M. Abbaspour-fard, Theoretical validation of a multi-sphere, discrete element model suitable for biomaterials handling simulation, Biosystems Engineering, vol.88, issue.2, pp.153-161, 2004.

F. Alonso-marroquín and Y. Wang, An efficient algorithm for granular dynamics simulations with complexshaped objects, Granular Matter, vol.11, issue.5, pp.317-329, 2009.

H. Bekker and J. B. Roerdink, An efficient algorithm to calculate the minkowski sum of convex 3d polyhedra, Computational Science-ICCS 2001, pp.619-628, 2001.

F. Camborde, C. Mariotti, and F. Donzé, Numerical study of rock and concrete behaviour by discrete element modelling, Computers and geotechnics, vol.27, issue.4, pp.225-247, 2000.

E. Coumans, Bullet 2.83 Physics Library manual, 2015.

P. Cundall and O. Strack, A discrete numerical model for granular assemblies, Geotechnique, vol.29, issue.1, pp.47-65, 1979.

P. A. Cundall, Formulation of a three-dimensional distinct element model-Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol.25, issue.3, pp.107-116, 1988.

R. Doe and . Cgal, Computational Geometry Algorithms Library, 2009.

A. D?iugys and B. Peters, An approach to simulate the motion of spherical and non-spherical fuel particles in combustion chambers, Granular matter, vol.3, issue.4, pp.231-266, 2001.

Y. Feng and D. Owen, A 2D polygon/polygon contact model: algorithmic aspects. Engineering Computations, vol.21, pp.265-277, 2004.

F. Y. Fraige, P. A. Langston, and G. Z. Chen, Distinct element modelling of cubic particle packing and flow, Powder Technology, vol.186, issue.3, pp.224-240, 2008.

E. G. Gilbert and C. Foo, Computing the distance between general convex objects in three-dimensional space. Robotics and Automation, IEEE Transactions on, vol.6, issue.1, pp.53-61, 1990.

E. G. Gilbert, D. W. Johnson, and S. S. Keerthi, A fast procedure for computing the distance between complex objects in three-dimensional space. Robotics and Automation, IEEE Journal, vol.4, issue.2, pp.193-203, 1988.

R. Hart, P. Cundall, and J. Lemos, Formulation of a three-dimensional distinct element model-Part II. Mechanical calculations for motion and interaction of a system composed of many polyhedral blocks, In International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol.25, pp.117-125, 1988.

S. Hentz, L. Daudeville, and F. V. Donzé, Identification and validation of a discrete element model for concrete, Journal of engineering mechanics, vol.130, issue.6, pp.709-719, 2004.
URL : https://hal.archives-ouvertes.fr/hal-02004500

D. Höhner, S. Wirtz, H. Kruggel-emden, and V. Scherer, Comparison of the multi-sphere and polyhedral approach to simulate non-spherical particles within the discrete element method: Influence on temporal force evolution for multiple contacts, Powder Technology, vol.208, issue.3, pp.643-656, 2011.

F. Jin, H. Xin, C. Zhang, and Q. Sun, Probability-based contact algorithm for non-spherical particles in DEM, Powder Technology, vol.212, issue.1, pp.134-144, 2011.

L. Jing, Formulation of discontinuous deformation analysis (dda)-an implicit discrete element model for block systems, Engineering Geology, vol.49, issue.3, pp.371-381, 1998.

M. Kodam, R. Bharadwaj, J. Curtis, B. Hancock, and C. Wassgren, Cylindrical object contact detection for use in discrete element method simulations. part II-Experimental validation, Chemical Engineering Science, vol.65, issue.22, pp.5863-5871, 2010.
DOI : 10.1016/j.ces.2010.08.007

H. Kruggel-emden, S. Rickelt, S. Wirtz, and V. Scherer, A study on the validity of the multi-sphere discrete element method, Powder Technology, vol.188, issue.2, pp.153-165, 2008.

P. Langston, U. Tüzün, and D. Heyes, Continuous potential discrete particle simulations of stress and velocity fields in hoppers: transition from fluid to granular flow, Chemical Engineering Science, vol.49, issue.8, pp.1259-1275, 1994.

P. Langston, U. Tüzün, and D. Heyes, Discrete element simulation of granular flow in 2d and 3d hoppers: Dependence of discharge rate and wall stress on particle interactions, Chemical Engineering Science, vol.50, issue.6, pp.967-987, 1995.

Y. Lee, C. Fang, Y. Tsou, L. Lu, and C. Yang, A packing algorithm for three-dimensional convex particles, Granular Matter, vol.11, issue.5, pp.307-315, 2009.
DOI : 10.1007/s10035-009-0133-7

J. Li, P. A. Langston, C. Webb, and T. Dyakowski, Flow of sphero-disc particles in rectangular hoppers-a DEM and experimental comparison in 3D, Chemical Engineering Science, vol.59, issue.24, pp.5917-5929, 2004.

G. Lu, J. Third, and C. Müller, Discrete element models for non-spherical particle systems: From theoretical developments to applications, Chemical Engineering Science, vol.127, pp.425-465, 2015.
DOI : 10.1016/j.ces.2014.11.050

V. Luchnikov, N. Medvedev, L. Oger, and J. Troadec, Voronoi-delaunay analysis of voids in systems of nonspherical particles, Phys. Rev. E, vol.59, pp.7205-7212, 1999.

J. Mellmann, The transverse motion of solids in rotating cylinders-forms of motion and transition behavior, Powder Technology, vol.118, issue.3, pp.251-270, 2001.

A. Munjiza, J. F. Peters, M. A. Hopkins, R. Kala, and R. E. Wahl, A poly-ellipsoid particle for non-spherical discrete element method. Engineering Computations, vol.26, pp.645-657, 2009.

G. Nolan and P. Kavanagh, Random packing of nonspherical particles, Powder technology, vol.84, issue.3, pp.199-205, 1995.
DOI : 10.1016/0032-5910(95)98237-s

J. Park, Modeling the dynamics of fabric in a rotationg horizontal drum, 2003.

D. Petit, F. Pradel, G. Ferrer, and Y. Meimon, Shape effect of grain in a granular flow. Powders and grains, p.425, 2001.

L. Pournin, T. Liebling-;-r-garcía-rojo, H. Herrmann, and S. Mcnamara, A generalization of Distinct Element Method to tridimensional particles with complex shapes, Powders and Grains, vol.5805, pp.1375-1378, 2005.

A. D. Rakotonirina and A. Wachs, Grains3D, a flexible DEM approach for particles of arbitrary convex shape -Part II: parallel implementation and scalable performance, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01857743

S. Rémond, J. Gallias, and A. Mizrahi, Simulation of the packing of granular mixtures of non-convex particles and voids characterization, Granular Matter, vol.10, issue.3, pp.157-170, 2008.

Y. Song, R. Turton, and F. Kayihan, Contact detection algorithms for DEM simulations of tablet-shaped particles, Powder Technology, vol.161, issue.1, pp.32-40, 2006.

H. Tangri, Y. Guo, and J. Curtis, Packing of cylindrical particles: DEM simulations and experimental measurements, Powder Technology, vol.317, pp.72-82, 2017.
DOI : 10.1016/j.powtec.2017.03.058

G. Van-den-bergen, A fast and robust GJK implementation for collision detection of convex objects, Journal of Graphics Tools, vol.4, issue.2, pp.7-25, 1999.

A. Wachs, A DEM-DLM/FD method for direct numerical simulation of particulate flows: Sedimentation of polygonal isometric particles in a Newtonian fluid with collisions, Computers & Fluids, vol.38, issue.8, pp.1608-1628, 2009.

A. Wachs, L. Girolami, G. Vinay, and G. Ferrer, Grains3D, a flexible DEM approach for particles of arbitrary convex shape-Part I: Numerical model and validations, Powder Technology, vol.224, pp.374-389, 2012.
URL : https://hal.archives-ouvertes.fr/hal-02171452

J. R. Williams and R. O'connor, A linear complexity intersection algorithm for discrete element simulation of arbitrary geometries, Engineering computations, vol.12, issue.2, pp.185-201, 1995.

J. R. Williams and A. P. Pentland, Superquadrics and modal dynamics for discrete elements in interactive design. Engineering Computations, vol.9, pp.115-127, 1992.

Y. Wu, X. An, and A. Yu, DEM simulation of cubical particle packing under mechanical vibration, Powder Technology, vol.314, pp.89-101, 2017.

R. Yang, A. Yu, L. Mcelroy, and J. Bao, Numerical simulation of particle dynamics in different flow regimes in a rotating drum, Powder Technology, vol.188, issue.2, pp.170-177, 2008.

R. Yang, R. Zou, and A. Yu, Microdynamic analysis of particle flow in a horizontal rotating drum, Powder Technology, vol.130, issue.1-3, pp.138-146, 2003.

B. Zhao, X. An, Y. Wang, Q. Qian, X. Yang et al., 32 3 Relative error on (a) the volume and (b) components of the moment of inertia tensor, of a sphere, a cylinder and a glued convex made of two overlapping cylinders, as a function of the number of discretization points per direction, Powder Technology, vol.317, pp.171-180, 2017.

, 35 6 Sketch of the cylinder-wall impact test case

, Cylinder-wall impact test case: comparison of the computed dimensionless postimpact velocities for the real cylinder and the glued cylinder to the analytical solution, vol.37

, 6 is the number of elementary cylinders of the glued cylinder. EC denotes the normal force exerted on each elementary cylinder and SEC denotes the sum of the normal forces exerted on each elementary cylinder, i.e., the sum of the ECs, Cylinder-wall impact test case at an angle of 90 ? : normal contact force evolution with time. N = 1

, Cylinder-wall impact test case: glued-sphere approximations of the cylinder considered: (a)-(b) made of 9 glued spheres, (c)-(d) made of 54 glued spheres, p.40

, Cylinder-wall impact test case: comparison of the computed dimensionless postimpact velocities (a,b) for the 9 glued-sphere cylinder, and (c,d) for 54 glued sphere cylinder with the analytical solution

, Cube-wall impact test case: comparison of vertical position time evolution and x-component of angular velocity time evolution for a single cube and a glued convex cube obtained by gluing 8 smaller cubes of half the edge length of the single cube released with various initial angular position (? x , ? y ) = (0 o , 0 o ), (10 o , 10 o ), (25 o , 25 o ), (75 o , 75 o ) and (30 o , 0 o )

, 44 15 Tile spacers experiments: method to identify the free surface of the granular media. The blue dots depict the free surface and the red line the polynomial fitting function of high order

. .. Case, 49 20 Rotating drum filled with 3D crosses at various rotation rates: snapshots of the pattern of particles colored by their translational velocity magnitude (from blue (min) to red (max))

, Trajectory of a single particle at ? = 150 rpm over 10 s

, 52 23 Rotating drum filled with 2D crosses at various rotation rates: snapshots of the pattern of particles colored by their translational velocity magnitude (from blue (min) to red (max)), Avalanching regime of 3D crosses (a,b,c) at ? = 5 rpm and (d,e,f) at ? = 20 rpm