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The versatile physical properties of heterogeneous materials are intimatelyrelated to their complex microstructures, which can be statisticallycharacterized and modelled using various spatial correlation functionscontaining key structural features of the material's phases. An importantrelated problem is to inversely reconstruct the material microstructure fromlimited morphological information contained in the correlation functions. Here,we present in details a generalized lattice-point (GLP) method based on thelattice-gas model of heterogeneous materials that efficiently computes aspecific correlation function by updating the corresponding function associatedwith a slightly different microstructure. This allows one to incorporate thewidest class of lower-order correlation functions utilized to date, includingthose encoding topological connectedness information and interface statistics,into the Yeong-Torquato stochastic reconstruction procedure, and thus enablesone to obtain much more accurate renditions of virtual material microstructure,to determine the information content of various correlation functions and toselect the most sensitive microstructural descriptors for the material ofinterest. The utility of our GLP method is illustrated by modelling andreconstructing a wide spectrum of random heterogeneous materials, including"clustered" RSA disks, a metal-ceramic composite, a two-dimensional slice of aFontainebleau sandstone and a binary laser-speckle pattern, among otherexamples.

Modeling and Reconstructing Complex Heterogeneous Materials From  Lower-Order Spatial Correlation Functions Encoding Topological and Interface  Statistics