Angles in Laguerre tessellation models for solid foams

摘要

Geometric stochastic models proved to be very helpful to improve the understanding of how physical properties of materials depend on their microstructures. The microstructures of cellular materials are well modeled by random Laguerre tessellations generated by systems of non-overlapping spheres. We enrich the geometric characterization of Laguerre tessellations by computing angles between facets and angles between edges. Their distributions, which depend on the model parameters, are investigated in detail. To include angles in the model fit, we developed a method for estimating angles in 3D images of foams, e. g. obtained by micro-computed tomography. Furthermore, we analyzed the influence of different characteristics on the model's fit to samples of closed and open foams.