In-plane elastic properties of hierarchical nano-honeycombs: The role of the surface effect

In this paper, we analytically calculate the in-plane elastic properties (linear-elasticity and elastic buckling) of a new class of bio-inspired nano-honeycomb materials possessing a hierarchical architecture. Incorporating the surface effect, modifications to the classical results for macroscopic and nonhierarchical honeycombs are proposed, and the results are compared with those in the literature. A parametrical analysis reveals the influences of two key geometrical parameters on the overall elastic properties. We discuss the relevant mechanical properties, e.g. stiffness efficiency (stiffness-to-density ratio) and strength efficiency (strength-to-density ratio), which are indices reflecting the mechanical efficiency of materials, and discover that the structural strength can be optimized. The developed theory allows us to design a new class of nano materials with tailored mechanical properties at each hierarchical level and could be useful for many applications.