Stochastic Multiscale Modeling of Metal Foams

A procedure for the computation of eigenfrequencies for structures made of metal foam is proposed. The heterogeneity of the foam geometry has an influence on these macroscopic properties and has to be taken into account. This is done by fitting a model of the microstructure based on Laguerre tessellations by means of statistical information obtained from CT image analysis. As the length scale of the representative volume element is nearly of the same order as the length scale of the structures under consideration, classical homogenization techniques for the computation of effective properties can not be applied. A stochastic homogenization method that necessitates the computation of empirical marginal distributions and correlation functions for apparent properties defined on the mesoscale is proposed. This information allows to define random fields for elastic properties and the density on the structure level. Statistical properties of the eigenfrequencies can then be inferred.