Generation of stochastic cellular structures with anisotropic cell characteristics on the basis of ellipsoid packings

In the present study, an algorithm to generate anisotropic polygonal cellular structures based on ellipsoid packing is presented. The aim of this process is to obtain structures with different-sized cells which have significantly non-spherical aspect ratios and different orientations in space. The developed method is an extension of the classical Voronoï process in Laguerre geometry which is well-suited to define cell structures with an optimum surface to volume ratio. Different examples show that with this new space division process a number of cellular structures with extremely different characteristics of their cell shape, size and orientation in space can be computed. The generation of such different cellular structures is a useful tool in the multiscale analysis of anisotropic microstructured media with uncertain microstructures exhibiting microstructural anisotropies such as process-related anisotropic structural foams or anisotropic metallic grain agglomerates.