Micromechanical Modeling of Three-dimensional Open-cell Foams

Abstract

Two micromechanics models for three-dimensional (3-D) opencell foams are presented. In the first model, an energy method based on Castigliano’s second theorem is utilized. The analysis is performed on a tetrakaidecahedral unit cell, which is subjected to compression on its two opposite square faces. The thirty-six struts of the unit cell are treated as uniform slender beams undergoing linearly elastic deformations, and the twenty-four vertices as rigid joints. All three deformation mechanisms of the cell struts (i.e., stretching, shearing and bending) possible under the specified loading are incorporated, and four different strut cross section shapes (i.e., circle, square, equilateral triangle and Plateau border) are treated in a unified manner, unlike in earlier models. Two closed-form formulas for determining the effective Young’s modulus and Poisson’s ratio of open-cell foams are provided. These two formulas are derived by using the composite homogenization theory and contain more parameters than those included in existing models. The new formulas explicitly show that the elastic properties of the foam depend on the relative foam density, the shape and size of the strut cross section, and the Young’s modulus and Poisson’s ratio of the strut material. The predicted values of the effective Young’s modulus and Poisson’s ratio for carbon foams compare favorably with those based on existing models and experimental data.