The effects of regularity on the geometrical properties of Voronoi tessellations

Zhu, Hanxing ORCID: https://orcid.org/0000-0002-3209-6831, Zhang, P., Balint, D., Thorpe, S. M., Elliott, J. A., Windle, A. H. and Lin, J. 2014. The effects of regularity on the geometrical properties of Voronoi tessellations. Physica A: Statistical Mechanics and its Applications 406 , pp. 42-58. 10.1016/j.physa.2014.03.012

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Abstract

This study comprehensively quantifies the effects of regularity on the geometrical properties of a random three-dimensional Voronoi tessellation (VT), where regularity was defined as the ratio of the minimum seed distance to the seed distance of the correlated body-centred cubic lattice. A scheme to generate Voronoi tessellations with controlled regularity is proposed, which was used to simulate 106 cells for a series of regularities. The results were used to derive probability distributions for the properties of the tessellation, including faces and edges per cell, vertex and dihedral cell angles, cell areas and volumes, etc. An understanding of the relation between a simple, measurable parameter characterizing the degree of regularity of a Voronoi tessellation and its geometrical properties is essential in generating virtual microstructures that are statistically representative of reality; the statistical results are also relevant to all other applications involving random Voronoi tessellations. Finally, an application is presented of the proposed Voronoi tessellation generation scheme applied to micromechanical modelling of grain structures with defined regularities for crystal plasticity finite element analysis.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Subjects:	T Technology > TA Engineering (General). Civil engineering (General)
Uncontrolled Keywords:	3D Voronoi tessellations; Geometrical properties; Regularity; Virtual grain structure; Micromechanics.
Publisher:	Elsevier
ISSN:	0378-4371
Last Modified:	27 Oct 2022 08:56
URI:	https://orca.cardiff.ac.uk/id/eprint/63842

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