**6. Conclusions**

We propose a user-friendly multi-scale virtual workflow for estimating the fiber orientation of an injection-molded fiber reinforced thermoplastic part. To do this, we use a particle-based mechanistic model, which is able to evaluate the fiber orientation under shear flow and elongational flow. We validate the mechanistic model under elongational flow in front of experimental data using long fibers [17,18]. The estimations of the mechanistic model are in agreemen<sup>t</sup> with the experimental results. By exploiting the mechanistic model, we find that the fiber orientation evolution under elongational flow is independent of the fiber length, the fiber volume content, and the elongational rate for short fibers. There is however a slight sensitivity to variations of the matrix polymer viscosity. In future work, it would be interesting to study the influence of fiber flexibility on the fiber orientation phenomenon, in particular for long fibers.

At the macro-scale, we introduce a novel flow-dependent fiber orientation model that is able to adjust the fiber orientation evolution as a function of the local flow type by using an objective scaling parameter: the Manas-Zloczower number. This is reached by defining flow specific retarding and anisotropic diffusion parameters. We implement the 3D flow-dependent fiber orientation model in Moldflow using a Solver API feature. The fiber orientation results from our flow-dependent fiber orientation model are compared to μCT scans in three different injection-molded parts. The novel model gives not only comparable, but in some cases, more accurate results than current existing models. Additionally, it is the only model, that provides good results in a plate and a complex part. This shows that the flow dependency provides a more general modeling approach in front of the existing macroscopic fiber orientation models. We believe that the global performance of the model can still increase by incorporating fiber orientation-viscosity coupling in the macroscopic simulation. In our flow-dependent model, the fiber orientation evolution speed scales linearly between shear and elongation flows. A future enhancement could be the use of a different scaling approach and the incorporation of rotational flows. This novel multi-scale simulation approach consisting of the mechanistic model and the flow-dependent macro-model is significantly faster when compared to workflows with experimental parameter identification.
