The effective viscosity of particle reinforced thermoplastic melt shows strongly anisotropic behavior and is also shear rate-dependent. The traditional homogenization method may face challenge due to extremely expensive computational cost, when the non-linear effective viscosities on all the directions of Particle Reinforced Thermoplastics (PRT) are demanded. This paper approaches this challenge with the FEM-Cluster based reduced order Analysis (FCA) method [1]. The governing equations are solved by minimizing a cluster-based dual formulation of the dissipating energy, where the cluster-wise Admissible Shear Stress (ASS) set is obtained by FCA together with a Spectrum Analysis Algorithm (SAA). In addition, considering the fact that there is a lack of effective method for determining the proper number of clusters, a cluster metric is developed, which relates the given number of clusters and the prediction accuracy of FCA method. This metric can be easily used in the offline stage to pre-estimate the applicability of the obtained clusters on the given loading conditions with a small amount of additional computation.

中文翻译：

---

用于预测颗粒增强热塑性熔体有效粘度的 FCA 方法和用于测量簇的度量


颗粒增强热塑性熔体的有效粘度表现出很强的各向异性行为，并且还与剪切速率有关。当需要颗粒增强热塑性塑料 （PRT） 所有方向的非线性有效粘度时，传统的均质化方法可能会因极其昂贵的计算成本而面临挑战。本文使用基于 FEM 集群的降阶分析 （FCA） 方法 [1] 来应对这一挑战。控制方程是通过最小化基于簇的耗散能量对偶公式来求解的，其中簇允许的剪切应力 （ASS） 集由 FCA 和频谱分析算法 （SAA） 获得。此外，考虑到缺乏确定适当聚类数的有效方法，开发了一个聚类度量，该度量将给定的聚类数与 FCA 方法的预测准确性相关联。此指标可以很容易地在离线阶段使用，通过少量的额外计算来预先估计获得的集群在给定加载条件下的适用性。