This research has shown that a sixth-order closure is required to improve the accuracy of fiber orientation calculations beyond the fourth-order truncation limit when representing the orientation distribution function Ψ. Our fitted sixth-order closure INV₆ is formed using a general expression for a fully symmetric sixth-order tensor from a fourth-order tensor, which is written as

The coefficients β_i are defined as a linear function of the invariants I of the fourth-order tensor a_ijkl.

In Simple Shear flow, our new fitted INV₆ closure may be used to represent the second-order tensor a_ij better than that provided by fourth-order closures such as the ORT of VerWeyst (1999). The fiber orientation distribution function can be reconstructed from an Nth order orientation tensor. As shown here, our newly developed sixth-order fitted closure INV₆ yields a significant improvement in accuracy when compared with fourth-order closures.

An Invariant Based Fitted Closure of the Sixth-Order Orientation Tensor for Short-Fiber Suspensions. D.A. Jack and D.E. Smith, Journal of Rheology 49(5):1091-1115, 2005.

Sixth-Order Fitted Closures from the Second-Moment of the Fiber Orientation Distribution for Short fiber Reinforced Polymer Melt Flow Simulations. D.A. Jack and D.E. Smith. Accepted for publication in Journal of Thermoplastic Composites, 2005.

Sixth-Order Fitted Closure Methods for Short-Fiber Reinforced Polymer Composite Systems. D.A. Jack and D.E. Smith. The 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Palm Springs, California, April, 2004.

Investigating the Use of Sixth-Order Orientation Tensors in Polymer Composite Melt Flow Simulations. D.A. Jack and D.E. Smith. NUMIFORM 2004, The 8th International Conference on Numerical Methods in Industrial Forming Processes, Columbus, Ohio, June, 2004.

A Fitted Closure of the Sixth-Order Orientation Tensor for Short-Fiber Reinforced Polymer Composite Modeling. D.A. Jack and D.E. Smith. FPCM-7, the 7th International Conference on Flow Processes in Composite Materials, Newark, Delaware, July, 2004.

• U.S. National Science Foundation
• U.S. Department of Education