Effects of cell shape and cell wall thickness variations on the elastic properties of two-dimensional cellular solids

The Voronoi tessellation technique and the finite element method are utilized to investigate the microstructure-property relations of two-dimensional cellular solids having irregular cell shapes and non-uniform cell wall thickness. Twenty finite element models are constructed for each type of honeycomb samples (specimens) to obtain the mean values and standard deviations of the effective elastic properties. Spatially periodic boundary conditions are applied to each specimen containing 360 complete cells. The simulation results indicate that the elastic moduli increase as cell shapes become more irregular, but decrease as cell wall thickness gets less uniform. The Poisson's ratios are insignificantly affected by the presence of these two types of imperfections. The effect of the interaction between the co-existing cell shape and cell wall thickness imperfections on the elastic moduli is found to be weak. Bending remains as the dominant deformation mechanism in a loaded honeycomb having irregular cell shapes and/or non-uniform cell wall thickness. In addition, it is revealed that such imperfect honeycombs can be regarded as isotropic.