In-plane elastic properties of hierarchical cellular solids

In this paper, we analytically calculate the in-plane linear-elastic properties of a new class of bio-inspired nano-honeycomb materials possessing a hierarchical architecture, which is often observed in natural materials. Incorporating the surface tension, peculiar of the nano-scale, modifications of the classical results for macroscopic and nonhierarchical honeycombs are proposed. A parametrical analysis reveals the influences of relative density and of two key geometrical parameters on the overall elastic properties. We discover optimal values for some of the mechanical properties, e. g. stiffness-to-density ratio. The developed theory allows us to design a new class of materials with tailored elastic properties at each hierarchical level and could be useful for many applications. (C) 2010 Published by Elsevier Ltd.