Advancing front packing algorithms have proven to be very efficient in 2D for obtaining high density sets of particles, especially disks. However, the extension of these algorithms to 3D is not a trivial task. In the present paper, an advancing front algorithm for obtaining highly dense sphere packings is presented. It is simpler than other advancing front packing methods in 3D and can also be used with other types of particles. Comparison with respect to other packing methods have been carried out and a significant improvement in the volume fraction (VF) has been observed. Moreover, the quality of packings was evaluated with indicators other than VF. As additional advantage, the number of generated particles with the algorithm is linear with respect to time.

No abstract

A novel algorithm to reproduce the arrangement of grains in polycrystalline materials was recently published by the authors. In this original approach, a dense package of circles (or spheres) with the same distribution as the grains is generated to produce a set of Voronoi cells that are later modified to Laguerre cells representing the original structure. This algorithm was successfully applied to materials with somewhat equidimensional grains; however, it fails for long-shaped grains. In this paper, modifications are provided in order to overcome these drawbacks. This is accomplished by moving each vertex of the Voronoi cells in such a way that the vertex should be equidistant from the particles with respect to the Euclidean distance. The algorithm is applied to packages of ellipses and spherocylinders in 2D. An example for a package of spheres is also provided to illustrate the application for a simple 3D case. The adherence between the generated packages and the corresponding tessellations is verified by means of the Jaccard coefficient (J). Several packages are generated randomly and the distribution of J coefficients is investigated. The obtained values satisfy the theoretical restraints and the quality of the proposed algorithm is statistically validated.

SUMMARYThe generation of a set of particles with high initial volume fraction is a major problem in the context of discrete element simulations. Advancing front algorithms provide an effective means to generate dense packings when spherical particles are assumed. The objective of this paper is to extend an advancing front algorithm to a wider class of particles with generic size and shape. In order to get a dense packing, each new particle is placed in contact with other two (or three in 3D) particles of the advancing front. The contact problem is solved analytically using wrapping intersection technique. The results presented herein will be useful in the application of these algorithms to a wide variety of practical problems. Examples of geometric models for applications to biomechanics and cutting tools are presented.