Skip to main content
SpringerLink
Log in

Packing simulation of thin flexible particles using a novel discrete element model

  • Published:
Computational Particle Mechanics Aims and scope Submit manuscript

Abstract

In discrete element method simulations for industrial applications, long, flat, bendable particles are often approximated as rods with circular cross sections. However, such crude approximation of the particle geometry raises questions on the ability to reproduce the material bulk properties. Therefore, we describe a novel discrete element representation of flexible, flat, thin particles, consisting of a triangulated mass-spring model of the particle’s neutral plane, with the thickness of the particle incorporated in customised contact models. We validate the model with experiments of packing after gravitational deposition and sinusoidal excitation, where we show that the model correctly predicts the packing density for long, flexible, flat particles. Furthermore, we benchmark the model against a circular cross-sectional flexible rod model. Investigation of the dynamics of densification under vibrational compaction shows that the Kohlrausch–Williams–Watts stretched exponential law is well suited to describe the compaction dynamics of the described particles. The novel foil model provides insights in the bulk behaviour of flexible flat particles, otherwise difficult or even impossible to obtain theoretically or experimentally for random orientations. Applications of the model could include the modelling of fabrics, biological material like leaves, soft plastic, and paper.

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. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Baraff D, Witkin A (1998) Large steps in cloth simulation. In: Proceedings of the 25th Annual Conference on computer graphics and interactive techniques, SIGGRAPH ’98. Association for computing machinery, New York, NY, USA, pp 43–54

  2. Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B (Methodological) 57(1):289–300

  3. Cleary PW (2010) DEM prediction of industrial and geophysical particle flows. Particuology 8(2):106–118

    Article  Google Scholar 

  4. Cundall PA, Strack OD (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65

    Article  Google Scholar 

  5. Diels E, Odenthal T, Keresztes J, Vanmaercke S, Verboven P, Nicolai B, Saeys W, Ramon H, Smeets B (2016) Development of a visco-elastoplastic contact force model and its parameter determination for apples. Postharvest Biology and Technology 120:157–166

    Article  Google Scholar 

  6. Diels E, Wang Z, Nicolai B, Ramon H, Smeets B (2019) Discrete element modelling of tomato tissue deformation and failure at the cellular scale. Soft Matter 15(16):3362–3378

    Article  Google Scholar 

  7. Džiugys A, Peters B (2001) A new approach to detect the contact of two dimensional elliptical particles. International Journal for Numerical and Analytical Methods in Geomechanics 25(15):1487–1500

    Article  Google Scholar 

  8. Engineering ToolBox: Metals and alloys, densities. www.engineeringtoolbox.com/metal-alloys-densities-d_50.html (2004 - accessed 25 January 2021)

  9. Gay Neto, A., Pimenta, P.M., Wriggers, P.: A master-surface to master-surface formulation for beam to beam contact. Part I: frictionless interaction. Computer methods in applied mechanics and engineering 303, 400–429 (2016)

  10. Gusev AA, Hine PJ, Ward IM (2000) Fiber packing and elastic properties of a transversely random unidirectional glass/epoxy composite. Composites science and technology 60(4):535–541

    Article  Google Scholar 

  11. Hestenes MR, Stiefel E (1952) Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards 49:409–435

    Article  MathSciNet  Google Scholar 

  12. Kemper S, Lang T, Frerichs L (2014) Der überlagerte Schnitt im Scheibenmähwerk Ergebnisse aus Feldversuchen und Simulation [The overlapping cut in the disc mower - results from from field tests and simulation]. Landtechnik 69(4):171–175

    Google Scholar 

  13. Ketterhagen WR, Am Ende MT, Hancock BC (2009) Process modeling in the pharmaceutical industry using the discrete element method. Journal of Pharmaceutical Sciences 98(2):442–470

    Article  Google Scholar 

  14. Kuwabara G, Kono K (1987) Restitution coefficient in a collision between two spheres. Japanese J Appl Phy 26(Part 1, No. 8): 1230–1233

  15. Langston P, Kennedy AR, Constantin H (2015) Discrete element modelling of flexible fibre packing. Comput Mat Sci 96(Part A): 108–116

  16. Leblicq T, Smeets B, Ramon H, Saeys W (2016) A discrete element approach for modelling the compression of crop stems. Computers and Electronics in Agriculture 123:80–88

    Article  Google Scholar 

  17. Leblicq T, Vanmaercke S, Ramon H, Saeys W (2015) Discrete element modelling of bendable tubes. International Journal of Mechanical Sciences 94–95:75

    Article  Google Scholar 

  18. Lu G, Third JR, Müller CR (2015) Discrete element models for non-spherical particle systems: From theoretical developments to applications. Chemical Engineering Science 127:425–465

    Article  Google Scholar 

  19. Markauskas D, Kruggel-Emden H, Scherer V (2018) Numerical analysis of wet plastic particle separation using a coupled DEM-SPH method. Powder technology 325:218–227

    Article  Google Scholar 

  20. Mcdowell G, Li H (2016) Discrete element modelling of scaled railway ballast under triaxial conditions. Granular Matter 18(3):1–10

    Article  Google Scholar 

  21. Mpacts: Mpacts simulation software. (accessed 22 February 2021)

  22. Nicolas M, Mathonnet JE, Dalloz B, Sornay P (2017) Granular compaction and stretched exponentials - Experiments and a numerical stochastic model. EPJ Web of Conferences 140:8001

    Article  Google Scholar 

  23. O’Sullivan C (2011) Particle-based discrete element modeling: Geomechanics Perspective. International Journal of Geomechanics 11(6):449–464

    Article  Google Scholar 

  24. Parkhouse JG, Kelly A (1995) The random packing of fibres in three dimensions. Proceedings of the Royal Society of London. SeriesA: Mathematical and Physical Sciences 451(1943): 737–746

  25. Philippe P, Bideau D (2002) Compaction dynamics of a granular medium under vertical tapping. Europhysics Letters 60(5):677–683

    Article  Google Scholar 

  26. Pieczywek PM, Zdunek A (2017) Compression simulations of plant tissue in 3D using a mass-spring system approach and discrete element method. Soft Matter 13(40):7318–7331

    Article  Google Scholar 

  27. Richard P, Nicodemi M, Delannay R, Ribière P, Bideau D (2005) Slow relaxation and compaction of granular systems. Nature Materials 4(2):121–128

    Article  Google Scholar 

  28. Smeets B, Odenthal T, Keresztes J, Vanmaercke S, Van Liedekerke P, Tijskens E, Saeys W, Van Oosterwyck H, Ramon H (2014) Modeling contact interactions between triangulated rounded bodies for the discrete element method. Computer Methods in Applied Mechanics and Engineering 277:219–238

    Article  MathSciNet  Google Scholar 

  29. Smeets B, Odenthal T, Vanmaercke S, Ramon H (2015) Polygon-based contact description for modeling arbitrary polyhedra in the discrete element method. Computer Methods in Applied Mechanics and Engineering 290:277–289

    Article  MathSciNet  Google Scholar 

  30. Soliman S, Sant S, Nichol JW, Khabiry M, Traversa E, Khademhosseini A (2011) Controlling the porosity of fibrous scaffolds by modulating the fiber diameter and packing density. Journal of Biomedical Materials Research. Part A 96A(3):566–574

    Article  Google Scholar 

  31. Tijskens E, Ramon H, Baerdemaeker J (2003) Discrete element modelling for process simulation in agriculture. Journal of Sound and Vibration 266(3):493–514

    Article  Google Scholar 

  32. Toll S (1998) Packing mechanics of fiber reinforcements. Polymer Engineering and Science 38(8):1337–1350

    Article  Google Scholar 

  33. Vandewalle N, Lumay G, Gerasimov O, Ludewig F (2007) The influence of grain shape, friction and cohesion on granular compaction dynamics. European Physical Journal E 22(3):241–248

    Article  Google Scholar 

  34. Villarruel FX, Lauderdale BE, Mueth DM, Jaeger HM (2000) Compaction of rods: relaxation and ordering in vibrated, anisotropic granular material. Physical Review E – Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 61(6B), 6914–6921

  35. Wachs A, Girolami L, Vinay G, Ferrer G (2012) Grains3D, a flexible DEM approach for particles of arbitrary convex shape Part I: Numerical model and validations. Powder technology 224:374–389

    Article  Google Scholar 

  36. Wriggers P, Zavarise G (1997) On contact between three-dimensional beams undergoing large deflections. Communications in numerical methods in engineering 13(6):429–438

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

M.L. is an SB PhD fellow at Research Foundation Flanders (FWO) with grant 1S67917N.   B.S. acknowledges support from the Research Foundation Flanders (FWO) grant 12Z6118N, and KU Leuven internal funding C14/18/055. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Author information

Authors and Affiliations

  1. KU Leuven - University of Leuven, Department of Biosystems (BIOSYST), Division of Mechatronics, Biostatistics and Sensors (MeBioS), Kasteelpark Arenberg 30, 3001, Leuven, Belgium

    Leman Mathias, Saeys Wouter & Smeets Bart

  2. CNH Industrial, Léon Claeysstraat 3A, 8210, Zedelgem, Belgium

    Leblicq Tom

  3. Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria Paris Sorbonne Université LJLL, 2 Rue Simone IFF, 75012, Paris, France

    Pešek Jiří

Authors
  1. Leman Mathias
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saeys Wouter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Leblicq Tom
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pešek Jiří
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Smeets Bart
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Smeets Bart.

Ethics declarations

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.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 971 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mathias, L., Wouter, S., Tom, L. et al. Packing simulation of thin flexible particles using a novel discrete element model. Comp. Part. Mech. 9, 407–420 (2022). https://doi.org/10.1007/s40571-021-00419-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40571-021-00419-9

Keywords

Search

Navigation