Size-Dependent and Tunable Elastic and Geometric Properties of Hierarchical Nano-Porous Materials

Simple closed form results for all the elastic constants of the first order nano-sized hexagonal honeycombs and body-centred-cubic (BCC) open-celled foams, and their self-similar hierarchical cellular materials are obtained in this paper. It is found that if the cell wall/strut thickness of the first order honeycomb or open-celled foam is at the nano-meter scale, the elastic properties of the hierarchical porous materials are not only size-dependent owing to the surface elasticity effects, but also tunable because the amplitude of the initial surface stress/strain is adjustable and controllable. In addition, the cell diameter, cross-sectional area and volume, the total surface area and the electric capacitance of the nano-structured hierarchical honeycombs and open-celled foams can be controlled to vary over a large range. What is more, if the surface modulus of the solid material is negative, a nano-structured hierarchical cellular material could possibly be controlled to collapse automatically.