Fitting three-dimensional Laguerre tessellations to foam structures

Abstract

Foam models, especially random tessellations, are powerful tools to study the relations between the geometric structure of foams and their physical properties. In this paper, we propose the use of random Laguerre tessellations, weighted versions of the well-known Voronoi tessellations, as models for the microstructure of foams. Based on geometric characteristics estimated from a tomographic image of a closed-cell polymer foam, we fit a Laguerre tessellation model to the material. It is shown that this model allows for a better fit of the geometric structure of the foam than some classical Voronoi tessellation models

Early-stage oxidation behavior at high temperatures of SiSiC cellular architectures in a porous burner

“…10 depicts SEM images from the surface of the oxide layers, characterized by silica wires. This is similar to what is reported as transition from active to passive oxidation mode in presence of oxygen [29]. This silica layer was loosely attached to the substrate resulting spallation in some zones, likely during heating and cooling ramps.…”

“…The cell length was kept 7 mm. Random structures were generated from Laguerre Tessellation [29] with similar average geometrical parameters. All templates were 3D printed with the same strut diameter Ds¼0.4 mm using 3DLPrinter-HD 2.0 (Robot Factory S.r.l., It), with a resolution of 10 and 50 mm in vertical and horizontal axes, respectively.…”

Optimal polyhedral description of 3D polycrystals: Method and application to statistical and synchrotron X-ray diffraction data

“…For reproducing grain size distributions, seeds are often determined from a dense packing of spheres [36,37]. For foams, seeds can be determined from the geometry and arrangement of their walls [38]. For grain centroids and volumes provided by synchrotron X-ray diffraction experiments, seeds can also be determined using simple schemes [40].…”

“…Laguerre tessellations are a generalization of Voronoi tessellations and are becoming increasingly popular for modelling materials such as polycrystals [36,37] or foams [38]. Similarly to Voronoi tessellations, Laguerre tessellations are generated from a set of seeds [39], but the seeds are more delicate to set, so that different strategies were developed for different applications.…”

Random Tessellations and Boolean Random Functions

“…The Laguerre tessellation [9,10] is a generalization of the Voronoi tessellation, where to each Poisson point x k is attached a random radius R k . The cell is now defined from the power P (x,…”