Three dimensional modeling of complex heterogeneous materials via statistical microstructural descriptors

Heterogeneous materials have been widely used in many engineering applications. Achieving optimal material performance requires a quantitative knowledge of the complex material microstructure and structural evolution under external stimuli. Here, we present a framework to model material microstructure via statistical morphological descriptors, i.e., certain lower-order correlation functions associated with the material’s phases. This allows one to reduce the large data sets for a complete specification of all of the local states in a microstructure to a handful of simple scalar functions that statistically capture the salient structural features of the material. Stochastic reconstruction techniques can then be employed to investigate the information content of the correlation functions, suggest superior and sensitive structural descriptors as well as generate realistic virtual 3D microstructures from the given limited structural information. The framework is employed to successfully model a variety of materials systems including an anisotropic aluminium alloy, a polycrystalline tin solder, the structural evolution in a binary lead-tin alloy when aged, and a model structure of hard-sphere packing. Our framework also has ramifications in the development of integrated computational material design schemes and 4D materials modeling techniques.