Microstructure models for cellular materials

Laguerre tessellations generated by random sphere packings are promising models for the microstructure of cellular or polycrystalline materials. In this paper, the case of hard sphere packings with lognormal or gamma distributed volumes is investigated. The dependence of the geometric characteristics of the Laguerre cells on the volume fraction of the sphere packing and the coefficient of variation of the volume distribution is studied in detail. The moments of certain cell characteristics are described by polynomials, which allows to fit tessellation models to real materials without further simulations. The procedure is demonstrated by the examples of open polymer and aluminium foams.