Delineation of the space of 2-point correlations in a composite material system

The complete set of 2-point correlations for a composite material system with a large number of local states (e.g. polycrystalline metals) forms a vast and unwieldy data set containing a large amount of redundant information. The interrelations in these correlations have been well characterized for composite material systems with two local states, but only a small number have been delineated for the composite systems with many local states. This paper presents an analysis of interrelations between the complete set of 2-point correlations for composite material systems through their spectral representations via discrete Fourier transforms. These interrelations are used to delineate a compact and convex space that bounds the set of all physically realizable 2-point correlations called the 2-point correlations hull. The representation of any given microstructure in this hull, and the techniques to produce a representative volume element are also explored in this paper.