Physics Of The Deformation Of Densely Packed Granular Materials, The by Koenders M. A. C.;

Author:Koenders, M. A. C.; [Неизв.]
Language: eng
Format: epub
ISBN: 9781786348258
Publisher: World Scientific Publishing Company
Published: 2020-07-26T21:00:00+00:00

Figure 5.1. Illustration of Voronoi tiling.

A tiling is introduced via the definition of the Voronoi boundaries — [Voronoi, 1908]. This definition (which can be used in a far wider context than just for granular materials) defines a boundary as the collection of points that have the shortest distance to a set of given points (called the generators). An illustration shown in Fig. 5.1 may be helpful to understand the definition. Take an assembly of discs and for the ‘set of given points’ use the centres of the discs. The Voronoi boundaries then look as shown in Fig. 5.2. It produces a space-filling tiling. This would be satisfactory for the purposes of granular media if all the discs were of equal size. But because they are not of an equal size the boundaries end up cutting through the particles. The desire is to employ the Voronoi boundaries later on and associate them with particle interactions. The definition of a Voronoi boundary is then changed slightly to ensure that each particle lies within a tile.

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