An efficient algorithm for granular dynamics simulations with complex-shaped objects

One of the most difficult aspect of the realistic modeling of granular materials is how to capture the real shape of the particles. Here we present a method to simulate two-dimensional granular materials with complex-shaped particles. The particle shape is represented by the classical concept of a Minkowski sum, which permits the representation of complex shapes without the need to define the object as a composite of spherical or convex particles. A well defined interaction force between these bodies is derived. The algorithm for identification of neighbor particles reduces force calculations to O(N), where N is the number of particles. The method is much more efficient, accurate and easier to implement than other models. We prove that the algorithm is consistent with energy conservation, which is numerically verified using non-dissipative granular dynamics simulations. Biaxial test simulations on dissipative granular systems demonstrate the relevance of shape in the strength and stress fluctuations at the critical state.

[1]  T. Liebling,et al.  A generalization of distinct element method to tridimensional particles with complex shapes , 2005 .

[2]  Peter Mora,et al.  Implementation of Particle-scale Rotation in the 3-D Lattice Solid Model , 2006 .

[3]  H. Herrmann,et al.  Indeterminacy and the onset of motion in a simple granular packing. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Arshad Kudrolli,et al.  Friction in Granular Layers: Hysteresis and Precursors , 1997 .

[5]  T. Ng,et al.  A three-dimensional discrete element model using arrays of ellipsoids , 1997 .

[6]  Brian Mirtich,et al.  V-Clip: fast and robust polyhedral collision detection , 1998, TOGS.

[7]  I Vardoulakis,et al.  Effect of rolling on dissipation in fault gouges. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Mahmood A. Khwaja,et al.  An ellipse-based discrete element model for granular materials , 1993 .

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

[10]  Y. Ta,et al.  Discrete element simulation of crushable soil , 2003 .

[11]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[12]  P. A. Cundall,et al.  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 , 1988 .

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

[14]  S. Luding,et al.  Energy flows in vibrated granular media , 1998 .

[15]  R. Tolman,et al.  The Principles of Statistical Mechanics. By R. C. Tolman. Pp. xix, 661. 40s. 1938. International series of monographs on physics. (Oxford) , 1939, The Mathematical Gazette.

[16]  Luc Sibille,et al.  A numerical photogrammetry technique for measuring microscale kinematics and fabric in Schneebeli materials , 2007 .

[17]  Peter Eberhard,et al.  Collision Detection and Administration Methods for Many Particles with Different Sizes , 2007 .

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

[19]  Michel Saint Jean,et al.  The non-smooth contact dynamics method , 1999 .

[20]  Fernando Alonso-Marroquin,et al.  Spheropolygons: A new method to simulate conservative and dissipative interactions between 2D complex-shaped rigid bodies , 2008 .

[21]  H J Herrmann,et al.  Calculation of the incremental stress-strain relation of a polygonal packing. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  H. Herrmann,et al.  Characterization of the material response in granular ratcheting. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Thorsten Pöschel,et al.  Computational Granular Dynamics , 2005 .

[24]  I Vardoulakis,et al.  Role of anisotropy in the elastoplastic response of a polygonal packing. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Roux,et al.  Fracture of disordered, elastic lattices in two dimensions. , 1989, Physical review. B, Condensed matter.

[26]  G. Pelzl,et al.  Banana-Shaped Compounds—A New Field of Liquid Crystals , 1999 .

[27]  J A McCammon,et al.  Accommodating protein flexibility in computational drug design. , 2000, Molecular pharmacology.

[28]  A. A. Mirghasemi,et al.  Influence of particle shape on engineering properties of assemblies of two-dimensional polygon-shaped particles , 2002 .

[29]  I. Vardoulakis,et al.  The "Stress-Dilatancy" Hypothesis Revisited: Shear-Banding Related Instabilities (IWS-ATHENS 2003「地盤力学における予測とシュミレーション手法」特集号) , 2005 .

[30]  Hans Jürgen Herrmann,et al.  Biaxial test simulations using a packing of polygonal particles , 2008 .

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

[32]  M. Bolton,et al.  The fractal crushing of granular materials , 1996 .

[33]  Paul W. Cleary,et al.  DEM prediction of particle flows in grinding processes , 2008 .

[34]  Félix Darve,et al.  Instabilities in granular materials and application to landslides , 2000 .

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

[36]  Antoinette Tordesillas,et al.  Force chain buckling, unjamming transitions and shear banding in dense granular assemblies , 2007 .

[37]  D. Wood.  Soil Behaviour and Critical State Soil Mechanics , 1991 .

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

[39]  G.G.W. Mustoe,et al.  Material Flow Analyses of Noncircular-Shaped Granular Media Using Discrete Element Methods , 2001 .