Models for cellular materials are random tessellations, that is space-filling systems of non-overlapping polytopes. A particularly versatile model are Laguerre tessellations - a generalization of the well-known Voronoi tessellation allowing to control the cell sizes much better: Each generating point is assigned a weight that can be interpreted as a sphere radius. The cell volume distribution of a Laguerre tessellation generated by a system of non-overlapping spheres is closely related to the sphere volumes.
The model is fit by minimizing a distance function between several characteristics of the model and the real microstructure where the latter are measured from 3D image data. Modelling combined with numerical simulation of materials properties enables optimization of the microstructure.