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. © 2009 John Wiley & Sons, Ltd.