Geometrical modeling of granular structures in two and three dimensions. Application to nanostructures

A granular structure can be modeled by a parallelepiped containing spherical balls in three dimensions or by a rectangle filled with disks in two dimensions. These grains (spherical balls or disks) are separated by interfaces called grain boundaries and their size correspond to a size distribution, which is obtained experimentally. The geometrical modeling of such a structure consists in determining the repartition of the set of disjoint grains according to these specifications. In this paper, a new constructive algorithm based on an advancing-front approach, usually used in the context of mesh generation, is proposed. This algorithm is nearly linear in complexity, robust and fast in both two and three dimensions. Enhancements in computing time and density are observed and reported via comparisons with existing methods. Moreover, we propose a method to transform spherical balls (disks) into polyhedral (polygonal) cells similar to the real grain shapes. Examples of nanostructure modeling in two and three dimensions are presented. Copyright © 2009 John Wiley & Sons, Ltd.

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

[2]  Subra Suresh,et al.  Mechanical behavior of nanocrystalline metals and alloys , 2003 .

[3]  J. A. George.  Computer implementation of the finite element method , 1971 .

[4]  Olle Häggström,et al.  Nearest Neighbor and Hard Sphere Models in Continuum Percolation , 1996 .

[5]  Brian McPherson,et al.  The Role of Particle Packing in Modeling Rock Mechanical Behavior using Discrete Elements , 2002 .

[6]  J. C. Schön,et al.  Simulation of random close packed discs and spheres , 1993 .

[7]  Patricia Ann Thomas.  Discontinuous deformation analysis of particulate media , 1997 .

[8]  Akira Murakami,et al.  Initial Packing in Discrete Element Modeling , 2002 .

[9]  David R. Owen,et al.  Filling domains with disks: an advancing front approach , 2003 .

[10]  Charles H. Bennett,et al.  Serially Deposited Amorphous Aggregates of Hard Spheres , 1972 .

[11]  A. J. Matheson.  Computation of a random packing of hard spheres , 1974 .

[12]  Jian Lu,et al.  An investigation of surface nanocrystallization mechanism in Fe induced by surface mechanical attrition treatment , 2002 .

[13]  Jodrey,et al.  Computer simulation of close random packing of equal spheres. , 1985, Physical review. A, General physics.

[14]  W. Visscher,et al.  Random Packing of Equal and Unequal Spheres in Two and Three Dimensions , 1972, Nature.

[15]  B. Lubachevsky,et al.  Geometric properties of random disk packings , 1990 .

[16]  Serge Leroueil,et al.  An efficient technique for generating homogeneous specimens for DEM studies , 2003 .

[17]  James W. Evans,et al.  Random and cooperative sequential adsorption , 1993 .

[18]  S. Lo.  A NEW MESH GENERATION SCHEME FOR ARBITRARY PLANAR DOMAINS , 1985 .

[19]  Liang Cui,et al.  Analysis of a triangulation based approach for specimen generation for discrete element simulations , 2003 .

[20]  Frank H. Stillinger,et al.  Systematic Approach to Explanation of the Rigid Disk Phase Transition , 1964 .

[21]  Katalin Bagi,et al.  An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies , 2005 .

[22]  Jian Lu,et al.  Nanostructure formation mechanism of α-titanium using SMAT , 2004 .

[23]  David R. Owen,et al.  Sphere packing with a geometric based compression algorithm , 2005 .

[24]  Jian Lu,et al.  Nanostructured surface layer on metallic materials induced by surface mechanical attrition treatment , 2004 .

[25]  R. Feynman.  There's plenty of room at the bottom , 1999 .

[26]  Kenji Shimada,et al.  Anisotropic tetrahedral meshing via bubble packing and advancing front , 2003 .

[27]  Katalin Bagi,et al.  A quasi-static numerical model for micro-level analysis of granular assemblies , 1993 .

[28]  Rainald Löhner,et al.  A general advancing front technique for filling space with arbitrary objects , 2004 .