Effective elastic properties of periodic hexagonal honeycombs

We investigate the elastic behavior of periodic hexagonal honeycombs over a wide range of relative densities and cell geometries, using both analytical and numerical approaches. Previous modeling approaches are reviewed and their limitations identified. More accurate estimates of all nine elastic constants are obtained by modifying the analysis of Gibson and Ashby (1997) to account for the nodes at the intersection of the vertical and inclined members. The effect of the nodes becomes significant at high relative densities. We then compare the new analytical equations with previous analytical models, with a numerical analysis based on a computational homogenization technique and with data for rubber honeycombs over a wide range of relative densities and cell geometries. The comparisons show that both the new analytical equations and numerical solutions give a remarkably good description of the data. The results provide new insights into understanding the mechanics of honeycombs and designing new cellular materials in the future.