Microstructures, Optimization, Polycrystalline material, Processing


BA acknowledges financial support provided by the MRSEC Program of the National Science Foundation under Award Number DMR-9632556. SK acknowledges financial support from National Science Foundation under Award Number CMS-9732699. BA, SK and HG also acknowledge support from the NSF-CIRE program centered at Florida A&M University, facilitating collaborations. Support was also provided by the College of Engineering and Technology at BYU (AH, BH and ML). Computations were performed on the new SGI Origin 2000 supercomputer at Brigham Young University, donated by Ira Fulton. 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 fixed-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 specified design objectives and constraints, is represented by one or more surfaces (often hyperplanes) of finite 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.

Original Publication Citation

Journal of the Mechanics and Physics of Solids 49 (21) 1639-1663

Document Type

Peer-Reviewed Article

Publication Date


Permanent URL


Elsevier Ltd.




Ira A. Fulton College of Engineering and Technology


Mechanical Engineering