Skip to main content
SpringerLink
Log in

Discrete element modeling of cantilever beams subjected to geometric nonlinearity and particle–structure interaction

  • Published:
Computational Particle Mechanics Aims and scope Submit manuscript

Abstract

The discrete element method (DEM) is a general discrete modeling technique traditionally used to model granular material and discontinuous phenomena such as fracture and fragmentation of solids. We investigate the efficacy of DEM to model deformable elastic continua, cantilever beams in particular, and describe their mechanical behavior under loading. Of distinct interest is the ability of DEM to capture geometric nonlinearity in their large-displacement response. A case study is presented to demonstrate the utility of this approach in particle–structure problems that involve large structural displacements. We simulated an array of these cantilever beams in large elastic oscillations amidst a particulate environment, modeled using DEM. Mobile particles encounter the deflecting beams in their paths and can be redirected for capture based on net forces and moments that act on them. The dynamics of the ensuing particle–structure interactions is simulated, and factors regulating the efficiency of particle capture are examined.

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

Similar content being viewed by others

Availability of data and material

Modeling data may be requested from the authors.

References

  1. Zhou EH, Martinez FD, Fredberg JJ (2013) Cell rheology: mush rather than machine. Nat Mater 12(3):184–185

    Article  Google Scholar 

  2. Braun T, Ghatkesar MK, Backmann N, Grange W, Boulanger P, Letellier L, Lang H-P, Bietsch A, Gerber C, Hegner M (2009) Quantitative time-resolved measurement of membrane protein–ligand interactions using microcantilever array sensors. Nat Nanotechnol 4(3):179

    Article  Google Scholar 

  3. Sitti M (2004) Atomic force microscope probe based controlled pushing for nanotribological characterization. IEEE/ASME Trans Mechatron 9(2):343–349

    Article  Google Scholar 

  4. Wendeler C, Volkwein A, Roth A, Denk M, Wartmann S (2007) Field measurements and numerical modelling of flexible debris flow barriers. Debris-Flow Hazards Mitig Mech Predict Assess Millpress, Rotterdam, pp 681–687

  5. Yang X, Liu M, Peng S, Huang C (2016) Numerical modeling of dam-break flow impacting on flexible structures using an improved SPH–EBG method. Coast Eng 108:56–64

    Article  Google Scholar 

  6. Wu K, Yang D, Wright N, Khan A (2018) An integrated particle model for fluid–particle–structure interaction problems with free-surface flow and structural failure. J Fluids Struct 76:166–184

    Article  Google Scholar 

  7. Tuhkuri J, Polojärvi A (2018) A review of discrete element simulation of ice–structure interaction. Philosoph Trans R Soc Math Phys Eng Sci 376(2129):20170335

    Google Scholar 

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

    Article  Google Scholar 

  9. Cundall PA (1988) Formulation of a three-dimensional distinct element model—Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int J Rock Mech Min Sci Geomech Abstr, Pergamon, pp 107–116

  10. Hart R, Cundall P, Lemos J (1988) Formulation of a three-dimensional distinct element model—Part II. Mechanical calculations for motion and interaction of a system composed of many polyhedral blocks. Int J Rock Mech Min Sci Geomech Abstr, Elsevier, pp 117–125

  11. Munjiza AA, Knight EE, Rougier E (2011) Computational mechanics of discontinua. Wiley, New York

    Book  Google Scholar 

  12. Munjiza A (2009) Special issue on the discrete element method: aspects of recent developments in computational mechanics of discontinua. Eng Comput 3:851

    Google Scholar 

  13. Potyondy DO, Cundall P (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364

    Article  Google Scholar 

  14. Tavarez FA, Plesha ME (2007) Discrete element method for modelling solid and particulate materials. Int J Numer Meth Eng 70(4):379–404

    Article  Google Scholar 

  15. Weerasekara N, Powell M, Cleary P, Tavares LM, Evertsson M, Morrison R, Quist J, Carvalho R (2013) The contribution of DEM to the science of comminution. Powder Technol 248:3–24

    Article  Google Scholar 

  16. Richards K, Bithell M, Dove M, Hodge R (2004) Discrete–element modelling: methods and applications in the environmental sciences. Philos Trans R Soc London Ser Math Phys Eng Sci 362(1822):1797–1816

    Article  MathSciNet  Google Scholar 

  17. Cundall PA (2001) A discontinuous future for numerical modelling in geomechanics? Proc Inst Civil Eng Geotech Eng 149(1):41–47

    Article  Google Scholar 

  18. Xu Q, Ye J (2019) An adaptively coupled DEM–FEM algorithm for geometrical large deformation analysis of member structures. Comput Part Mech, pp 1–13

  19. Qi N, Ye JH (2013) Geometric nonlinear analysis with large deformation of member structures by discrete element method. J Southeast Univ Nat Sci Ed 43(5):917–922

    Google Scholar 

  20. Guo Y, Wassgren C, Hancock B, Ketterhagen W, Curtis J (2013) Validation and time step determination of discrete element modeling of flexible fibers. Powder Technology 249:386–395

    Article  Google Scholar 

  21. O’Sullivan C (2011) Particulate discrete element modelling: a geomechanics perspective. CRC Press, New York

    Book  Google Scholar 

  22. Pöschel T, Schwager T (2005) Computational granular dynamics: models and algorithms. Springer, Berlin

    Google Scholar 

  23. Hertz H (1881) On the contact of elastic solids. Z Reine Angew Mathematik 92:156–171

    MATH  Google Scholar 

  24. Mindlin RD (1949) Compliance of elastic bodies in contact. J Appl Mech ASME 16:259–268

    Article  MathSciNet  Google Scholar 

  25. Mindlin RD (1953) Elastic spheres in contact under varying oblique forces. J Appl Mech 20:327–344

    MathSciNet  MATH  Google Scholar 

  26. Johnson KL (1987) Contact mechanics. Cambridge University Press, Cambridge

    Google Scholar 

  27. Tsuji Y, Tanaka T, Ishida T (1992) Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol 71(3):239–250

    Article  Google Scholar 

  28. Shen Z, Jiang M, Thornton C (2016) DEM simulation of bonded granular material. Part I: contact model and application to cemented sand. Comput Geotech 75:192–209

    Article  Google Scholar 

  29. Kimball C, Tsai L-W (2002) Modeling of flexural beams subjected to arbitrary end loads. J Mech Des 124(2):223–235

    Article  Google Scholar 

  30. Banerjee A, Bhattacharya B, Mallik A (2008) Large deflection of cantilever beams with geometric non-linearity: analytical and numerical approaches. Int J Non-Linear Mech 43(5):366–376

    Article  Google Scholar 

  31. Zhang A, Chen G (2013) A comprehensive elliptic integral solution to the large deflection problems of thin beams in compliant mechanisms. J Mech Robot 5(2):337

    Article  Google Scholar 

  32. Trahair NS (2005) Nonlinear elastic nonuniform torsion. J Struct Eng 131(7):1135–1142

    Article  Google Scholar 

  33. Timoshenko SP, Gere JM (2009) Theory of elastic stability. Courier Corporation, London

    Google Scholar 

  34. Riisgård HU, Larsen PS (2001) Minireview: ciliary filter feeding and bio-fluid mechanics—present understanding and unsolved problems. Limnol Oceanogr 46(4):882–891

    Article  Google Scholar 

  35. Ward JE (1996) Biodynamics of suspension-feeding in adult bivalve molluscs: particle capture, processing, and fate. Invert Biol 10:218–231

    Article  Google Scholar 

  36. den Toonder JM, Onck PR (2013) Microfluidic manipulation with artificial/bioinspired cilia. Trends Biotechnol 31(2):85–91

    Article  Google Scholar 

  37. Belardi J, Schorr N, Prucker O, Rühe J (2011) Artificial cilia: generation of magnetic actuators in microfluidic systems. Adv Funct Mater 21(17):3314–3320

    Article  Google Scholar 

  38. Bhattacharya A, Buxton GA, Usta OB, Balazs AC (2012) Propulsion and trapping of microparticles by active cilia arrays. Langmuir 28(6):3217–3226

    Article  Google Scholar 

  39. Whiting JG, Mayne R, Adamatzky A (2018) A parallel modular biomimetic cilia sorting platform. Biomimetics 3(2):5

    Article  Google Scholar 

  40. Hanasoge S, Ballard M, Hesketh PJ, Alexeev A (2017) Asymmetric motion of magnetically actuated artificial cilia. Lab Chip 17(18):3138–3145

    Article  Google Scholar 

  41. Hanasoge S, Hesketh PJ, Alexeev A (2018) Metachronal motion of artificial magnetic cilia. Soft Matter 14(19):3689–3693

    Article  Google Scholar 

Download references

Acknowledgements

Helpful discussions with the members of the Multidisciplinary and Multiscale Design and Device (M2D2) laboratory in the Mechanical Engineering Department at the Indian Institute of Science are gratefully acknowledged.

Funding

This project was funded in part by the Abdul Kalam Technology Innovation Fellowship to GKA.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Science, Bengaluru, India

    Prasenjit Ghosh & G. K. Ananthasuresh

Authors
  1. Prasenjit Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. K. Ananthasuresh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Prasenjit Ghosh or G. K. Ananthasuresh.

Ethics declarations

Conflict of interest

None.

Code availability

Code may be requested from the authors.

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

Ghosh, P., Ananthasuresh, G.K. Discrete element modeling of cantilever beams subjected to geometric nonlinearity and particle–structure interaction. Comp. Part. Mech. 8, 637–651 (2021). https://doi.org/10.1007/s40571-020-00360-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40571-020-00360-3

Keywords

Search

Navigation