SpringerLink
Log in

A fracture model for the deformable spheropolygon-based discrete element method

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

Abstract

A deformable spheropolygon-based discrete element method is developed to predict the evolution of fracture by coupling the finite element method (FEM) and the spheropolygon-based discrete element method (DEM). Within the framework of the coupling method, the spheropolygon-based DEM is adopted to capture the discontinuum behaviors, while the continuum behaviors are analyzed by the FEM. By introducing the fracture model of joint elements based on fracture mechanics, a continuous-discontinuous coupling approach for simulating the fracture of quasi-brittle materials is presented. The tensile failure is described with the fictitious crack model, meanwhile, the Mohr–Coulomb failure criterion with a tension cut-off is employed to determine the shear failure state. Finally, the results of numerical simulations indicate that this novel method is versatile in simulating the whole process of quasi-brittle materials from continuum to discontinuum, including the initiation and propagation of cracks, and the collision of fragments after the failure of brittle materials.

Graphic abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (France)

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
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35

Similar content being viewed by others

References

  1. Yu, J., Liu, G.Y., Cai, Y.Y., Zhou, J.F., Liu, S.Y., Tu, B.X.: Time-dependent deformation mechanism for swelling soft-rock tunnels in coal mines and its mathematical deduction. Int. J. Geomech. 20(3), 0401918 (2020)

  2. Komodromos, P.: A simplified updated Lagrangian approach for combining discrete and finite element methods. Comput. Mech. 35(4), 305–313 (2005)

    Article  Google Scholar 

  3. Mao, J., Zhao, L.H., Di, Y.T., Liu, X.N., Xu, W.Y.: A resolved CFD-DEM approach for the simulation of landslides and impulse waves. Comput. Methods Appl. Mech. Eng. 359, 112750 (2020)

  4. Cervera, M., Chiumenti, M.: Smeared crack approach: Back to the original track. Int. J. Numer. Anal. Met. 30(12), 1173–1199 (2006)

    Article  Google Scholar 

  5. Roth, S.N., Leger, P., Soulaimani, A.: A combined XFEM-damage mechanics approach for concrete crack propagation. Comput. Methods Appl. Mech. Eng. 283, 923–955 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  6. Shi, G.H., Goodman, R.E.: Two dimensional discontinuous deformation analysis. Int. J. Numer. Anal. Met. 9(6), 541–556 (1985)

    Article  Google Scholar 

  7. Fan, H., Zheng, H., Wang, J.F.: A generalized contact potential and its application in discontinuous deformation analysis. Comput. Geotech. 99, 104–114 (2018)

    Article  Google Scholar 

  8. Shi, G.H.: Manifold method of material analysis. Trans. Army Conf. Appl. Math. Comp. US Army Res. Office 57–76 (1991)

  9. Zhang, H.H., Li, L.X., An, X.M., Ma, G.W.: Numerical analysis of 2-D crack propagation problems using the numerical manifold method. Eng. Anal. Bound. Elem. 34(1), 41–50 (2010)

    Article  MathSciNet  Google Scholar 

  10. Wu, Z.J., Wong, L.N.Y.: Frictional crack initiation and propagation analysis using the numerical manifold method. Comput. Geotech. 39, 38–53 (2012)

    Article  Google Scholar 

  11. Cundall, P.A.: A computer model for simulating progressive, large-scale movements in blocky rock systems. Paper presented at the Proceedings of symposium of international society of rock mechanics, Nancy, France, pp II-8 (1971)

  12. Sator, N., Hietala, H.: Damage in impact fragmentation. Int J Fracture 163(1–2), 101–108 (2010)

    Article  Google Scholar 

  13. Rabczuk, T., Eibl, J.: Simulation of high velocity concrete fragmentation using SPH/MLSPH. Int. J. Numer. Meth. Eng. 56(10), 1421–1444 (2003)

    Article  Google Scholar 

  14. Das, R., Cleary, P.W.: Effect of rock shapes on brittle fracture using smoothed particle hydrodynamics. Theor Appl Fract Mech 53(1), 47–60 (2010)

    Article  Google Scholar 

  15. An, H.M., Liu, H.Y., Han, H.Y., Zheng, X., Wang, X.G.: Hybrid finite-discrete element modelling of dynamic fracture and resultant fragment casting and muck-piling by rock blast. Comput. Geotech. 81, 322–345 (2017)

    Article  Google Scholar 

  16. Zhu, J.B., Deng, X.F., Zhao, X.B., Zhao, J.: A numerical study on wave transmission across multiple intersecting joint sets in rock masses with UDEC. Rock Mech Rock Eng 46(6), 1429–1442 (2013)

    Article  ADS  Google Scholar 

  17. Zhao, L.H., Liu, X.N., Mao, J., Shao, L.Y., Li, T.C.: Three-dimensional distance potential discrete element method for the numerical simulation of landslides. Landslides 17(2), 361–377 (2019)

  18. Liu, K., Liu, W.: Application of discrete element method for continuum dynamic problems. Arch. Appl. Mech. 76(3–4), 229–243 (2006)

    Article  ADS  Google Scholar 

  19. Mollon, G., Zhao, J.D.: 3D generation of realistic granular samples based on random fields theory and Fourier shape descriptors. Comput. Method. Appl. Mech. 279, 46–65 (2014)

    Article  Google Scholar 

  20. Effeindzourou, A., Chareyre, B., Thoeni, K., Giacomini, A., Kneib, F.: Modelling of deformable structures in the general framework of the discrete element method. Geotext Geomembr. 44(2), 143–156 (2016)

    Article  Google Scholar 

  21. Baram, R.M., Lind, P.G.: Deposition of general ellipsoidal particles. Phys. Rev. E 85(4), 041301 (2012)

  22. Rubio-Largo, S.M., Lind, P.G., Maza, D., Hidalgo, R.C.: Granular gas of ellipsoids: analytical collision detection implemented on GPUs. Comput. Part Mech. 2(2), 127–138 (2015)

    Article  Google Scholar 

  23. You, Y., Liu, M.L., Ma, H.Q., Xu, L., Liu, B., Shao, Y.L., Tang, Y.P., Zhao, Y.Z.: Investigation of the vibration sorting of non-spherical particles based on DEM simulation. Powder Technol. 325, 316–332 (2018)

    Article  Google Scholar 

  24. Lu, G., Third, J.R., Muller, C.R.: Critical assessment of two approaches for evaluating contacts between super-quadric shaped particles in DEM simulations. Chem. Eng. Sci. 78, 226–235 (2012)

    Article  Google Scholar 

  25. Podlozhnyuk, A., Pirker, S., Kloss, C.: Efficient implementation of superquadric particles in Discrete Element Method within an open-source framework. Comput. Part Mech. 4(1), 101–118 (2017)

    Article  Google Scholar 

  26. Khazeni, A., Mansourpour, Z.: Influence of non-spherical shape approximation on DEM simulation accuracy by multi-sphere method. Powder Technol. 332, 265–278 (2018)

    Article  Google Scholar 

  27. Lu, G., Third, J.R., Muller, C.R.: Discrete element models for non-spherical particle systems: from theoretical developments to applications. Chem. Eng. Sci. 127, 425–465 (2015)

    Article  Google Scholar 

  28. Liu, L., Ji, S.Y.: A new contact detection method for arbitrary dilated polyhedra with potential function in discrete element method. Int. J. Numer. Methods Eng. (2020)

  29. Zhang, H., Chen, G.Q., Zheng, L., Han, Z., Zhang, Y.B., Wu, Y.Q., Liu, S.G.: Detection of contacts between three-dimensional polyhedral blocks for discontinuous deformation analysis. Int. J. Rock Mech. Min. Sci. 78, 57–73 (2015)

    Article  Google Scholar 

  30. Munjiza, A.: The Combined Finite-Discrete Element Method. Wiley, Hoboken, NJ (2004)

    Book  Google Scholar 

  31. Fathani, T.F., Karnawati, D., Wilopo, W.: An integrated methodology to develop a standard for landslide early warning systems. Nat. Hazard Earth Syst. 16(9), 2123–2135 (2016)

    Article  ADS  Google Scholar 

  32. Godinez, H.C., Rougier, E., Osthus, D., Lei, Z., Knight, E., Srinivasan, G.: Fourier amplitude sensitivity test applied to dynamic combined finite-discrete element methods-based simulations. Int. J. Numer. Anal. Met. 43(1), 30–44 (2019)

    Article  Google Scholar 

  33. Yan, C.Z., Zheng, H.: A new potential function for the calculation of contact forces in the combined finite-discrete element method. Int. J. Numer. Anal. Met. 41(2), 265–283 (2017)

    Article  Google Scholar 

  34. Zhao, L.H., Liu, X.N., Mao, J., Xu, D., Munjiza, A., Avital, E.: A novel contact algorithm based on a distance potential function for the 3D discrete-element method. Rock Mech. Rock Eng. 51(12), 3737–3769 (2018)

    Article  ADS  Google Scholar 

  35. Liu, L., Ji, S.Y.: Bond and fracture model in dilated polyhedral DEM and its application to simulate breakage of brittle materials. Granul. Matter 21(3), 41 (2019)

  36. Hopkins, A., Mark.: Polyhedra faster than spheres?. Eng. Comput. 31(3), 567–583 (2014)

  37. Galindo-Torres, S.A., Pedroso, D.M.: Molecular dynamics simulations of complex-shaped particles using Voronoi-based spheropolyhedra. Phys. Rev. E 81(6), 061303 (2010)

  38. Mark, A., Hopkins, Jukka, Tuhkuri: Compression of floating ice fields. J. Geophys. Res. Oceans 104, 5815–15825 (1999)

  39. Alonso-Marroquin, F.: Spheropolygons: A new method to simulate conservative and dissipative interactions between 2D complex-shaped rigid bodies. Epl-Europhys. Lett. 83(1), 14001 (2008)

  40. Galindo-Torres, S.A., Pedroso, D.M., Williams, D.J., Muhlhaus, H.B.: Strength of non-spherical particles with anisotropic geometries under triaxial and shearing loading configurations. Granul. Matter 15(5), 531–542 (2013)

    Article  Google Scholar 

  41. Behraftar, S., Torres, S.A.G., Scheuermann, A., Williams, D.J., Marques, E.A.G., Avarzaman, H.J.: A calibration methodology to obtain material parameters for the representation of fracture mechanics based on discrete element simulations. Comput. Geotech. 81, 274–283 (2017)

    Article  Google Scholar 

  42. Ji, S., Sun, S., Yan, Y.: Discrete element modeling of dynamic behaviors of railway ballast under cyclic loading with dilated polyhedra. Int. J. Numer. Anal. Met. 41(2), 180–197 (2017)

    Article  Google Scholar 

  43. Alonso-Marroquin, F., Wang, Y.C.: An efficient algorithm for granular dynamics simulations with complex-shaped objects. Granul. Matter 11(5), 317–329 (2009)

    Article  Google Scholar 

  44. Galindo-Torres, S.A., Pedroso, D.M., Williams, D.J., Li, L.: Breaking processes in three-dimensional bonded granular materials with general shapes. Comput. Phys. Commun. 183(2), 266–277 (2012)

    Article  ADS  Google Scholar 

  45. Hughes, T.J.R., Liu, W.K.: Nonlinear finite element analysis of shells: Part I. three-dimensional shells. Comput. Method Appl. Mech. 26(3), 331–362 (1981)

  46. Hughes, T.J.R., Liu, W.K.: Nonlinear finite element analysis of shells-part II. two-dimensional shells. Comput. Methods Appl. Mech. Eng. 27(2), 167–181 (1981)

  47. Zhou, X.P., Cheng, H.: Multidimensional space method for geometrically nonlinear problems under total Lagrangian formulation based on the extended finite-element method. J. Eng. Mech. 143(7), 04017036 (2017)

    Article  Google Scholar 

  48. Hillerborg, A., Modéer, M., Petersson, P.-E.: Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem. Concr. Res. 6(6), 773–781 (1976)

    Article  Google Scholar 

  49. Zheng, F., Zhuang, X.Y., Zheng, H., Jiao, Y.Y., Rabczuk, T.: Kinetic analysis of polyhedral block system using an improved potential-based penalty function approach for explicit discontinuous deformation analysis. Appl. Math. Model. 82, 314–335 (2020)

    Article  MathSciNet  Google Scholar 

  50. Zheng, F., Leung, Y.F., Zhu, J.B., Jiao, Y.Y.: Modified predictor-corrector solution approach for efficient discontinuous deformation analysis of jointed rock masses. Int. J. Numer. Anal. Met. 43(2), 599–624 (2019)

    Article  Google Scholar 

  51. Neto, D.M., Oliveira, M.C., Menezes, L.F.: Surface smoothing procedures in computational contact mechanics. Arch. Comput. Method E 24(1), 37–87 (2017)

    Article  MathSciNet  Google Scholar 

  52. Patel, S., Martin, C.D.: Evaluation of tensile Young’s modulus and Poisson’s ratio of a bi-modular rock from the displacement measurements in a Brazilian test. Rock Mech. Rock Eng. 51(2), 361–373 (2018)

    Article  ADS  Google Scholar 

  53. Hondros, G.: The evaluation of Poisson’s ratio and the modulus of materials of low tensile resistance by the Brazilian (indirect tensile) test with particular reference to concrete. Austral. J. Appl. Sci. 10, 243–268 (1959)

    Google Scholar 

  54. Petersson, P.E.: Crack growth and development of fracture zones in plain concrete and similar materials. Sweden: University of Lund (1981)

  55. Galvez, J.C., Elices, M., Guinea, G.V., Planas, J.: Mixed mode fracture of concrete under proportional and nonproportional loading. Int. J. Fract. 94(3), 267–284 (1998)

    Article  Google Scholar 

  56. Murray, Y., Abu-Odeh, A., Bligh, R.: Evaluation of LS-DYNA Concrete Material Model 159 (2007)

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 52009034), the 15th Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (Grant No. 151073), the Priority Academic Program Development of Jiangsu Higher Education Institutions (Grant YS11001), the 111 Project and Qing Lan Project.

Funding

This study was funded by the National Natural Science Foundation of China (Grant No. 52009034), the 15th Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (Grant No. 151073), the Priority Academic Program Development of Jiangsu Higher Education Institutions (Grant YS11001), the 111 Project and Qing Lan Project.

Author information

Authors and Affiliations

  1. College of Water Conservancy and Hydropower Engineering, Hohai University, **kang Rd., Nan**g, 210098, China

    Lanhao Zhao, Linyu Shao, Jia Mao, Kailong Mu & Tongchun Li

Authors
  1. Lanhao Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Linyu Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jia Mao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kailong Mu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Tongchun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Lanhao Zhao, Linyu Shao, Jia Mao, Kailong Mu, Tongchun Li. The first draft of the manuscript was written by Linyu Shao and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Jia Mao.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

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

Zhao, L., Shao, L., Mao, J. et al. A fracture model for the deformable spheropolygon-based discrete element method. Granular Matter 24, 50 (2022). https://doi.org/10.1007/s10035-022-01206-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10035-022-01206-w

Keywords

Search

Navigation