Modeling heterogeneous materials via two-point correlation functions. II. Algorithmic details and applications

In the first part of this series of two papers, we proposed a theoretical formalism that enables one to model and categorize heterogeneous materials (media ) via two- point correlation functions S-2 and introduced an efficient heterogeneous- medium (re ) construction algorithm called the lattice- point algorithm. Here we discuss the algorithmic details of the lattice- point procedure and an algorithm modification using surface optimization to further speed up the (re ) construction process. The importance of the error tolerance, which indicates to what accuracy the media are (re ) constructed, is also emphasized and discussed. We apply the algorithm to generate three- dimensional digitized realizations of a Fontainebleau sandstone and a boron- carbide/ aluminum composite from the two- dimensional tomographic images of their slices through the materials. To ascertain whether the information contained in S-2 is sufficient to capture the salient structural features, we compute the two- point cluster functions of the media, which are superior signatures of the microstructure because they incorporate topological connectedness information. We also study the reconstruction of a binary laser- speckle pattern in two dimensions, in which the algorithm fails to reproduce the pattern accurately. We conclude that in general reconstructions using S-2 only work well for heterogeneous materials with single- scale structures. However, two- point information via S-2 is not sufficient to accurately model multiscale random media. Moreover, we construct realizations of hypothetical materials with desired structural characteristics obtained by manipulating their two- point correlation functions.