Skip to main content
SpringerLink
Log in

Role of packing defects in force networks of hexagonally packed structures using discrete element method

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

Packed structures are an essential part of nuclear reactors, food, chemical, transport, and process industries. Since the safety and quality of products in the packed structures is of high priority, identifying critical failure spots in packed structures is of utmost importance. The present study aims to identify critical spots in the hexagonally packed structures under mechanical loads in the presence of defects. The role of defects in the formation of force networks is also investigated in this work. The granular mechanics approach is used to analyze the analogous force pattern formation in packed structures. Discrete element method (DEM) is used to simulate the particle interaction in the granular assembly. The hexagonal packing, in X-Y plane, is created by stacking the horizontal contacting particle chains in X-direction, and thus creating inclined contact chains in the Y-direction. Hexagonal packings display two stable force network formations corresponding to compression along X and Y-direction. The effect of point defect and stacking fault on the force network is investigated. The presence of point defect is shown to induce high force concentration near the defect zone. When the assembly is compressed along X-direction, force redistribution at the defect zone increases the force levels in inclined force chains. When the assembly is compressed along Y-direction, the point defect induces zones with lesser force levels. Further, the study explores various levels of force zones induced in the system. The effect of the presence of multiple point defects in the system is analyzed further. The distance between two point defects and their loading direction induces a different set of force chains. Stacking fault is found to induce strong vertical force chains at the defect zone, unlike point defect. However, multiple stacking faults affect only the horizontal force chains near the defect zone. The present study highlights the formation of critical spots as well as lower force zones and also provides useful insights to design efficient packing structures.

Graphical Abstract

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

References

  1. Van Antwerpen, W., Du Toit, C.G., Rousseau, P.G.: A review of correlations to model the packing structure and effective thermal conductivity in packed beds of mono-sized spherical particles. Nucl. Eng. Des. 240(7), 1803–1818 (2010)

    Article  Google Scholar 

  2. Zhang, C.S., Ying, A., Abdou, M.A., Park, Y.-H.: Ceramic breeder pebble bed packing stability under cyclic loads. Fusion Eng. Des. 109, 267–271 (2016)

    Article  Google Scholar 

  3. Gong, B., Cheng, H., Feng, Y., Luo, X., Wang, L., Wang, X.: Effect of pebble size distribution and wall effect on inner packing structure and contact force distribution in tritium breeder pebble bed. Energies 14(2), 449 (2021)

    Article  Google Scholar 

  4. Gazetas, G., Apostolou, M.: Nonlinear soil–structure interaction: foundation uplifting and soil yielding. In: Proceedings Third UJNR Workshop on Soil-Structure Interaction, pp. 29–30 (2004)

  5. Ahmed, M., Mohamed, M.H., Mallick, J., Hasan, M.A., et al.: 3d-analysis of soil-foundation-structure interaction in layered soil. Open J. Civ. Eng. 4(04), 373 (2014)

    Article  Google Scholar 

  6. Hadzalic, E., Ibrahimbegovic, A., Dolarevic, S.: Failure mechanisms in coupled soil-foundation systems. Coupled Syst. Mech. 7, 27–42 (2018)

    Google Scholar 

  7. Aste, T., Di Matteo, T., Galleani d’Agliano, E.: Stress transmission in granular matter. J. Phys.: Condens. Matter 14(9), 2391 (2002)

    ADS  Google Scholar 

  8. Campbell, C.S.: A problem related to the stability of force chains. Granul. Matter 5(3), 129–134 (2003)

    Article  MATH  Google Scholar 

  9. Vijayan, A., Annabattula, R.K.: Semi-analytical framework for stress-conductivity correlations in periodic granular assemblies under compaction. Int. J. Adv. Eng. Sci. Appl. Math. (2021). https://doi.org/10.1007/s12572-021-00294-w

  10. Vijayan, A., Gan, Y., Annabattula, R.K.: Evolution of fabric in spherical granular assemblies under the influence of various loading conditions through dem. Granul. Matter 22(2), 1–15 (2020)

    Article  Google Scholar 

  11. Paternoster, A., Van Camp, J., Vanlanduit, S., Weeren, A., Springael, J., Braet, J.: The performance of beer packaging: Vibration damping and thermal insulation. Food Packag. Shelf Life 11, 91–97 (2017)

    Article  Google Scholar 

  12. Ortiz, C., Blasco, J., Balasch, S., Torregrosa, A.: Shock absorbing surfaces for collecting fruit during the mechanical harvesting of citrus. Biosys. Eng. 110(1), 2–9 (2011)

    Article  Google Scholar 

  13. Ma, S., Karkee, M., Han, F., Sun, D., Zhang, Q.: Effect of air pressure and shaking frequency on fruit damage in mechanical harvesting of apples. In: 2017 ASABE Annual International Meeting, page 1. American Society of Agricultural and Biological Engineers (2017)

  14. Wang, W., Huazhong, L., Zhang, S., Yang, Z.: Damage caused by multiple impacts of litchi fruits during vibration harvesting. Comput. Electron. Agric. 162, 732–738 (2019)

    Article  Google Scholar 

  15. Desmet, M., Lammertyn, J., Scheerlinck, N., Verlinden, B.E., Nicolaı, B.M.: Determination of puncture injury susceptibility of tomatoes. Postharvest Biol. Technol. 27(3), 293–303 (2003)

    Article  Google Scholar 

  16. Komarnicki, P., Stopa, R., Szyjewicz, D., Młotek, M.: Evaluation of bruise resistance of pears to impact load. Postharvest Biol. Technol. 114, 36–44 (2016)

    Article  Google Scholar 

  17. Dalle Donne, M., Günther, E., Schumacher, G., Sordon, G., Vollath, D., Wedemeyer, H., Werle, H.: Research and development work for the lithium orthosilicate pebbles for the karlsruhe ceramic breeder blanket. J. Nucl. Mater. 179, 796–799 (1991)

    ADS  Google Scholar 

  18. Zhou, Q., Gao, Y., Liu, K., Xue, L., Yan, Y.: Fabrication of li2tio3 pebbles by a selective laser sintering process. Fusion Eng. Des. 100, 166–170 (2015)

    Article  Google Scholar 

  19. Tan, G., Song, S., Xin, H., Cai, L., Li, Y., Zhang, Y.: Efficient fabrication of high strength li2tio3 ceramic pebbles via improved rolling ball method assisted by sesbania gum binder. Ceram. Int. (2021)

  20. Li, Z.: The effect of compressibility, loading position and probe shape on the rupture probability of tomato fruits. J. Food Eng. 119(3), 471–476 (2013)

    Article  Google Scholar 

  21. Opara, U.L., Pathare, P.B.: Bruise damage measurement and analysis of fresh horticultural produce—a review. Postharvest Biol. Technol. 91, 9–24 (2014)

    Article  Google Scholar 

  22. Li, Z., Li, P., Yang, H., Liu, J.: Internal mechanical damage prediction in tomato compression using multiscale finite element models. J. Food Eng. 116(3), 639–647 (2013)

    Article  Google Scholar 

  23. Allais, I., Alvarez, G.: Analysis of heat transfer during mist chilling of a packed bed of spheres simulating foodstuffs. J. Food Eng. 49(1), 37–47 (2001)

    Article  Google Scholar 

  24. Pathare, P.B., Opara, U.L., Vigneault, C., Delele, M.A., FAl-Said, A.-J.: Design of packaging vents for cooling fresh horticultural produce. Food Bioprocess Technol. 5(6), 2031–2045 (2012)

    Article  Google Scholar 

  25. Van Zeebroeck, M., Tijskens, E., Dintwa, E., Kafashan, J., Loodts, J., De Baerdemaeker, J., Ramon, H.: The discrete element method (dem) to simulate fruit impact damage during transport and handling: Case study of vibration damage during apple bulk transport. Postharvest Biol. Technol. 41(1), 92–100 (2006)

    Article  Google Scholar 

  26. Van Zeebroeck, M., Darius, P., De Ketelaere, B., Ramon, H., Tijskens, E., et al.: The effect of fruit factors on the bruise susceptibility of apples. Postharvest Biol. Technol. 46(1), 10–19 (2007)

    Article  Google Scholar 

  27. Scheffler, O.C., Coetzee, C.J., Opara, U.L.: A discrete element model (dem) for predicting apple damage during handling. Biosys. Eng. 172, 29–48 (2018)

    Article  Google Scholar 

  28. Annabattula, R.K., Gan, Y., Zhao, S., Kamlah, M.: Mechanics of a crushable pebble assembly using discrete element method. J. Nucl. Mater. 430(1–3), 90–95 (2012a)

    Article  ADS  Google Scholar 

  29. Annabattula, R.K., Gan, Y., Kamlah, M.: Mechanics of binary and polydisperse spherical pebble assembly. Fusion Eng. Des. 87, 853–858 (2012)

    Article  Google Scholar 

  30. Mitterlehner, T., Kartnig, G., Haider, M.: Analysis of the thermal ratcheting phenomenon in packed-bed thermal energy storage using discrete element method. FME Trans. 48(2), 427–431 (2020)

    Article  Google Scholar 

  31. Yi, C., Liu, Y., Qing-song, M., Qi, Y., et al.: Force transmission in three-dimensional hexagonal-close-packed granular arrays with point defect submitted to a point load. Granular Matter 9(3–4), 195–203 (2007)

    Article  Google Scholar 

  32. Tsoungui, O., Vallet, D., Charmet, J.-C.: Use of contact area trace to study the force distributions inside 2d granular systems. Granular Matter 1(2), 65–69 (1998)

    Article  Google Scholar 

  33. Peters, J.F., Muthuswamy, M., Wibowo, J., Tordesillas, A.: Characterization of force chains in granular material. Phys. Rev. E 72(4), 041307 (2005)

    Article  ADS  Google Scholar 

  34. Zadeh, A.A., Barés, J., Brzinski, T.A., Daniels, K.E., Dijksman, J., Docquier, N., Everitt, H.O., Kollmer, J.E., Lantsoght, O., Wang, D., et al.: Enlightening force chains: a review of photoelasticimetry in granular matter. Granular Matter 21(4), 1–12 (2019)

    Google Scholar 

  35. Zhang, L., Jun-Qi, W., Zhang, J.: Force-chain identification in quasi-2d granular systems. In AIP Conference Proceedings 1542, 397–400 (2013)

    Article  ADS  Google Scholar 

  36. Iikawa, N., Bandi, M.M., Katsuragi, H.: Force-chain evolution in a two-dimensional granular packing compacted by vertical tappings. Phys. Rev. E 97(3), 032901 (2018)

    Article  ADS  Google Scholar 

  37. Seguin, A.: Experimental study of some properties of the strong and weak force networks in a jammed granular medium. Granular Matter 22(2), 1–8 (2020)

    Article  Google Scholar 

  38. Yi C.-H., Mu, Q.-S., Tian-De, M.: Discrete element method simulation on the force chains in the two-dimensional granular system under gravity. ACTA PHYSICA SINICA 58(11), 7750–7755 (2009)

  39. Guo, P.: Critical length of force chains and shear band thickness in dense granular materials. Acta Geotech. 7(1), 41–55 (2012)

    Article  Google Scholar 

  40. Nguyen, T.C., Le, L.M., Ly, H.-B., Le, T.-T.: Numerical investigation of force transmission in granular media using discrete element method. Vietnam J. Mech 42, 153–171 (2020)

    Google Scholar 

  41. Luding, S.: Stress distribution in static two-dimensional granular model media in the absence of friction. Phys. Rev. E 55(4), 4720 (1997)

    Article  ADS  Google Scholar 

  42. Yi, C., Liu, Y., Miao, T., Qing-song, M., Qi, Y.: Force transmission in three-dimensional hexagonal-close-packed granular arrays with point defect submitted to a point load. Granular Matter 9(3), 195–203 (2007)

    Article  Google Scholar 

  43. Wensrich, C.M., Kisi, E.H., Luzin, V., Rawson, A., Kirstein, O.: Evolution of a contact force network in a 2d granular assembly: an examination using neutron diffraction. Granular Matter 23(3), 1–7 (2021)

    Article  Google Scholar 

  44. Huntley, J.M.: Vacancy effects on the force distribution in a two-dimensional granular pile. Phys. Rev. E 48(5), 4099 (1993)

    Article  ADS  Google Scholar 

  45. Desu, R.K., Moorthy, A., Annabattula, R.K.: Dem simulation of packing mono-sized pebbles into prismatic containers through different filling strategies. Fusion Eng. Des. 127, 259–266 (2018)

    Article  Google Scholar 

  46. Dai, W., Reimann, J., Hanaor, D., Ferrero, C., Gan, Y.: Modes of wall induced granular crystallisation in vibrational packing. Granular Matter 21(2), 1–16 (2019)

    Article  Google Scholar 

  47. Amirifar, R., Dong, K., Zeng, Q., An, X., Aibing, Yu.: Effect of vibration mode on self-assembly of granular spheres under three-dimensional vibration. Powder Technol. 380, 47–58 (2021)

    Article  Google Scholar 

  48. Oda, M.: Initial fabrics and their relations to mechanical properties of granular material. Soils Found. 12(1), 17–36 (1972)

    Article  Google Scholar 

  49. Oda, M.: The mechanism of fabric changes during compressional deformation of sand. Soils Found. 12(2), 1–18 (1972)

    Article  Google Scholar 

  50. Oda, M., Konishi, J., Nemat-Nasser, S.: Some experimentally based fundamental results on the mechanical behaviour of granular materials. Géotechnique 30, 479–495 (1980)

    Article  Google Scholar 

  51. Oda, M., Konishi, J., Nemat-Nasser, S.: Experimental micromechanical evaluation of strength of granular materials: effects of particle rolling. Mech. Mater. 1, 269–283 (1982)

    Article  Google Scholar 

  52. Ken-Ichi, K.: Distribution of directional data and fabric tensors. Int. J. Eng. Sci. 22, 149–164 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  53. O'Sullivan, C.: Particulate discrete element modelling: a geomechanics perspective. Taylor & Francis (2011)

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

    Article  Google Scholar 

  55. Kloss, C., Goniva, C., Hager, A., Amberger, S., Pirker, S.: Models , algorithms and validation for opensource DEM and CFD-DE. Progr. Comput. Fluid Dyn. 12, 140–152 (2012)

    Article  MathSciNet  Google Scholar 

  56. Banerjee, A., Chanda, A., Das, R.: Historical origin and recent development on normal directional impact models for rigid body contact simulation: a critical review. Arch. Comput. Methods Eng. 24(2), 397–422 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  57. Langstreth Johnson, K., Johnson, K.L.: Contact mechanics. Cambridge University Press (1987)

  58. Di Renzo, A., Maio, F.P.D.: An improved integral non-linear model for the contact of particles in distinct element simulations. Chem. Eng. Sci. 60(5), 1303–1312 (2005)

    Article  Google Scholar 

  59. Verlet, L.: Computer“ experiments’’ on classical fluids. i. thermodynamical properties of lennard-jones molecules. Phys. Rev. 159(1), 98 (1967)

    Article  ADS  Google Scholar 

  60. Swope, W.C., Andersen, H.C., Berens, P.H., Wilson, K.R.: A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters. J. Chem. Phys. 76(1), 637–649 (1982)

    Article  ADS  Google Scholar 

  61. Yi Chen-Hong, M., Qing-Sun, Tian-De, M.: The dem simulation for two-dimensional granular system with point defects. ACTA PHYSICA SINICA 57(6), 3636–3640 (2008)

    Article  Google Scholar 

  62. Spannuth, M.J., Mueggenburg, N.W., Jaeger, H.M., Nagel, S.R.: Stress transmission through three-dimensional granular crystals with stacking faults. Granular Matter 6(4), 215–219 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Delhi, Delhi, 110016, India

    Akhil Vijayan & Arnab Banerjee

  2. Department of Mechanical Engineering, National Institute of Technology Tiruchirappalli, Tiruchirappalli, 620015, India

    Raghuram Karthik Desu

Authors
  1. Akhil Vijayan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arnab Banerjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Raghuram Karthik Desu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Raghuram Karthik Desu.

Ethics declarations

Compliance with Ethical Standards

Declaration on conflict of interest: The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vijayan, A., Banerjee, A. & Desu, R.K. Role of packing defects in force networks of hexagonally packed structures using discrete element method. Granular Matter 24, 23 (2022). https://doi.org/10.1007/s10035-021-01185-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10035-021-01185-4

Keywords

Search

Navigation