English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Fiber-orientation tensors describe the relevant features of thefiber-orientation distribution compactly and are thus ubiquitous ininjection-molding simulations and subsequent mechanical analyses. Inengineering applications to date, the second-order fiber-orientation tensor isthe basic quantity of interest, and the fourth-order fiber-orientation tensoris obtained via a closure approximation. Unfortunately, such a descriptionlimits the predictive capabilities of the modeling process significantly,because the wealth of possible fourth-order fiber-orientation tensors is notexploited by such closures, and the restriction to second-orderfiber-orientation tensors implies artifacts. Closures based on the second-orderfiber-orientation tensor face a fundamental problem - which fourth-orderfiber-orientation tensors can be realized? In the literature, only necessaryconditions for a fiber-orientation tensor to be connected to afiber-orientation distribution are found. In this article, we show that thetypically considered necessary conditions, positive semidefiniteness and atrace condition, are also sufficient for being a fourth-order fiber-orientationtensor in the physically relevant case of two and three spatial dimensions.Moreover, we show that these conditions are not sufficient in higherdimensions. The argument is based on convex duality and a celebrated theorem ofD. Hilbert (1888) on the decomposability of positive and homogeneouspolynomials of degree four. The result has numerous implications for modelingthe flow and the resulting microstructures of fiber-reinforced composites, inparticular for the effective elastic constants of such materials.

On the phase space of fourth-order fiber-orientation tensors