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Open AccessFeature PaperArticle

Analysis and Evaluation of Fiber Orientation Reconstruction Methods

TU Dortmund University, Mechanical Engineering, Chair of Plastics Technology, Leonhard-Euler-Str. 5, 44227 Dortmund, Germany
PART Engineering GmbH, Friedrich-Ebert-Straße 75, 51429 Bergisch Gladbach, Germany
Author to whom correspondence should be addressed.
J. Compos. Sci. 2019, 3(3), 67;
Received: 24 May 2019 / Revised: 14 June 2019 / Accepted: 1 July 2019 / Published: 4 July 2019
(This article belongs to the Special Issue Feature Papers in Journal of Composites Science in 2019)
PDF [9630 KB, uploaded 4 July 2019]


The calculation of the fiber orientation of short fiber-reinforced plastics with the Fokker–Planck equation requires a considerable numerical effort, which is practically not feasible for injection molding simulations. Therefore, only the fiber orientation tensors are determined, i.e., by the Folgar–Tucker equation, which requires much less computational effort. However, spatial fiber orientation must be reconstructed from the fiber orientation tensors in advance for structural simulations. In this contribution, two reconstruction methods were investigated and evaluated using generated test scenarios and experimentally measured fiber orientation. The reconstruction methods include spherical harmonics up to the 8th order and the method of maximum entropy, with which a Bingham distribution is reconstructed. It is shown that the quality of the reconstruction depends massively on the original fiber orientation to be reconstructed. If the original distribution can be regarded as a Bingham distribution in good approximation, the method of maximum entropy is superior to spherical harmonics. If there is no Bingham distribution, spherical harmonics is more suitable due to its greater flexibility, but only if sufficiently high orders of the fiber orientation tensor can be determined exactly. View Full-Text
Keywords: maximum entropy; spherical harmonics; fiber orientation; ODF; reconstruction; injection molding maximum entropy; spherical harmonics; fiber orientation; ODF; reconstruction; injection molding

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Breuer, K.; Stommel, M.; Korte, W. Analysis and Evaluation of Fiber Orientation Reconstruction Methods. J. Compos. Sci. 2019, 3, 67.

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