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On the Phase Space of Fourth-Order Fiber-Orientation Tensors

Bauer, Julian Karl 1,2; Schneider, Matti 1; Böhlke, Thomas ORCID iD icon 1
1 Institut für Technische Mechanik (ITM), Karlsruher Institut für Technologie (KIT)
2 Institut für Mechanik (IFM), Karlsruher Institut für Technologie (KIT)

Abstract:

Fiber-orientation tensors describe the relevant features of the fiber-orientation distribution compactly and are thus ubiquitous in injection-molding simulations and subsequent mechanical analyses. In engineering applications to date, the second-order fiber-orientation tensor is the basic quantity of interest, and the fourth-order fiber-orientation tensor is obtained via a closure approximation. Unfortunately, such a description limits the predictive capabilities of the modeling process significantly, because the wealth of possible fourth-order fiber-orientation tensors is not exploited by such closures, and the restriction to second-order fiber-orientation tensors implies artifacts. Closures based on the second-order fiber-orientation tensor face a fundamental problem – which fourth-order fiber-orientation tensors can be realized? In the literature, only necessary conditions for a fiber-orientation tensor to be connected to a fiber-orientation distribution are found. In this article, we show that the typically considered necessary conditions, positive semidefiniteness and a trace condition, are also sufficient for being a fourth-order fiber-orientation tensor in the physically relevant case of two and three spatial dimensions. ... mehr


Verlagsausgabe §
DOI: 10.5445/IR/1000155249
Veröffentlicht am 27.01.2023
Originalveröffentlichung
DOI: 10.1007/s10659-022-09977-2
Scopus
Zitationen: 4
Web of Science
Zitationen: 4
Dimensions
Zitationen: 5
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Mechanik (IFM)
Institut für Technische Mechanik (ITM)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 03.2023
Sprache Englisch
Identifikator ISSN: 0374-3535, 1573-2681
KITopen-ID: 1000155249
Erschienen in Journal of Elasticity
Verlag Springer
Seiten 161-184
Vorab online veröffentlicht am 12.01.2023
Schlagwörter Fiber-orientation tensor, Injection molding, Closure approximation, Effective elastic stiffness, Fiber-reinforced composite
Nachgewiesen in Dimensions
Scopus
Web of Science
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