AmericanChemicalSociety.com

Narrative

Two-phase heterogeneous materials abound in the petroleum and energy-related fields. A fascinating inverse problem that we made significant progress in solving 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. A novel aim of this proposal was to use the construction algorithm to categorize random microstructures for the first time. This enabled us to generate a specific class of three-dimensional microstructures at will and subsequently performed 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 was 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 employed 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. This also enables one to estimate the transport, electromagnetic and mechanical properties of the computer-generated two-phase materials that have specified lower-order statistics. This new endeavor provides a means to select heterogeneous materials with desired or optimal macroscopic properties.