Summary
The Distinct Element Method (DEM) is a popular tool to perform granular media simulations. The two key elements this requires are an adequate model for inter-particulate contact forces and an efficient contact detection method. Originally, this method was designed to handle spherical-shaped grains that allow for efficient contact detection and simple yet realistic contact force models. Here we show that both properties carry over to grains of a much more general shape called spheropolyhedra (Minkowski sums of spheres and polyhedra). We also present some computational experience and results with the new model.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abreu, C.R.A., Tavares, F.W., Castier, M.: Influence of particle shape on the packing and on the segregation of spherocylinders via Monte Carlo simulations. Powder Technol. 134(1–2), 167–180 (2003)
Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Clarendon, Oxford (1987)
Attali, D., Boissonnat, J.-D.: A linear bound on the complexity of the Delaunay triangulation of points on polyhedral surfaces. Discrete Comput. Geom. 31(3), 369–384 (2004)
Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 29(1), 47–65 (1979)
Ferrez, J.-A.: Dynamic triangulations for efficient 3D simulation of granular materials. Thèse № 2432, EPFL (2001)
Ferrez, J.-A., Liebling, T.M.: Dynamic triangulations for efficient detection of collisions between spheres with applications in granular media simulations. Philos. Mag. B 82(8), 905–929 (2002)
Gel’fand, I.M., Kapranov, M.M., Zelevinsky, A.V.: Discriminants of polynomials of several variables and triangulations of Newton polyhedra. Leningrad Math. J. 2, 449–505 (1990)
Makse, H.A., Havlin, S., King, P.R., Stanley, H.E.: Spontaneous stratification in granular mixtures. Nature 386, 379–382 (1997)
Matuttis, H.-G., Luding, S., Herrmann, H.J.: Discrete element methods for the simulation of dense packings and heaps made of spherical and non-spherical particles. Powder Technol. 109(1–3), 278–292 (2000)
Müller, D.: Techniques informatiques efficaces pour la simulation de mileux granulaires par des méthodes d’éléments distincts. Thèse № 1545, EPFL (1996)
Müller, D., Liebling, T.M.: Detection of collisions of polygons by using a triangulation. In: Raous, M., et al. (eds.) Contact Mechanics, pp. 369–372. Plenum, New York (1995)
Muth, B., Eberhard, P., Luding, S.: Collisions between particles of complex shapes. In: García-Rojo, R., Herrmann, H.J., McNamara, S. (eds.) Powders and Grains 2005, vol. II, pp. 1379–1383. Balkema, Rotterdam (2005)
Muth, B., Müller, M.-K., Eberhard, P., Luding, S.: Contacts between many bodies. Mach. Dyn. Prob. 28(1), 101–114 (2004)
O’Connor, R.M.: A distributed discrete element modeling environment—algorithms, implementation and applications. Ph.D. thesis, MIT (1996)
Pournin, L.: On the behavior of spherical and non-spherical grain assemblies, its modeling and numerical simulation. Thèse № 3378, EPFL (2005)
Pournin, L., Liebling, T.M.: Constrained paths in the flip-graph of regular triangulations. Comput. Geom. 37(2), 134–140 (2007)
Pournin, L., Liebling, T.M., Mocellin, A.: Molecular-dynamics force models for better control of energy dissipation in numerical simulations of dense granular media. Phys. Rev. E 65, 011302 (2002)
Pournin, L., Weber, M., Tsukahara, M., Ferrez, J.-A., Ramaioli, M., Liebling, T.M.: Three-dimensional distinct element simulation of spherocylinder crystallization. Granul. Matter 7(2–3), 119–126 (2005)
Ramaioli, M.: Granular flow simulations and experiments for the food industry. Thèse № 3997, EPFL (2007)
Ramaioli, M., Pournin, L., Liebling, T.M.: Numerical and experimental investigation of alignment and segregation of vibrated granular media composed of rods and spheres. In: García-Rojo, R., Herrmann, H.J., McNamara, S. (eds.) Powders and Grains 2005, vol. II, pp. 1359–1363. Balkema, Rotterdam (2005)
Ramaioli, M., Pournin, L., Liebling, T.M.: Vertical ordering of rods under vertical vibration. Phys. Rev. E 76(2), 021304 (2007)
Samet, H.: The quadtree and related hierarchical data structures. ACM Comput. Surv. 16, 187–260 (1984)
Schinner, A.: Fast algorithms for the simulation of polygonal particles. Granul. Matter 2(1), 35–43 (1999)
Sigurgeirsson, H., Stuart, A., Wan, W.-L.: Algorithms for particle-field simulations with collisions. J. Comput. Phys. 172, 766–807 (2001)
Walton, O.R., Braun, R.L.: Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional discs. J. Rheol. 30, 949–980 (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Pournin, L., Liebling, T.M. (2009). From Spheres to Spheropolyhedra: Generalized Distinct Element Methodology and Algorithm Analysis. In: Cook, W., Lovász, L., Vygen, J. (eds) Research Trends in Combinatorial Optimization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76796-1_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-76796-1_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76795-4
Online ISBN: 978-3-540-76796-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)