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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

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 Web of Science
Scopus
Dimensions
Relationen in KITopen

Verlagsausgabe §
DOI: 10.5445/IR/1000155249
Veröffentlicht am 27.01.2023
Originalveröffentlichung
DOI: 10.1007/s10659-022-09977-2
Scopus
Zitationen: 5
Web of Science
Zitationen: 4
Dimensions
Zitationen: 7
Seitenaufrufe: 101
seit 27.01.2023
Downloads: 67
seit 05.02.2023
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