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. A descriptor-based characterization method is proposed to provide a quantitative representation of material morphology using a small set of microstructure descriptors covering features of material composition, dispersion status, and phase geometry at different levels of representation. A descriptor-based multi-phase microstructure reconstruction algorithm is developed which allows efficient stochastic reconstruction of microstructures for Finite Element Analysis (FEA) of material behavior. 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. 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 employs state-of-the-art computational design methods such as Design of Experiment (DOE), metamodeling, statistical sensitivity analysis, and multi-objective optimization. The proposed methodology is demonstrated using the design of a polymer nanocomposites system.

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