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

TL;DR

This paper introduces a generalized lattice-point method that enhances the reconstruction of complex heterogeneous material microstructures from lower-order spatial correlation functions, improving accuracy and understanding of material properties.

Contribution

The paper presents a novel generalized lattice-point method that efficiently incorporates diverse correlation functions into stochastic reconstruction, enabling more accurate modeling of complex heterogeneous materials.

Findings

Successfully reconstructed various heterogeneous materials including sandstone and composite materials.

Enhanced the accuracy of microstructure modeling using a wide range of correlation functions.

Demonstrated the method's versatility across different material types.

Abstract

The versatile physical properties of heterogeneous materials are intimately related to their complex microstructures, which can be statistically characterized and modelled 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 generalized lattice-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, including those encoding topological connectedness information and interface statistics, 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 microstructural descriptors for the material of interest. The utility of our GLP method is illustrated by modelling and reconstructing a wide spectrum of random heterogeneous materials, including "clustered" RSA disks, a metal-ceramic composite, a two-dimensional slice of a Fontainebleau sandstone and a binary laser-speckle pattern, among other examples.