The orientation distribution function (ODF) is expanded in terms of generalized spherical harmonics and bounds on the resulting texture coefficients are derived. A necessary and sufficient condition for satisfaction of the normalization property of the ODF is also provided. These results are of significance in, for example, microstructural optimization of materials and predicting texture coefficients based on wave velocity measurements.
Bounds on Texture Coefficients
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, June 5, 2002; final revision, July 26, 2002. Associate Editor: L. T. Wheeler. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Chair, Department of Mechanics and Environmental Engineering, University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Nadeau, J. C., and Ferrari, M. (March 27, 2003). "Bounds on Texture Coefficients ." ASME. J. Appl. Mech. March 2003; 70(2): 200–203. https://doi.org/10.1115/1.1533808
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