Effective elastic properties of nanoporous materials with hierarchical structure

We investigate the effective elastic properties of nanoporous materials with hierarchical structures, which exhibit a distinct dependence on the characteristic sizes of their microstructure. A core-shell model is first used to account for the effects of both surface tension and surface elasticity. We derive the effective Young's modulus of porous materials with one level of nanosized open or closed cells with surface effects. Then hierarchically structured nanoporous materials consisting of nanosized cells nested in another level of microsized lattice structure are considered to correlate their effective properties with the hierarchical structure. Particular attention is paid to nanoporous gold with multimodal ligament size distributions.