In designing a microstructural materials system, there are several key questions associated with design representation, design evaluation, and design synthesis: how to quantitatively represent the design space of a heterogeneous microstructure system using a small set of design variables, how to efficiently reconstruct statistically equivalent microstructures for design evaluation, and how to quickly search for the optimal microstructure design to achieve the desired material properties. This paper proposes a new descriptor-based methodology for designing microstructural materials systems. It is proposed to use a small set of microstructure descriptors to represent material morphology features quantitatively. The descriptor set should be able to cover microstructure features at different levels, including composition, dispersion status, and phase geometry. A descriptor-based multiphase microstructure reconstruction algorithm is developed accordingly that allows efficient stochastic reconstructions of microstructures in both 2D and 3D spaces for finite element analysis (FEA) of material behavior. Finally, the descriptor-based representation allows the use of parametric optimization approach to search the optimal microstructure design that meets the target material properties. To improve the search efficiency, this paper integrates state-of-the-art computational design methods such as design of experiment (DOE), metamodeling, statistical sensitivity analysis, and multi-objective optimization, into one design optimization framework to automate the microstructure design process. The proposed methodology is demonstrated using the design of a polymer nanocomposites system. The choice of descriptors for polymer nanocomposites is verified by establishing a mapping between the finite set of descriptors and the infinite dimensional correlation function.

In designing microstructural materials systems, one of the key research questions is how to represent the microstructural design space quantitatively using a descriptor set that is sufficient yet small enough to be tractable. Existing approaches describe complex microstructures either using a small set of descriptors that lack sufficient level of details, or using generic high order microstructure functions of infinite dimensionality without explicit physical meanings. We propose a new machine learning-based method for identifying the key microstructure descriptors from vast candidates as potential microstructural design variables. With a large number of candidate microstructure descriptors collected from literature covering a wide range of microstructural material systems, a four-step machine learning-based method is developed to eliminate redundant microstructure descriptors via image analyses, to identify key microstructure descriptors based on structure–property data, and to determine the microstructure design variables. The training criteria of the supervised learning process include both microstructure correlation functions and material properties. The proposed methodology effectively reduces the infinite dimension of the microstructure design space to a small set of descriptors without a significant information loss. The benefits are demonstrated by an example of polymer nanocomposites optimization. We compare designs using key microstructure descriptors versus using empirically chosen microstructure descriptors as a demonstration of the proposed method.