Abstract
Most materials, produced either in nature or in factories, possess hierarchical structures, and understanding the role which hierarchy plays in their mechanical and physical behavior is a fundamental issue. The conventional scaling law established for porous materials with relatively larger characteristic sizes of microstructures does not hold for nanoporous materials because of the neglect of surface effects. The present paper aims at investigating the macroscopic effective elastic modulus of hierarchical nanoporous materials, which shows a distinct dependence on the characteristic sizes of nanostructures. Surface effects are taken into account by using the theory of surface elasticity. The effective elastic moduli of nanoporous open-cell foams with two or more structural levels are analytically given to correlate their macroscopic mechanical property with the geometric and material parameters at different levels.