Abstract
We propose a method for the simulation of particle fragmentation based on the calculation of the strain energy field inside the particle. The topography of strain energy is calculated in terms of internal stress using the principles of damage and fracture mechanics. Numerical calculation of the energy field’s ridges is used to determine the breakage criterion as well as the shape of the post-breakage fragments. This method provides a physical-based understanding of the breakage effect in granular material.
Similar content being viewed by others
References
Koohmishi, M., Palassi, M.: Evaluation of the strength of railway ballast using point load test for various size fractions and particle shapes. Rock Mech. Rock Eng. 49, 2655–2664 (2016)
Karatza, Z., And, E., Papanicolopulos, S.A., Viggiani, G., Ooi, J.Y.: Effect of particle morphology and contacts on particle breakage in a granular assembly studied using X-ray tomography. Granul. Matter 21(44), 1–13 (2019)
Casini, F., Viggiani, G.M.B., Springman, S.M.: Breakage of an artificial crushable material under loading. Granul. Matter 15, 661–673 (2013)
Sohn, C., Zhang, Y.D., Cil, M., Buscarnera, G.: Experimental assessment of continuum breakage models accounting for mechanical interactions at particle contact. Granul. Matter 19(67), 1–14 (2017)
Hardin, B.O.: Crushing of soil particles. J. Geotech. Geoenviron. 111, 1177–1192 (1985)
McDowell, G.R., Bolton, M.D., Robertson, D.: The fractal crushing of granular materials. J. Mech. Phys. Solids 44, 2079–2101 (1996)
Lee, L.K., Farhoomand, I.: Compressibility and crushing of granular soil in anisotropic triaxial compression. Can. Geotech. J. IV(1), 69–85 (1967)
Bono, J.D., Mcdowell, G.R.: Particle breakage criteria in discrete-element modelling. Gotechnique 66, 1014–1027 (2016)
Astrom, J.A., Herrmann, H.J.: Fragmentation of grains in a two-dimensional packing. Eur. Phys. J. B 5, 551–554 (1998)
Tsoungui, O., Vallet, D., Charmet, J.C.: Numerical model of crushing of grains inside two-dimensional granular materials. Powder Technol. 105, 190–198 (1999)
Cantor, D., Estrada, N., Azma, E.: Split-cell method for grain fragmentation. Comput. Geotech. 67, 150–156 (2015)
Elias, J.: Simulation of railway ballast using crushable polyhedral particles. Powder Technol. 264, 458–465 (2014)
Gladkyy, A., Kuna, M.: DEM simulation of polyhedral particle cracking using a combined Mohr–Coulomb–Weibull failure criterion. Granul. Matter 19, 41 (2017)
McDowell, G.R., Harireche, O.: Discrete element modelling of yielding and normal compression of sand. Géotechnique 53(4), 299–304 (2002)
Zhang, Y.D., Buscarnera, G., Einav, I.: Grain size dependence of yielding in granular soils interpreted using fracture mechanics, breakage mechanics and Weibull statistics. Gotechnique 66(2), 149–160 (2015)
McDowell, G.R., Bolton, M.D.: On the micromechanics of crushable aggregates. Gotechnique 48(5), 667–679 (1998)
Olsson, W.A.: Grain size dependence of yield stress in marble. J. Geophys. Res. 79(32), 4859–4862 (1974)
Yashima, S., Kanda, Y., Sano, S.: Relationships between particle size and fracture energy or impact velocity required to fracture as estimated from single particle crushing. Powder Technol. 51, 277–282 (1987)
Lee, D.M.: The Angles of Friction of Granular Fills. University of Cambridge PhD dissertation. Dec (1992)
Alonso-Marroqun, Fernando: Static equations of the Cosserat continuum derived from intra-granular stresses. Granul. Matter 13(3), 189–196 (2011)
Jiang, Y., Herrmann, H.J., Alonso-Marroquín, F.: A boundary-spheropolygon element method for modelling sub-particle stress and particle breakage. Comput. Geotech. 113, 103087 (2019)
Griffith, A.A.: The phenomena of rupture and flow in solids. Philos. Trans. R. Soc. Lond. Ser. A 221(587), 163–198 (1921)
Lemaitre, J., Chaboche, J.L.: Aspect phenomenologique de la rupture par endommagement. J. Mec. Appl. 2(3), 317–365 (1978)
Chaboche, J.L.: Continuum damage mechanics: part I-general concepts. J. Appl. Mech. 55, 59–64 (1988)
Lajtai: Brittle fracture in compression. Int. J. Fract. 10(4), 525–536 (1974)
Hoek, E., Bieniawshi, Z.T.: Brittle fracture propagation in rock under compression. Int. J. Fract. Mech. 1(3), 137–155 (1965)
Salami, Y., Dano, C., Hicher, P.: An experimental study on the influence of the coordination number on grain crushing. Eur. J. Environ. Civ. Eng. 23(3), 432–448 (2019)
Tang, C.A., Liu, H.Y., Zhu, W.C., Yang, T.H., Li, W.H., Song, L., Lin, P.: Numerical approach to particle breakage under different loading conditions. Powder Technol. 143–144, 130–143 (2004)
Lindeberg, T.: Edge detection and ridge detection with automatic scale selection. Int. J. Comput. Vis. 30(2), 117–156 (1998)
Brace, W.F., Bombolakis, E.G.: A note on brittle crack growth in compression. J. Geophys. Res. 68(12), 1–5 (1963)
Carmona, H.A., Kun, F., Andrade, J.S., Herrmann, H.J.: Computer simulation of fatigue under diametrical compression. Phys. Rev. E 75, 046115 (2007)
Artoni, R., Neveu, A., Descantes, Y., Richard, P.: Effect of contact location on the crushing strength of aggregates. J. Mech. Phys. Solids 122, 406–417 (2019)
Hurly, R.C., Lind, J., Pagan, D.C., Akin, M.C., Herbold, E.B.: In situ grain fracture mechanics during uniaxial compaction of granular solids. J. Mech. Phys. Solids 112, 273–290 (2018)
Khanlari, G., Rafiei, B., Abdilor, Y.: An experimental investigation of the Brazilian tensile strength and failure patterns of Laminated sandstones. Rock Mech. Rock Eng. 48, 843–852 (2015)
Sukumaran, B., Einav, I., Dyskin, A.: Qualitative assessment of the influence of coordination number on crushing strength using DEM. 5th World Congress on Particle, pp. 1–8. Orlando, FL (2006)
Acknowledgements
We deeply thank the anonymous reviewers for their valuable comments, all of which helped us to improve the quality of this paper. This research is financially supported by Australia research council (ARC) linkage project Performance of granular matrix under heavy haul cyclic loading (LP160100280).
Author information
Authors and Affiliations
Corresponding author
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.
Rights and permissions
About this article
Cite this article
Jiang, Y., Alonso-Marroquín, F., Herrmann, H.J. et al. Particle fragmentation based on strain energy field. Granular Matter 22, 69 (2020). https://doi.org/10.1007/s10035-020-01038-6
Received:
Published:
DOI: https://doi.org/10.1007/s10035-020-01038-6