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Nonlinear optimization for compact representation of orientation distributions based on generalized spherical harmonics
•An optimization procedure for the compaction of crystallographic texture data is developed.•The procedure is based on the spectral representation of orientation distributions using generalized spherical harmonics basis.•Gradient vector and Hessian matrix are derived analytically and implemented to...
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Published in: | Journal of the mechanics and physics of solids 2024-06, Vol.187, p.105609, Article 105609 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | •An optimization procedure for the compaction of crystallographic texture data is developed.•The procedure is based on the spectral representation of orientation distributions using generalized spherical harmonics basis.•Gradient vector and Hessian matrix are derived analytically and implemented to facilitate a rapid convergence of the procedure in Matlab.•Case studies involving metals with cubic, hexagonal, and orthorhombic crystal structures demonstrated utility of the procedure.•The procedure is an essential tool for compacting input texture data in metal forming process simulations with crystal plasticity.
An orientation distribution is a necessary input in any crystal plasticity simulation. The computational time involved in crystal plasticity simulations scales linearly with the number of crystal orientations in the input distributions. Reducing the number of crystal orientations in representing the input orientation distributions quantitatively is a critical and necessary requirement for performing computationally efficient crystal plasticity simulations of deformation processes. A procedure for the compaction of orientation distribution functions (ODFs) relying on a spectral representation using series of generalized spherical harmonics (GSH) basis functions was recently developed. Linear fitting of the spectral representation of an ODF containing a compact set of weighted orientations towards a full-size ODF containing many crystal orientations was in the core of the procedure. This paper advances the compaction procedure by replacing the linear with a nonlinear optimization in Matlab for which a suitably defined error, gradient, and Hessian matrix are derived to allow for more efficient, accurate, and greater compactions. The utility of the new procedure is to allow for not only fitting the weights of a compacted set of orientations but to allow for optimizing weighted orientations or a combination of optimizing weights and orientations. The new compaction procedure has been successfully applied to compactions of large ODFs of cubic, hexagonal, and orthorhombic polycrystalline metals. In doing so, the evolution of texture, twinning, and stress-strain are predicted at large plastic strains with compact ODFs to agree with the corresponding full size ODFs using crystal plasticity models. In closing, guidance for effective texture compaction trading off the accuracy and computational gains are provided. |
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ISSN: | 0022-5096 |
DOI: | 10.1016/j.jmps.2024.105609 |