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Asymptotic fiber orientation states of the quadratically closed Folgar-Tucker equation and a subsequent closure improvement

Karl, Tobias 1,2; Gatti, Davide 2; Frohnapfel, Bettina 2; Böhlke, Thomas 1
1 Institut für Technische Mechanik (ITM), Karlsruher Institut für Technologie (KIT)
2 Institut für Strömungsmechanik (ISTM), Karlsruher Institut für Technologie (KIT)


Anisotropic fiber-reinforced composites are used in lightweight construction, which is of great industrial relevance. During mold filling of fiber suspensions, the microstructural evolution of the local fiber arrangement and orientation distribution is determined by the local velocity gradient. Based on the Folgar–Tucker equation, which describes the evolution of the second-order fiber orientation tensor in terms of the velocity gradient, the present study addresses selected states of deformation rates that can locally occur in complex flow fields. For such homogeneous flows, exact solutions for the asymptotic fiber orientation states are derived and discussed based on the quadratic closure. In contrast to the existing literature, the derived exact solutions take into account the fiber-fiber interaction. The analysis of the asymptotic solutions relying upon the common quadratic closure shows disadvantages with respect to the predicted material symmetry, namely, the anisotropy is overestimated for strong fiber-fiber interaction. This motivates us to suggest a novel normalized fully symmetric quadratic closure. Two versions of this new closure are derived regarding the prediction of anisotropic properties and the fiber orientation evolution. ... mehr

Verlagsausgabe §
DOI: 10.5445/IR/1000136118
Veröffentlicht am 17.07.2022
DOI: 10.1122/8.0000245
Zitationen: 8
Web of Science
Zitationen: 8
Zitationen: 8
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Strömungsmechanik (ISTM)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2021
Sprache Englisch
Identifikator ISSN: 0148-6055, 1520-8516
KITopen-ID: 1000136118
Erschienen in Journal of Rheology
Verlag American Institute of Physics (AIP)
Band 65
Heft 5
Seiten 999-1022
Vorab online veröffentlicht am 16.07.2021
Nachgewiesen in Scopus
Web of Science
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