Effective elastic constants of two-dimensional cellular materials with deep and thick cell walls

In order to analyse the elastic constants of cellular materials with deep and thick cell walls, finite element analysis using two kinds of unit cell approach (stiffness matrix method and compliance matrix method) is performed which is applicable to any orthotropic cellular materials. Comparison between results from the FEA, the theories presented in this paper and experiments of previous investigators indicate that the elastic constants of cellular materials with thick cell walls depend not only on the relative density but also on the joint stiffening effect. Approximate formulae under generalised plane strain conditions are also presented for the purpose of obtaining the effective elastic constants for cellular materials with deep and thick cell walls. A satisfactory agreement was found with experimental results obtained on a deep and thick cellular material. The results indicate that the previous models in which the wall of cellular materials is treated as a simple beam are not adequate to evaluate the effective elastic constants of cellular materials with deep and thick cell walls. In addition, considerable attention needs for the measurement of effective Young's modulus of square cellular materials in the two soft directions because it is strongly affected by misalignment errors.