New 3D geometrical deposition methods for efficient packing of spheres based on tangency.

*(English)*Zbl 1352.74086Summary: The morphology of many natural and man-made materials at different length scales can be simulated using particle-packing methods. This paper presents two novel 3D geometrical collective deposition algorithms for packed assemblies with prescribed distribution of radii: the ’planar deposition’ and the ‘3D-clew’ method. The ’planar deposition’ method mimics an orderly granular flow through a funnel by stacking up spirally ordinated planar assemblies of spheres capable of achieving the theoretical maximum for monodisperse aggregates. The ’3D-clew’ method, instead, mimics the winding of a clew of yarn, thus yielding densely packed 3D polydispersed assemblies in terms of void ratio of the aggregate. The morphologies of such geometrically generated assemblies, achieved at several orders of magnitude reduced computational cost, are comparable with those consolidated uni-directionally by means of discrete element method. In addition, significantly faster simulations of mechanical consolidation of granular media have been performed when relying upon the proposed geometrically generated assemblies as starting configurations.

##### Keywords:

granular assembly; tangency condition; geometrical packing algorithm; 3D deposition; discrete element method (DEM)
PDF
BibTeX
XML
Cite

\textit{F. De Cola} et al., Int. J. Numer. Methods Eng. 104, No. 12, 1085--1114 (2015; Zbl 1352.74086)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Guises R Numerical simulation and characterisation of the packing of granular materials U.K. 2008 |

[2] | Cocks, Constitutive modelling of powder compaction - I. Theoretical concepts, Mechanics of materials 39 pp 392– (2007) |

[3] | Weltje, Packing states of ideal reservoir sands: insights from simulation of porosity reduction by grain rearrangement, Sedimentary Geology 242 pp 52– (2011) |

[4] | Liu, Dynamic simulation of powder compact by random packing of monosized and polydisperse particles, Journal of Materials Science Letters 19 pp 841– (2000) |

[5] | Mostofinejad, A new DEM based method to predict packing density of coarse aggregates considering their grading and shapes, Construction and Building Materials 35 pp 414– (2012) |

[6] | Sheng, Atomic packing and short-to-medium-range order in metallic glasses, Nature 439 pp 419– (2006) |

[7] | Truskett, Towards a quantification of disorder in materials: distinguishing equilibrium and glassy sphere packings, Physical Review E 62 pp 993– (2000) |

[8] | Rintoul, Computer simulations of dense hardsphere systems, The Journal of Chemical Physics 105 (20) pp 9285– (1996) |

[9] | Gaskell, Glassy metals II, Topics in Applied Physics 53 pp 5 (1 page)– (1983) |

[10] | Holder JKL Quantum structures in photovoltaic devices U.K., 2013 |

[11] | German, Particle Packing Characteristics (1989) |

[12] | Gan, Predicting packing characteristics of particles of arbitrary shapes, KONA 22 pp 82– (2004) |

[13] | Tao, Discrete element method modeling of non-spherical granular flow in rectangular hopper, Chemical Engineering and Processing: Process Intensification 49 (2) pp 151– (2010) |

[14] | Buechler, Efficient generation of densely packed convex polyhedra for 3D discrete and finite-discrete element methods, International Journal for Numerical Methods in Engineering 94 (1) pp 1– (2013) · Zbl 1352.65473 |

[15] | Gauss, Untersuchungen über die Eigenschaften der positiven ternären quadratischen Formen von Ludwig August Seeber, Göttingische Gelehrte Anzeigen 9 (1831) pp 188– (1840) |

[16] | Hales, A proof of the Kepler conjecture, Annals of Mathematics 162 pp 1065– (2005) · Zbl 1096.52010 |

[17] | Donev, Improving the density of jammed disordered packings using ellipsoids, Science 303 (5660) pp 990– (2004) |

[18] | Torquato, Is random close packing of spheres well defined?, Physical Reviewe Letters 84 (10) pp 2064– (2000) |

[19] | Mueller, Numerical simulation of packed beds with monosized spheres in cylindrical containers, Powder Technology 92 pp 179– (1997) |

[20] | Garai, Upper bound on the disordered density of sphere packing and the Kepler conjecture, eprint arXiv:1001.1714 (2010) |

[21] | Zou, Evaluation of the packing characteristics of mono-sized non-spherical particles, Powder Technology 88 pp 71– (1996) |

[22] | Visscher, Random packing of equal and unequal spheres in two and three dimensions., Nature 239 pp 504– (1972) |

[23] | Feng, Filling domain with disks: an advancing front approach, International Journal for Numerical Methods in Engineering 56 pp 699– (2003) · Zbl 1078.74679 |

[24] | O’Connor, Discrete element modeling of sand production, International Journal of Rock Mechanics and Mining Sciences 34 (3) pp 231. e1– (1997) |

[25] | Mollon G Zhao J Realistic generation and packing of dem sand samples Seoul, Korea 2012 |

[26] | Martinez, Packmol: a package for building initial configurations for molecular dynamics simulations, Journal of Computational Chemistry 30 (13) pp 2157– (2009) · Zbl 05745528 |

[27] | Westman, The packing of particles, Journal of the American Ceramic Society 13 (10) pp 767– (1930) |

[28] | McGeary, Mechanical packing of spherical particles, Journal of the American Ceramic Society 44 pp 513– (2006) |

[29] | Wouterse, Effect of particle shape on the density and microstructure of random packings, Journal of Physics: Condensed Matter 19 (40) pp 406215 (14pp)– (2007) |

[30] | Aparicio, On the representation of random packings of spheres for sintering simulations, Acta Metallurgica et Materialia 43 (10) pp 3873– (1995) |

[31] | Lo, Generation of tetrahedral mesh of variable element size by sphere packing over an unbounded 3d domain, Computer Methods in Applied Mechanics and Enigneering 194 pp 5002– (2005) · Zbl 1093.65017 |

[32] | Haggstrom, Nearest neighbour and hard sphere models in continuum percolation, Random Structures & Algorithms 9 pp 295– (1996) · Zbl 0866.60088 |

[33] | Stoyan, Random sets: models and statistics, International Statistical Review 66 (1) pp 1– (1998) · Zbl 0906.60006 |

[34] | Jerier, Packing spherical discrete elements for large scale simulations, Computer Methods in Applied Mechanics and Engineering 199 pp 1668– (2010) · Zbl 1231.74480 |

[35] | Moon, Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions (1988) |

[36] | Parrinello, Crystal structure and pair potentials: a molecular-dynamics study, Physical Review Letters 45 pp 1196– (1980) |

[37] | Henrich, Simulations of the influence of rearrangement during sintering, Acta Materialia 55 (2) pp 753– (2007) |

[38] | Penumadu, Triaxial compression behavior of sand and gravel using artificial neural networks (ANN), Computers and Geotechnics 24 (3) pp 207– (1999) |

[39] | Kim, High-resolution neutron and x-ray imaging of granular materials, Journal of Geotechnical and Geoenvironmental Engineering 139 (5) pp 715– (2013) |

[40] | Munjiza, The Combined Finite-discrete Element Method (2004) · Zbl 1194.74452 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.