Developing new fitted closure approximations for short-fiber reinforced polymer composites
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Short-fiber polymer composites are greatly used throughout the industry for many applications. The orientation state of the short-fibers within the matrix defines the material properties of the composite structure. It is necessary to develop accurate models and a complete understanding of fiber orientation. Material properties of the composite structure depend on the orientation state of the individual fibers inside of the polymer matrix. Calculating the exact orientation of each fiber is computationally expensive; to address this problem equations have been developed based on the orientation distribution of fibers inside the polymer matrix. A form of the distribution equation has been proposed where the orientation of the fibers is represented by a fourth-order tensor. These tensors capture the behavior of the fibers in a compact form. However, the time evolution equation requires that for each lower order tensor, you must make an approximation for the next higher even order tensor. These closure approximations have been a subject of research for many years. This work will explore many closures that have been used and revisit fitting methods and introduce new concepts in fitting, such as different regression types of the fitted polynomials. A new time derivative based closure will also be introduced which gives improved results and shows a need for more investigation of this type of closure.