A new methodology to establish upper bounds on open-cell foam homogenized moduli

The methodology to determine upper bounds on homogenized linear elastic moduli of cellular solids, described for the two-dimensional case in Dimitrovová and Faria (1999), is extended to three-dimensional open-cell foams. Besides the upper bounds the methodology provides necessary and sufficient conditions on the optimal media. These conditions are written in terms of generalized internal forces and geometrical parameters. In some cases dependence on internal forces can be replaced by geometrical expressions. In such cases optimality of some medium under consideration can be verified directly from the microstructure, without any additional calculation. Some of the bounds derived in this paper have not yet been published along with a proof of their optimality.

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