Compaction mechanics of a polydisperse crushable spherical granular assembly using discrete element method


The macroscopic behaviour of an assembly of polydisperse spherical particles is studied using a numerical model based on discrete element method (DEM), which accounts for the microscopic interactions between individual particles and their damage. DEM models particle–particle interactions enabling to understand the influence of microscopic particle–particle interactions on the macroscopic response. The method is used to stimulate the mechanical response of a polydisperse particle assembly under uniaxial compressive load. The influence of damage rate and the initial packing fraction on the macroscopic stress–strain response is investigated. The analysis shows that the initial nonlinear elastic behaviour is influenced by the initial packing factor, whereas the critical stress is influenced by both initial packing fraction and damage rate. It is also observed that critical stress occurs when the assembly reaches a particular damage state. Furthermore, the failure behaviour of different sized particles within a polydisperse assembly is also investigated. The experimental data from the literature show that the crush strength of the particle of given size is observed to vary over a range. Such variation of crush strengths for a given particle size is also implemented in the present work.

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  1. 1.

    Pupeschi, S., Knitter, R., Kamlah, M.: Effective thermal conductivity of advanced ceramic breeder pebble beds. Fusion Eng. Des. 116, 73–80 (2017)

    Article  Google Scholar 

  2. 2.

    Reimann, J., Hermsmeyer, S.: Thermal conductivity of compressed ceramic breeder pebble beds. Fusion Eng. Des. 61, 345–351 (2002)

    Article  Google Scholar 

  3. 3.

    Moscardini, M., Gan, Y., Pupeschi, S., Kamlah, M.: Discrete element method for effective thermal conductivity of packed pebbles accounting for the Smoluchowski effect. Fusion Eng. Des. 127, 192–201 (2018)

    Article  Google Scholar 

  4. 4.

    Piazza, G., Jörg Reimann, E., Günther, R.K., Roux, N., Lulewicz, J.D.: Characterisation of ceramic breeder materials for the helium cooled pebble bed blanket. J. Nucl. Mater. 307, 811–816 (2002)

    Article  Google Scholar 

  5. 5.

    Peeketi, Akhil Reddy, Moscardini, Marigrazia, Vijayan, Akhil, Gan, Yixiang, Kamlah, Marc, Annabattula, Ratna Kumar: Effective thermal conductivity of a compacted pebble bed in a stagnant gaseous environment: An analytical approach together with DEM. Fusion Eng. Des. 130, 80–88 (2018)

    Article  Google Scholar 

  6. 6.

    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)

    Article  Google Scholar 

  7. 7.

    Annabattula, R.K., Gan, Y., Zhao, S., Kamlah, M.: Mechanics of a crushable pebble assembly using discrete element method. J. Nucl. Mater. 430, 90–95 (2012)

    Article  Google Scholar 

  8. 8.

    Lew, V., Jon, T., Ying, A., Abdou, M.: A discrete element method study on the evolution of thermomechanics of a pebble bed experiencing pebble failure. Fusion Eng. Des. 89(7), 1151–1157 (2014)

    Google Scholar 

  9. 9.

    Gan, Y., Kamlah, M.: Discrete element modelling of pebble beds: with application to uniaxial compression tests of ceramic breeder pebble beds. J. Mech. Phys. Solids 58(2), 129–144 (2010)

    Article  Google Scholar 

  10. 10.

    Ying, A., Akiba, M., Boccaccini, L.V., Casadio, S., Dell’Orco, G., Enoeda, M., Hayashi, K., Hegeman, J.B., Knitter, R., van der Laan, J., et al.: Status and perspective of the R&D on ceramic breeder materials for testing in ITER. J. Nucl. Mater. 367, 1281–1286 (2007)

    Article  Google Scholar 

  11. 11.

    Reimann, J., Boccaccini, L., Enoeda, M., Ying, A.Y.: Thermomechanics of solid breeder and Be pebble bed materials. Fusion Eng. Des. 61, 319–331 (2002)

    Article  Google Scholar 

  12. 12.

    Zaccari, N.: Aquaro, donato: mechanical characterization of Li2TiO3 and Li4SiO4 pebble beds: experimental determination of the material properties and of the pebble bed effective values. Fusion Eng. Des. 82(15), 2375–2382 (2007)

    Article  Google Scholar 

  13. 13.

    Löbbecke, B., Knitter, R.: Procurement and quality control of Li\(_4\)SiO\(_4\) pebbles for testing of breeder unit mock-ups. Report on TW6-TTBB-006-D2, FZK Fusion (2007)

  14. 14.

    Zhao, S.: Multiscale modeling of thermomechanical properties of ceramic pebbles. Ph.D. Thesis, Karlsruhe Institute of Technology (2010)

  15. 15.

    Desu, R.K., Chaudhuri, P., Annabattula, R.K.: High temperature oedometric compression of Li2TiO3 pebble beds for Indian TBM. Fusion Eng. Des. 136, 945–949 (2018)

    Article  Google Scholar 

  16. 16.

    Annabattula, R.K., Kolb, M., Gan, Y., Rolli, R., Kamlah, M.: Size-dependent crush analysis of lithium orthosilicate pebbles. Fusion Sci. Technol. 66, 136–141 (2014)

    Article  Google Scholar 

  17. 17.

    Gan, Y., Kamlah, M., Reimann, J.: Computer simulation of packing structure in pebble beds. Fusion Eng. Des. 85(10–12), 1782–1787 (2010)

    Article  Google Scholar 

  18. 18.

    Desu, R.K., Annabattula, R.K.: Particle size effects on the contact force distribution in compacted polydisperse granular assemblies. Granul. Matter 21(2), 29 (2019)

    Article  Google Scholar 

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Correspondence to Raghuram Karthik Desu.

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Desu, R.K., Gan, Y., Kamlah, M. et al. Compaction mechanics of a polydisperse crushable spherical granular assembly using discrete element method. Int J Adv Eng Sci Appl Math (2021).

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  • Crushing
  • Polydispersed granular assembly
  • Discrete element method