From Spheres to Spheropolyhedra: Generalized Distinct Element Methodology and Algorithm Analysis

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.

[1]  T. Liebling,et al.  Numerical and experimental investigation of alignment and segregation of vibrated granular media composed of rods and spheres , 2005 .

[2]  T. Liebling,et al.  Molecular-dynamics force models for better control of energy dissipation in numerical simulations of dense granular media. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Jean-Albert Ferrez,et al.  Dynamic triangulations for efficient 3D simulation of granular materials , 2001 .

[4]  Jean-Daniel Boissonnat,et al.  A Linear Bound on the Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces , 2004, Discret. Comput. Geom..

[5]  Alexander Schinner,et al.  Fast algorithms for the simulation of polygonal particles , 1999 .

[6]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[7]  Didier Müller,et al.  Techniques informatiques efficaces pour la simulation de milieux granulaires par des méthodes d'éléments distincts , 1996 .

[8]  Marco Ramaioli,et al.  Granular flow simulations and experiments for the food industry , 2008 .

[9]  Th. M. Liebling,et al.  Detection of Collisions of Polygons by Using a Triangulation , 1995 .

[10]  Lionel Pournin,et al.  On the behavior of spherical and non-spherical grain assemblies, its modeling and numerical simulation , 2005 .

[11]  R. O'Connor,et al.  A distributed discrete element modeling environment: algorithms, implementation and applications , 1996 .

[12]  W. Mittig,et al.  Shell evolution and the N = 34 “magic number” , 2007 .

[13]  Hanan Samet,et al.  The Quadtree and Related Hierarchical Data Structures , 1984, CSUR.

[14]  R. L. Braun,et al.  Viscosity, granular‐temperature, and stress calculations for shearing assemblies of inelastic, frictional disks , 1986 .

[15]  A. Stuart,et al.  Algorithms for particle-field simulations with collisions , 2001 .

[16]  Shlomo Havlin,et al.  Spontaneous stratification in granular mixtures , 1997, Nature.

[17]  Peter Eberhard,et al.  Contacts Between Many Bodies , 2004 .

[18]  T. Liebling,et al.  Vertical ordering of rods under vertical vibration. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  P. Eberhard,et al.  Collisions between particles of complex shape , 2005 .

[20]  Thomas M. Liebling,et al.  Constrained paths in the flip-graph of regular triangulations , 2007, Computational geometry.

[21]  Frederico W. Tavares,et al.  Influence of particle shape on the packing and on the segregation of spherocylinders via Monte Carlo simulations , 2003 .

[22]  J.-A. Ferrez,et al.  Dynamic triangulations for efficient detection of collisions between spheres with applications in granular media simulations , 2002 .

[23]  T. Liebling,et al.  Three-dimensional distinct element simulation of spherocylinder crystallization , 2005 .

[24]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[25]  Hans J. Herrmann,et al.  Discrete element simulations of dense packings and heaps made of spherical and non-spherical particles , 2000 .