The commonly used flow models for Fiber Reinforced Polymers (FRPs) often neglect the flow-induced anisotropy of the suspension, but with increasing fiber volume fraction, this plays an important role. There exist already some models which count on this effect. They are, however, phenomenological and need a fitted model parameter. In this paper, a micromechanically-based constitutive law is proposed which considers the flow-induced anisotropic viscosity of the fiber suspension. The introduced viscosity tensor can handle arbitrary anisotropy of the fluid-fiber suspension which depends on the actual fiber orientation distribution. Assuming incompressible material behaviour, a homogenization method for unidirectional structures in contribution with orientation averaging is used to determine the effective viscosity tensor. The motion of rigid ellipsoidal fibers induced by the flow of the matrix material is described based on Jeffery’s equation. The reorientation of the fibers is modeled in two ways: by describing them with fiber orientation vectors, and by fiber orientation tensors. A numerical implementation of the introduced model is applied to representative flow modes. The predicted effective stress values depending on the actual fiber orientation distribution through the anisotropic viscosity are analyzed in transient and stationary flow cases. In the case of the assumed incompressibility, they show similar effective viscous material behaviour as the results obtained by the use of the Dinh-Armstrong constitutive law. The introduced model is a possible way to describe the flow-induced anisotropic viscosity of a fluid-fiber suspension based on the mean field theory.

中文翻译：

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短FRP中流动引起的各向异性粘度

常用的纤维增强聚合物（FRP）流动模型通常会忽略悬浮液的流动诱发各向异性，但是随着纤维体积分数的增加，这起着重要作用。已经存在一些依靠这种效果的模型。但是，它们是现象学的，需要拟合的模型参数。本文提出了一种基于微机械的本构定律，该定律考虑了纤维悬浮液的流动引起的各向异性粘度。引入的粘度张量可以处理取决于实际纤维取向分布的流体纤维悬浮液的任意各向异性。假设材料具有不可压缩的特性，则使用具有定向平均作用的单向结构的均质化方法来确定有效粘度张量。基于杰弗里方程描述了由基质材料的流动引起的刚性椭圆形纤维的运动。纤维的重新定向以两种方式建模：通过用纤维定向矢量描述纤维，以及通过纤维定向张量。引入的模型的数值实现被应用于代表性的流动模式。在瞬态和平稳流动情况下，将分析通过各向异性粘度实际取决于纤维取向分布的预测有效应力值。在假定不可压缩的情况下，它们显示出与使用Dinh-Armstrong本构定律获得的结果相似的有效粘性物质行为。