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Modeling polycrystalline materials with elongated grains
Author(s) -
Pérez Irvin,
Muniz de Farias Márcio,
Castro Manuel,
Roselló Roberto,
Recarey Morfa Carlos,
Medina Liosber,
Oñate E.
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6004
Subject(s) - voronoi diagram , equidistant , vertex (graph theory) , euclidean geometry , spheres , ellipse , centroidal voronoi tessellation , mathematics , void (composites) , algorithm , jaccard index , geometry , computer science , materials science , combinatorics , physics , composite material , artificial intelligence , pattern recognition (psychology) , graph , astronomy
Summary 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.