A New Methodology to Establish Upper Bounds on Open-Cell Foams Homogenized Properties

Abstract

The methodology for determining the upper bounds on the homogenized linear elastic properties 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 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, the 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 are published for the first time, along with a proof of their optimality.