A Generalized Lattice-Point Method for Reconstructing Heterogeneous Materials from Lower-Order Correlation Functions

The versatile physical properties of heterogeneous materials are intimately related to their complex microstructures, which can be statistically characterized and modeled using various spatial correlation functions containing key structural features of the material's phases. An important related problem is to inversely reconstruct the material microstructure from limited morphological information contained in the correlation functions. Here, we present in details a generalizedlattice-point (GLP) method based on the lattice-gas model of heterogeneous materials that efficiently computes a specific correlation function by updating the corresponding function associated with a slightly different microstructure. This allows one to incorporate the widest class of lower-order correlation functions utilized to date into the Yeong-Torquato stochastic reconstruction procedure, and thus enables one to obtain much more accurate renditions of virtual material microstructure, to determine the information content of various correlation functions and to select the most sensitive micro structural descriptors for the material of interest. The utility of our GLP method is illustrated by modeling and reconstructing a wide spectrum of random heterogeneous materials, including “clustered” RSA disks, a metal-ceramic composite, a two-dimensional slice of Fontainebleau sandstone and a binary laser-speckle pattern, among other examples.