Size effects of effective Young's modulus for periodic cellular materials

With the wide demands of cellular materials applications in aerospace and civil engineering, research effort sacrificed for this type of materials attains nowadays a higher level than ever before. This paper is focused on the prediction methods of effective Young's modulus for periodical cellular materials. Based on comprehensive studies of the existing homogenization method (HM), the G-A meso-mechanics method (G-A MMM) and the stretching energy method (SEM) that are unable to reflect the size effect, we propose the bending energy method (BEM) for the first time, and a comparative study of these four methods is further made to show the generality and the capability of capturing the size effect of the BEM method. Meanwhile, the underlying characteristics of each method and their relations are clarified. To do this, the detailed finite element computing and existing experimental results of hexagonal honeycombs from the literature are adopted as the standard of comparison for the above four methods. Stretch and bending models of periodical cellular materials are taken into account, respectively for the comparison of stretch and flexural displacements resulting from the above methods. We conclude that the BEM has the strong ability of both predicting the effective Young's modulus and revealing the size effect. Such a method is also able to predict well the variations of structural displacements in terms of the cell size under stretching and bending loads including the non-monotonous variations for the hexagonal cell. On the contrary, other three methods can only predict the limited results whenever the cell size tends to be infinitely small.