Orientation tensors are widely used to describe fiber distri-butions in short fiber reinforced composite systems. Although these tensors capture the stochastic nature of concentrated fiber suspensions in a compact form, the evolution equation for each lower order tensor is a function of the next higher order tensor. Flow calculations typically employ a closure that approximates the fourth-order orientation tensor as a function of the second order orientation tensor. Recent work has been done with eigen-value based and invariant based closure approximations of the fourth-order tensor. The effect of using lower order tensors tensors in process simulations by reconstructing the distribution function from successively higher order orientation tensors in a Fourier series representation is considered. This analysis uses the property that orientation tensors are related to the series expansion coefficients of the distribution function. Errors for several closures are investigated and compared with errors developed when using a reconstruction from the exact 2nd, 4th, and 6th order orientation tensors over a range of interaction coefficients from 10−4 to 10−1 for several flow fields.
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ASME 2003 International Mechanical Engineering Congress and Exposition
November 15–21, 2003
Washington, DC, USA
Conference Sponsors:
- Materials Division
ISBN:
0-7918-3719-X
PROCEEDINGS PAPER
Assessing the Use of Tensor Closure Methods With Orientation Distribution Reconstruction Functions
David A. Jack,
David A. Jack
University of Missouri at Columbia, Columbia, MO
Search for other works by this author on:
Douglas E. Smith
Douglas E. Smith
University of Missouri at Columbia, Columbia, MO
Search for other works by this author on:
David A. Jack
University of Missouri at Columbia, Columbia, MO
Douglas E. Smith
University of Missouri at Columbia, Columbia, MO
Paper No:
IMECE2003-42828, pp. 121-129; 9 pages
Published Online:
May 12, 2008
Citation
Jack, DA, & Smith, DE. "Assessing the Use of Tensor Closure Methods With Orientation Distribution Reconstruction Functions." Proceedings of the ASME 2003 International Mechanical Engineering Congress and Exposition. Materials. Washington, DC, USA. November 15–21, 2003. pp. 121-129. ASME. https://doi.org/10.1115/IMECE2003-42828
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