Micromechanical Analysis of Three-Dimensional Open-Cell Foams Using the Matrix Method for Space Frame Structures

摘要

A micromechanical model for three-dimensional open-cell foams is developed by using the matrix method for space frames in structural mechanics and tetrakaidcahedral unit cells. The effective elastic properties of foams are determined employing unit cells subjected to three different modes of loading. The thirty-six struts of each tetrakaidecahedral unit cell are treated as uniform slender beams, and the twenty-four vertices as rigid joints. All four- deformation mechanisms (i.e., stretching, shearing, bending and twisting) possible under the specified loadings are incorporated, and four different strut cross section shapes (i.e., circle, square, equilateral triangle and Plateau border) are treated in a unified manner. The formulas for determining the effective Young's modulus, Poisson's ratio and shear modulus of open-cell foams that are undergoing linearly elastic deformations are derived using the composite homogentization theory. The new formulas include all necessary parameters, unlike those provided by existing models.