Theoretical approximation of hydrodynamic and fiber-fiber interaction forces for macroscopic simulations of polymer flow process with fiber orientation tensors

Flow processes of discontinuous fiber reinforced polymers (FRPs) are the essence of several polymer-based manufacturing processes. FRPs show a transient chemo-thermomechanical matrix behavior and fiber-induced anisotropic physical properties. Therefore, they are one of the most complex materials used in volume production. The general flow behavior is influenced by fibers and their interactions with the matrix and other fibers. The consideration of individual fibers is numerically not capable for process simulation of FRP parts. Therefore, orientation tensors are used in macroscopic simulations, leading to a loss of information about the fiber network. Within this work, novel approximation schemes are presented to determine hydrodynamic and fiber-fiber contact forces with information provided by the second order fiber orientation tensor. Approximation of these forces can henceforth facilitate fiber breakage modeling in macroscopic process simulations. The results are verified by numerical simulations with individual fibers of different orientation states and lengths, showing good agreement with the verification results.