Scaling between elasticity and topological genus for random network nanomaterials

Abstract

We explore the hypothesis that the variation of the effective, macroscopic Young’s modulus, , of a random network material with its scaled topological genus, , and with the solid fraction, , can be decomposed into the product of - and -dependent functions. Based on findings for nanoporous gold, supplemented by the Gibson–Ashby scaling law for , we argue that both functions are quadratic in bending-dominated structures. We present finite-element-modeling results for of coarsened microstructures, in which and are decoupled. These results support the quadratic forms.