473–491 (1997)

    Article  Google Scholar 

  10. Britan, A., Ben-Dor, G., Levy, A., Igra, O.: Shock wave interaction with granular materials. In: Ball, G.J. et al. (eds.) Proceedings of the 22nd International Symposium on Shock Waves, pp. 1375–1380 (2000)

  11. Mikami, H., Kaneda, T., Sakamura, Y., Suzuki, T.: Head-on collisions of a planar shock wave with a dust layer, In: Kimura, T. (ed.) Theoretical and Applied Mechanics, vol. 49, pp. 263–270 (2000)

  12. Britan A., Ben-Dor G., Igra O., Shapiro H.: Shock wave attenuation by granular filters. Int. J. Multiph. Flow 27, 634–671 (2001)

    Article  Google Scholar 

  13. Glam B., Igra O., Britan A., Ben-Dor G.: Dynamics of stress wave propagation in a chain of photoelastic discs impacted by a planar shock wave; Part I, experimental investigation. Shock Waves 17, 1–14 (2007)

    Article  Google Scholar 

  14. Goldenberg A., Igra O., Britan A., Ben-Dor G.: Dynamics of stress wave propagation in a chain of photoelastic discs impacted by a planar shock wave; Part II, numerical investigation. Shock Waves 17, 15–27 (2007)

    Article  Google Scholar 

  15. Cundall P.A., Strack O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 29, 47–65 (1979)

    Article  Google Scholar 

  16. The Society of Powder Technology, Japan: Introduction to Powder Simulation (in Japanese). Sangyo-Tosho, Tokyo (1998)

  17. Duran J.: Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials. Springer, New York (1999)

    Google Scholar 

  18. Pöschel T., Schwager T.: Computational Granular Dynamics: Models and Algorithms. Springer, Berlin (2005)

    Google Scholar 

  19. Tanaka K., Nishida M., Kunimochi T., Takagi T.: Discrete element simulation and experiment for dynamic response of two-dimensional granular matter to the impact of a spherical projectile. Powder Technol. 124, 160–173 (2002)

    Article  Google Scholar 

  20. Nishida M., Tanaka K., Matsumoto Y.: Discrete element method simulation of the restitutive characteristics of a steel spherical projectile from a particulate aggregation. JSME Int. J. Ser. A 47, 438–447 (2004)

    Article  Google Scholar 

  21. Nishida, M., Tanaka, K., Ishida, T.: DEM simulation of wave propagation in two-dimensional ordered array of particles. In: Hannemann, K., Seiler, F. (eds.) Proceedings of the 26th International Symposium on Shock Waves, pp. 815–820 (2009)

  22. Nishida M., Tanaka Y.: DEM simulations and experiments for projectile impacting two-dimensional particle packings including dissimilar material layers. Granul. Matter 12, 357–368 (2010)

    Article  Google Scholar 

  23. Nishida M., Nagamatsu J., Tanaka T.: Discrete element method analysis of ejection and penetration of projectile impacting granular media. J. Solid Mech. Mater. Eng. 5(4), 164–178 (2011)

    Article  Google Scholar 

  24. Kano, J.: Study on powder simulation by particle methods (in Japanese). Doctor Thesis, Graduate School of Engineering, Doshisha University (1996)

  25. Timoshenko S.P., Goodier J.N.: Theory of Elasticity, 3rd edn, pp. 409–414. McGraw-Hill, Auckland (1970)

    MATH  Google Scholar 

  26. Sakakibara, Y.: Two-dimensional discrete element method analysis of a shock-loaded granular layer (in Japanese). Master Thesis, Graduate School of Mechanical Systems Engineering, Toyama Prefectural University (2006)

  27. Mindlin R.D.: Compliance of elastic bodies in contact. J. Appl. Mech. 16, 259–268 (1949)

    MATH  MathSciNet  Google Scholar 

  28. Mindlin R.D., Deresiewicz H.: Elastic spheres in contact under varying oblique forces. J. Appl. Mech. 20, 327–344 (1953)

    MATH  MathSciNet  Google Scholar 

  29. The POV-Team: POV-Ray Reference for POV-Ray Ver. 3.6.1. POV-Ray official site. http://www.povray.org. Accessed 25 Feb. 2011

  30. Roessig K.M., Foster J.C. Jr, Bardenhagen S.G.: Dynamic stress chain formation in a two-dimensional particle bed. Exp. Mech. 42, 329–337 (2002)

    Article  Google Scholar 

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Correspondence to Y. Sakamura.

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Communicated by O. Igra.

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Sakamura, Y., Komaki, H. Numerical simulations of shock-induced load transfer processes in granular media using the discrete element method. Shock Waves 22, 57–68 (2012). https://doi.org/10.1007/s00193-011-0347-6

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  • DOI: https://doi.org/10.1007/s00193-011-0347-6

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