This paper revisits the topic of mean field homogenization for short fiber reinforced composite materials. A short glass fiber reinforced thermoplastic polyamide 6.6 with a fiber mass fraction of $35\%$ is used as an example material for which microstructural analyses and experimental tests were performed. We cover a set of common models: the Self-Consistent (SC), Mori-Tanaka (MT), Ponte Castañeda-Willis (PCW), Interaction Direct Derivative (IDD) and Two-Step (TS) schemes. We first recast them into a unified formulation that permits a thorough theoretical comparison, including the topics of loss of major symmetry as well as connections between the models. We are able to show that the MT, PCW and IDD schemes can be expressed in a surprisingly similar form. This extends to the equations for prediction of effective stiffness and compliance tensors as well as the strain and stress localization tensors. Secondly, we address the resolution of the material microstructure within mean field homogenization schemes, comparing classical and more recent and efficient methods. Last, we benchmark the different mean field schemes and modeling approaches, including comparisons to numerical homogenization by Fast Fourier Transformation (FFT) and experimental data from tensile tests. These show that the MT and TS schemes are both capable of accurately modeling the composite material for complex orientations and homogeneous fiber phases. For possibly inhomogeneous fiber phases only the TS scheme yields both accurate and physically reasonable results. Other models such as the IDD or PCW are of great theoretical importance, but cannot be generally applied for the given material class.

本文重新讨论了短纤维增强复合材料的平均场均化问题。短玻璃纤维增​​强热塑性聚酰胺 6.6，纤维质量分数为$35\%$用作示例材料，对其进行微观结构分析和实验测试。我们涵盖了一组常见模型：Self-Consistent (SC)、Mori-Tanaka (MT)、Ponte Castañeda-Willis (PCW)、交互直接导数 (IDD) 和两步 (TS) 方案。我们首先将它们重铸成一个统一的公式，允许进行彻底的理论比较，包括主要对称性丢失的主题以及模型之间的联系。我们能够证明 MT、PCW 和 IDD 方案可以以惊人的相似形式表达。这扩展到用于预测有效刚度和柔度张量以及应变和应力定位张量的方程。其次，我们解决了平均场均匀化方案中材料微观结构的分辨率，比较经典的和最近的有效方法。最后，我们对不同的平均场方案和建模方法进行了基准测试，包括通过快速傅立叶变换 (FFT) 和拉伸测试的实验数据与数值均匀化的比较。这些表明 MT 和 TS 方案都能够准确地模拟复合材料的复杂取向和均匀纤维相。对于可能不均匀的纤维相，只有 TS 方案才能产生准确且物理上合理的结果。IDD 或 PCW 等其他模型具有重要的理论意义，但不能普遍应用于给定的材料类别。包括与通过快速傅立叶变换 (FFT) 进行的数值均匀化和拉伸试验的实验数据的比较。这些表明 MT 和 TS 方案都能够准确地模拟复合材料的复杂取向和均匀纤维相。对于可能不均匀的纤维相，只有 TS 方案才能产生准确且物理上合理的结果。IDD 或 PCW 等其他模型具有重要的理论意义，但不能普遍应用于给定的材料类别。包括与通过快速傅立叶变换 (FFT) 进行的数值均匀化和拉伸试验的实验数据的比较。这些表明 MT 和 TS 方案都能够准确地模拟复合材料的复杂取向和均匀纤维相。对于可能不均匀的纤维相，只有 TS 方案才能产生准确且物理上合理的结果。IDD 或 PCW 等其他模型具有重要的理论意义，但不能普遍应用于给定的材料类别。