MICROMECHANICAL ANALYSIS OF THREE-DIMENSIONALOPEN-CELL FOAMS USING THE MATRIX METHOD FORSPACE FRAME STRUCTURES

摘要

A micromechanical model for three-dimensional open-cell foams is developed by using the matrixmethod for space frames in structural mechanics and tetrakaidecahedral unit cells. The effective elasticproperties 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 thetwenty-four vertices as rigid joints. All four deformation mechanisms (I.e., stretching, shearing, bendingand twisting) possible under the specified loadings are incorporated, and four different strut cross sectionshapes (I.e., circle, square, equilateral triangle and Plateau border) are treated in a unified manner. Theformulas for determining the effective Young’s modulus, Poisson’s ratio and shear modulus of open-cellfoams that are undergoing linearly elastic deformations are derived using the composite homogenizationtheory. The new formulas include all necessary parameters, unlike those provided by existing models.These formulas indicate that the foam elastic properties depend on the relative foam density, the shapeand size of the strut cross section, and the Young’s modulus and Poisson’s ratio of the strut material. Byapplying the new model, a parametric study of sample cases is conducted for carbon foams, whosemodeling motivated this study. The predicted values of the effective properties agree favorably with thosebased on existing models and experimental data for the Mode I loading case, which is the only case thathas been well studied in the literature. Comparisons of the effective elastic properties for the three loadingcases quantitatively show that carbon foams exhibit certain degree of anisotropy.