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Gradient-Based Non-Linear Microstructure Design, Brent L. Adams, M. Lyon

Faculty Publications

The support of this research by the Army Research Office is gratefully acknowledged. M. Lyon is supported by a National Science Foundation Graduate Research Fellowship. Fourier analysis is implemented on the orientation distribution of a polycrystalline microstructure. The linearity and convexity of the Fourier space, with respect to orientation, allows one to consider all possible distributions by considering all linear combinations of single-grain orientations. The limits of the Fourier space are therefore defined by the solutions to a set of linear programming problems. A unique approach to the linear programming, similar to the Krylov subspace methods for obtaining solutions to …