Coupled Simulation of Flow-Induced Viscous and Elastic Anisotropy of Short-Fiber Reinforced Composites

The present work discusses the impact of the back coupling of the fiber orientation distribution on the base flow and on the fiber orientation itself during mold filling simulations. Flows through a channel and over a backward-facing step are investigated as representative abstracted real part geometries. Different closure approximations are considered for modeling the flow induced evolution of anisotropy. Results corresponding to the decoupled approach, in which the effect of fibers on local fluid properties is neglected, build the basis of comparison. The modeling is limited to a laminar, incompressible and isothermal flow of a fiber suspension consisting of rigid short fibers embedded in an isotropic Newtonian matrix fluid. A linear, anisotropic constitutive law is used in combination with a uniform fiber volume fraction of $10\,\%$ and an aspect ratio of $10$. To evaluate the impact of back coupling and of different closure methods in view of the solid the resulting anisotropic elastic properties are investigated based on the Mori-Tanaka method combined with an orientation average scheme. Regarding the possible range of the diagonal components of the orientation tensors the pointwise difference in fiber orientation between the decoupled and the coupled approach is found to be $\pm 10\,\%$ in the channel and $\pm 50\,\%$ in the backward-facing step, respectively. ... mehrThe viscosity and the elasticity tensor show both significant flow induced anisotropies as well as a strong dependence on closure and coupling.