Keywords: closed-cell foam, Alporas®, homogenized properties, upper-lower bounds, Wang tilings, two-dimensional homogenization.

In this paper, a homogenization model of high porosity metallic foams based on a two-dimensional finite element analysis is presented. The assumed model is wired, which allows for correct volume fractions of metallic phase contrary to planar models obtained from scanned images. Two types of boundary conditions, static and kinematic uniform, along with a number of representative volume elements of different sizes are explored in order to arrive at upper and lower bounds for effective moduli. The geometries of computational models are synthesized by means of Wang tiles with morphologies spatially consistent with target medium. Although, we are aware of the fact that the rigorous three-dimensional model would be optimal for a reliable judgment of resulting material parameters, the main benefit of this work is seen in the effective way the geometries of computational models are created and kept in the computer memory. Moreover, the proposed two dimensional analysis reveals many difficulties we would have to deal with in three dimensions anyway.

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