We show that mechanical design can be conducted where consideration of polycrystalline microstructure as a continuous design variable is facilitated by use of a spectral representation space. Design of a compliant ÿxed-guided beam is used as a case study to illustrate the main tenets of the new approach, called microstructure-sensitive design (MSD). Selection of the mechanical framework for the design (e.g., mechanical constitutive model) dictates the dimensionality of the pertinent representation. Microstructure is considered to be comprised of basic elements that belong to the material set. For the compliant beam problem, these are uni-axial distribution functions. The universe of pertinent microstructures is found to be the convex hull of the material set, and is named the material hull. Design performance, in terms of speciÿed design objectives and constraints, is represented by one or more surfaces (often hyperplanes) of ÿnite dimension that intersect the material hull. Thus, the full range of microstructure, and concomitant design performance, can be exploited for any material class. Optimal placement of the salient iso-property surfaces within the material hull dictates the optimal set of microstructures for the problem. Extensions of MSD to highly constrained design problems of higher dimension is also described.

An exhaustive branching technique is introduced for reconstructing discrete microstructures from twopoint statistic occurrences. It is shown that two-point statistics control microstructure, to the extent that exact replicas of discrete microstructures are produced when sufficient two-point statistic occurrences are matched. Efficiency comparisons between simulated-annealing methods and the exhaustive branching method are made on polycrystalline structures and some discussion on advancing the exhaustive branching method is given.

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