Evaluation of micromechanical methods to determine stiffness and strength properties of foams

The stiffness and strength properties of foams with tetrakaidecahedral unit cells are evaluated using both finite element-based micromechanics and analytical methods. The finite element analysis models the varying cross section of the struts exactly. The analytical methods assume the struts have constant cross section along the length. Equivalent constant cross section of the strut can be obtained by either matching the densities or by using harmonic averaging of the stiffness properties. A method in which the moment of inertia of the cross section is averaged is also considered. The comparison of properties obtained for the different equivalent constant cross-section foams shows the inability of the various averaging schemes to match the shear modulus and the strength properties, while the Young's modulus matches to some extent. The failure of the weakest cross section in the varying cross-section strut of the unit cell leads to a lower tensile strength in the actual foam compared to the uniform cross-section foams. The results suggest that although the use of simple analytical models for foam properties are attractive, they often lead to erroneous results, and hence exact modeling of the strut geometry is key to estimating the stiffness and strength properties of foams and other cellular solids.