Stochastic approach for determining properties of randomly structured materials: Effects of network connectivity

Abstract Nanoporous (NP) materials have promising potential uses in energy storage, catalysis, and high-radiation environments. However, wide application of NP materials—or other emerging materials with similarly complex and/or random structures—requires an understanding of and predictive models for structure–property relationships governing materials behavior. Structural complexity and randomness have been a longstanding challenge to understanding and modeling such materials. Here, we describe the Kentucky Random Structures Toolkit (KRaSTk), which addresses this challenge by allowing the stochastic generation of sets of many model representative volume elements (mRVEs) from a physically-motivated geometric seed description, and the calculation (via FEM) of both expected bulk effective properties and length-scale-dependent distributions of local properties. We demonstrate the applicability of this approach by showing that changes in network connectivity in a random, ligamented NP material have an effect on both elastic and bulk modulus that is independent of solid fraction, and is related to the presence of short-range disorder. The effect of varying network connectivity can be accounted for by adding a power law term to the Gibson-Ashby model for the stiffness of porous structures, such that E * / E s = C E ϕ 2 ( N C * − 3 ) n E and K * / K s = C K ϕ 2 ( N C * − 3 ) n K , for N C * the effective network connectivity. These findings highlight the potential of the stochastic mRVE approach implemented in KRaSTk for modeling and exploring the effects of complex and random structure that drive novel behaviors in emerging porous, nanocrystalline, or additively manufactured materials.