45764-AC10
Modeling Random Heterogeneous Materials Via Lower-Order Statistics
Two-phase heterogeneous materials abound in the petroleum
and energy-related fields. A fascinating inverse problem that has been receiving considerable
attention of late is the reconstruction or construction of realizations of
random two-phase heterogeneous materials with target lower-order microstructural statistics. We have solved this problem has been solved using stochastic optimization techniques.
In the ``construction" mode, the algorithm seeks to construct realizations
with prescribed lower-order functions. One aim of this
work is to use the construction algorithm to categorize random microstructures. This has enabled us to generate a specific class of three-dimensional microstructures at will and
subsequently perform any desired analysis of these computer-generated representations.
However, not every proposed lower-order microstructural function
corresponds to a realizable two-phase material. Thus, a fundamentally important
goal is the identification of strong and checkable exact necessary conditions for a
variety of lower-order functions, and then to identify a wide class of functions that can be realized and their associated microstructures. Because the construction algorithm is a powerful numerical tool in ascertaining whether a lower-order function is indeed realizable, we will use it not only to guide us in our search for analytical necessary conditions for each of the functions but to help us to determine the class of functions that can be realized.
