Optimized advance front method of packing dense ellipse for generating the convex polygon structure statistically equiva
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Optimized advance front method of packing dense ellipse for generating the convex polygon structure statistically equivalent with real material Libing Du1,2 • Xinrong Liu1,2
•
Yafeng Han1,2 • Zhiyun Deng1,2 • Yiliang Tu3
Received: 17 December 2019 / Revised: 4 August 2020 / Accepted: 28 September 2020 Ó OWZ 2020
Abstract A new constructive method, called optimized advance front method (OAFM), for ellipse packing is proposed. The OAFM allows particle rotation at several angles and movement along a local advance front. Combined with the ellipse approximated by four connected arcs and a series of sequential coordinate transformations, the OAFM generates dense ellipse packing with any imposed size, aspect ratio, and orientation distribution at a fastpacking speed, and the generated ellipse packing can satisfy an imposed spatial arrangement. Based on the approximation of ellipses by multicircles, Laguerre Voronoi Tessellation method constructs initial cells. The initial cells are then merged to create the convex polygon with the same size, aspect ratio, orientation, and location as that of the obtained ellipse. Three examples of ellipse packing and convex polygon demonstrate that the convex polygon generated can be statistically equivalent with the real material and satisfy an imposed spatial arrangement. Keywords Ellipse packing Optimized advancing front method Convex polygon
1 Introduction Granular materials, porous media, foams, and polycrystalline materials are composed of various particles that conform to certain particle sizes, orientations, aspect ratios, and satisfy certain spatial arrangements [2, 5, 33, 35, 42]. It is necessary to model a virtual cell structure that is statistically equivalent to the original material. The Voronoi Tessellation method (VTM) is a common technique for modeling the polygon structure of materials. The VTM partitions a plane into convex polygons with n points. Each polygon contains one generating point, and
& Xinrong Liu [email protected] 1
School of Civil Engineering, Chongqing University, Chongqing 400045, China
2
National Joint Engineering Research Center of Geohazards Prevention in The Reservoir Areas (Chongqing), Chongqing 400045, China
3
School of Civil Engineering, Chongqing Jiaotong University, Chongqing 400074, China
every point in a given polygon is closer to its generating point than to any other. The VTM is easy to implement and takes into account mean particle size. However, VTM is difficult to construct structures with an imposed particle size, orientation, and aspect ratio distribution. By scaling a Voronoi diagram using different length/width ratios and rotating at a specific angles, the polygon structure with specific aspect ratio and orientation can be generated [16]. Poisson Voronoi Tessellation can generate polygon that respects an imposed size distribution [12, 41]. In addition, the VTM is in conjunction with the inverse Monte Carlo method to generate polygon with an imposed size, orientation, distr
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