Stochastic multiscale modeling of metal foams

• We predict properties of metal foam structures from microstructure image analysis.
• We calibrate a Laguerre tessellation generator using geometric quantities.
• We analyze three dimensional volume elements of random microstructure samples.
• The procedure is applied to bending eigenfrequencies of metal foam beams.
• We are able to predict the scatter observed in experiments.

We propose a procedure for the computation of natural frequencies for structures made of metal foam. Because the heterogeneity of the foam geometry has an influence on macroscopic properties, the irregular geometry of the foam has to be taken into account. This is done by adapting a Laguerre tessellation to statistical descriptors of the geometry 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 cannot be applied. Therefore, we introduce a stochastic homogenization method based on empirical marginal distribution functions and correlation functions of apparent properties. This information allows us to define random fields for elastic properties and the mass density on the macroscopic level. Statistical properties of the natural frequencies can then be inferred.