Function-based reconstruction of the fiber orientation distribution function of short-fiber-reinforced polymers

Reconstruction of the fiber orientation distribution function (ODF) from injection molding simulation results is commonly performed using the so-called series-based approach. However, with the development of advanced material constitutive models, the need has emerged to overcome the drawbacks of this approach, such as negative values for certain orientation states and limitations in describing highly concentrated probabilities. In this work, an approach to shift the reconstruction procedure from series-based to function-based is proposed, achieved by deducing an appropriate two-parametric form of the ODF. We demonstrate that the proposed ODF can be uniquely reconstructed from the second-order orientation tensors obtained from the injection molding simulations and that the approach does not suffer from the aforementioned limitations, being capable of accurately describing even the extreme orientation states without yielding nonphysical results. Based on the proposed ODF, a new closure approximation is also developed and used to verify the deduced form in flow-induced orientation predictions.