Coupled Simulation of Flow-Induced Viscous and Elastic Anisotropy of Short-Fiber Reinforced Composites (Version 2)

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. 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 suspended 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 manufactured solid composite the resulting anisotropic elastic properties are investigated based on the Mori-Tanaka method combined with an orientation average scheme. Relative to the range $[0,1]$ the pointwise difference in fiber orientation between the decoupled and the coupled approach is found to be $\pm 10\,\%$ in the channel and $\pm 30\,\%$ in the backward-facing step, respectively. The viscosity and the elasticity tensor show both significant flow induced anisotropies as well as a strong dependence on closure and coupling.

本研究探讨了注塑成型模拟（mold filling simulations）过程中，纤维取向分布（fiber orientation distribution）的反向耦合（back coupling）对基流（base flow）以及纤维自身取向的影响。
研究涵盖槽道流动（channel flow）与后台阶流动（backward-facing step）两类工况。针对流动诱导的各向异性演化建模，本文采用了多种不同的封闭近似（closure approximations）方案。以忽略纤维对局部流体物性影响的解耦方法（decoupled approach）作为对比基准。
本建模仅限定于由刚性短纤维（rigid short fibers）悬浮于各向同性牛顿基液（isotropic Newtonian matrix fluid）中形成的纤维悬浮液（fiber suspension）的层流、不可压缩、等温流动场景，采用线性各向异性本构关系（linear anisotropic constitutive law）进行建模，纤维体积分数（fiber volume fraction）固定为10%，长径比（aspect ratio）为10。
为评估反向耦合与不同封闭近似方法对最终制备固态复合材料的影响，本文结合莫里-田中方法（Mori-Tanaka method）与取向平均方案（orientation average scheme），对所得的各向异性弹性物性展开了分析。相较于[0,1]区间，解耦方法与耦合方法在纤维取向上的逐点差异分别为：槽道流动中为±10%，后台阶流动中为±30%。黏度与弹性张量（elasticity tensor）均表现出显著的流动诱导各向异性，且对封闭近似与耦合方式存在较强的依赖性。