Advancing layer algorithm of dense ellipse packing for generating statistically equivalent polygonal structures

A new constructive algorithm, called Advancing layer algorithm, for the generation of dense ellipse packing is proposed. Compared to existing algorithms for filling a 2D domain by elliptical particles, the method allows to respect the imposed size, shape and spatial orientation distributions (i.e. the inertia tensor) and achieve high packing densities. In particular case of disk packing, the comparison with Optimized Dropping and Rolling method shows that the computational cost of the proposed methodology is lower for moderate polydispersities of particle size while achieving higher packing densities and more homogeneous placing of particles in the domain. Thanks to an approximation of each ellipse by a set of circles, polygonal structures are constructed on the base of obtained ellipse packing by Laguerre–Voronoï Tessellation method in good agreement with desired characteristics of cells (polygons).

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