Abstract
Discrete element modelling (DEM) is one of the most efficient computational approaches to the fracture processes of heterogeneous materials on mesoscopic scales. From the dynamics of single crack propagation through the statistics of crack ensembles to the rapid fragmentation of materials DEM had a substantial contribution to our understanding over the past decades. Recently, the combination of DEM with other simulation techniques like Finite Element Modelling further extended the field of applicability. In this paper we briefly review the motivations and basic idea behind the DEM approach to cohesive particulate matter and then we give an overview of on-going developments and applications of the method focusing on two fields where recent success has been achieved. We discuss current challenges of this rapidly evolving field and outline possible future perspectives and debates.
Similar content being viewed by others
References
H.J. Herrmann, S. Roux (eds.), Statistical Models for the Fracture of Disordered Media (Elsevier Science Publishers, Amsterdam, 1990)
E. Bouchaud, D. Jeulin, C. Prioul, S. Roux (eds.), Physical Aspects of Fracture (Kluwer Academic Publishers, New York, 2001)
M.J. Alava, P.K.V.V. Nukala, S. Zapperi, Adv. Phys. 55, 349 (2006)
P.A. Cundall, O.D. Strack, Geotechnique 29, 47 (1979)
M.P. Allen, D.J. Tildesley, Comuter Simulation of Liquids (Oxford University Press, Oxford, 1984)
L.D. Libersky, A.G. Petschek, Lect. Notes Phys. 395, 248 (1990)
A.T. Zehnder, Fracture Mechanics, Lecture Notes in Applied and Computational Mechanics 62 (Springer, Berlin, 2012)
T. Belytschko, R. Gracie, M. Xu, Concurrent Coupling of Atomistic, Continuum Models, edited by J. Fisch, Multiscale Methods: Bridging the Scales in Science and Engineering (Oxford University Press, Oxford, 2010), p. 93
T. Belytschko, W.K. Liu, B. Moran, Non-linear Finite Elements for Continua and Structures (John Wiley & Sons Inc., New York, 2001)
T. Belytschko, S.P. Xiao, Int. J. Mult. Comp. Engin. 1, 115 (2003)
A. Leonardi, F.K. Wittel, M. Mendoza, H.J. Herrmann, Comp. Part. Mech., 1 (2014)
E. Schlangen, E.J. Garboczi, Engrg. Fract. Mech. 57, 319 (1997)
D. Potyondy, P. Cundall, Int. J. Rock Mech. Min. Sci. 41, 1329 (2004)
G.A. D’Addetta, F. Kun, E. Ramm, H.J. Herrmann, Lect. Notes Phys. 568, 231 (2001)
G.A. D’Addetta, F. Kun, E. Ramm, Gran. Mat. 4, 77 (2002)
F. Kun, H.A. Carmona, J.S. Andrade, H.J. Herrmann, Phys. Rev. Lett. 100, 094301 (2008)
H.A. Carmona, F.K. Wittel, F. Kun, H.J. Herrmann, Phys. Rev. E 77, 051302 (2008)
T. Pöschel, T. Schwager, Computational Granular Dynamics (Springer, Berlin, 2005)
F. Kun, I. Varga, S. Lennartz-Sassinek, I.G. Main, Phys. Rev. Lett. 112, 065501 (2014)
F. Kun, I. Varga, S. Lennartz-Sassinek, I.G. Main, Phys. Rev. E 88, 062207 (2013)
W. Salvat, N. Mariani, G. Barreto, O. Martinez, Catal. Today 107–108, 513 (2005)
K. Bagi, Gran. Mat. 7, 31 (2005)
J.-F. Jerier, D. Imbault, F.-V. Donze, P. Doremus, Gran. Mat. 11, 43 (2009)
S. Hentz, F.V. Donze, L. Daudeville, Comput. Struct. 82 2509 (2004)
Y.T. Feng, D.R.J. Owen, Int. J. Numer. Meth. Engng. 56, 699 (2003)
L. Cui, C. O’Sullivan, Gran. Matt. 5, 135 (2003)
S. Luding, Gran. Mat. 10, 235 (2008)
B.K. Mishra, C. Thornton, Int. J. Min. Process. 61, 225 (2001)
M. Stojanova, S. Santucci, L. Vanel, O. Ramos, Phys. Rev. Lett. 112, 115502 (2014)
P.R. Sammonds, P.G. Meredith, I.G. Main, Nature 359, 228 (1992)
C.G. Hatton, I.G. Main, P.G. Meredith, J. Struct. Geol. 15, 1485 (1993)
I. Ojala, B.T. Ngwenya, I.G. Main, S.C. Elphick, J. Geophys. Res. 108, 2268 (2003)
R.C. Hidalgo, F. Kun, K. Kovács, I. Pagonabarraga, Phys. Rev. E 80, 051108 (2009)
H.J. Herrmann, F.K. Wittel, F. Kun, Physica A 371, 59 (2006)
J. Aström, Adv. Phys. 55, 247 (2006)
D.L. Turcotte, J. Geophys. Res. 91, 1921 (1986)
M. Khanal, W. Schubert, J. Tomas, Int. J. Miner. Process. 86, 104 (2008)
K.T. Chau, X.X. Wei, R.H.C. Wong, T.X. Yu, Mech. Mater. 32, 543 (2000)
T. Kadono, M. Arakawa, Phys. Rev. E 65, 035107(R) (2002)
F. Kun, F.K. Wittel, H.J. Herrmann, B.-H. Kröplin, K.-J. Maloy, Phys. Rev. Lett. 96, 025504 (2006)
J.A. Aström, F. Ouchterlony, R.P. Linna, J. Timonen, Phys. Rev. Lett. 92, 245506 (2004)
H. Katsuragi, D. Sugino, H. Honjo, Phys. Rev. E 68, 046105 (2003)
H. Katsuragi, S. Ihara, H. Honjo, Phys. Rev. Lett. 95, 095503 (2005)
F.K. Wittel, F. Kun, H.J. Herrmann, B.-H. Kroplin, Phys. Rev. Lett. 93, 035504 (2004)
F. Kun, H.J. Herrmann, Phys. Rev. E 59, 2623 (1999)
G. Timár, F. Kun, H.A. Carmona, H.J. Herrmann, Phys. Rev. E 86, 016113 (2012)
N.N. Myagkov, T.A. Shumikhin, Physica A 358, 423 (2005)
G. Timár, J. Blömer, F. Kun, H.J. Herrmann, Phys. Rev. Lett. 104, 095502 (2010)
H.A. Carmona, A.V. Guimaraes, J.S. Andrade Jr., I. Nikolakopoulos, F.K. Wittel, H.J. Herrmann (preparation)
E.S.C. Ching, Y.Y. Yiu, K.F. Lo, Physica A 265, 119 (1999)
N. Sator, S. Mechkov, F. Sausset, Europhys. Lett. 81, 44002 (2008)
N. Sator, H. Hietala, Int. J. Fract. 163, 101 (2010)
J.A. Aström, Phys. Rev. E 80, 046113 (2009)
M.J. Alava, P.K.V.V. Nukala, S. Zapperi, J. Phys. D 42, 214012 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Carmona, H., Wittel, F. & Kun, F. From fracture to fragmentation: Discrete element modeling. Eur. Phys. J. Spec. Top. 223, 2369–2382 (2014). https://doi.org/10.1140/epjst/e2014-02270-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2014-02270-3