Lionel Pournin - Numerical Simulation

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Spherocylinders will align vertically when shaken appropriately.

Most frequently, in numerical simulation of granular media, particles are modeled as spheres. During my PhD, I defined a model for particle shapes, spheropolyhedra [1,2] that has several good properties: the usual contact forces (including Cundall and Strack's one) can be generalized very easily to these shapes, and any non-spherical shape can be approached by some spheropolyhedron. Moreover, the triangulations- based contact detection method designed by Didier Müller and Jean-Albert Ferrez in the case of spheres also carries over very well with these shapes. All these ingredients have been implemented in a C++ simulation code developed at EPFL under the supervision of Prof. Liebling by Jean-Albert Ferrez and extended by Christophe Weibel, Mats Weber, Michel Tsukahara, and myself.

A spheropolyhedron is nothing else that the Minkowski sum of a polyhedron with a sphere. This produces a 'smoothed' polyhedron. Among the spheropolyhedra, those obtained using a simplex are called spherosimplices: balls, spherocylinders (rods like the ones you can see on the right), spherotriangles (triangular cookies), and spherotetrahedra (rounded tetrahedra) are the four kinds of 3-dimensional spherosimplices.

The simulation code has been used since then to investigate a number of phenomena occuring with granular media. The very first experiment was performed by Michel Tsukahara for his master's thesis: pour spherocylinders into a cylindrical container, with random initial orientation, and shake. Surprisingly, the particles may eventually order vertically [3], even under periodic boundary conditions. A possible explanation for this is the void-filling mechanism, as suggested by the PhD work of Marco Ramaioli [4,5].

Among the other phenomena the EPFL granular media simulation code contributed to study, one finds granular jamming about a circular aperture [6,7,8,9]. Note that spherotetrahedra could be nicely used to investigate Hilbert's eighteenth problem.

The code was running on the Linux cluster of the mathematics institute at EPFL until around 2008, and on the EPFL grid computing facility until june 2013.

[1]

A generalization of Distinct Element Method to tridimensional particles with complex shapes
L. Pournin and Th. M. Liebling, Powders and Grains 2005 Proceedings vol. II, 1375-1378, A.A.Balkema, Rotterdam (2005)

[2]

From spheres to spheropolyhedra: generalized Distinct Element Methodology and algorithm analysis
L. Pournin and Th. M. Liebling, Research Trends in Combinatorial Optimization, Springer, Berlin (2009)

[3]

Three-dimensional distinct element simulation of spherocylinder crystallization
L. Pournin, M. Weber, M. Tsukahara, J.-A. Ferrez, M. Ramaioli and Th. M. Liebling, Granular Matter 7(2-3), 119-126 (2005)

[4]

Vertical ordering of rods under vertical vibration
M. Ramaioli, L. Pournin and Th. M. Liebling, Phys. Rev. E 76(2), 021304 (2007)

[5]

Granular flow simulations and experiments for the food industry
M. Ramaioli, EPFL PhD Thesis #3997 (2007)

[6]

About the influence of friction and polydispersity on the jamming be havior of bead assemblies
L. Pournin, M. Ramaioli, P. Folly and Th. M. Liebling, Eur. Phys. J. E 23(2), 229-235 (2007)

[7]

Particle Shape versus Friction in Granular Jamming
L. Pournin, M. Tsukahara, and Th. M. Liebling, Powders and Grains 2009, AIP Conference Proceedings 1145, 499-502 (2009)

[8]

Simple Probabilistic Modeling of Granular Jamming and Validation Using DEM
M. Tsukahara, L. Pournin, and Th. M. Liebling, Powders and Grains 2009, AIP Conference Proceedings 1145, 507-510 (2009)

[9]

Jamming in granular media : modeling of experimental data
M. Tsukahara, EPFL PhD Thesis #4490 (2009)