An orientation corrected shaking method for the microstructure generation of short fiber-reinforced composites with almost planar fiber orientation

We present an algorithm for generating short fiber-reinforced microstructures with almost planar fiber orientation. The orientation corrected shaking (OCS) method achieves a high accuracy regarding the volume fraction, fiber length distribution and fiber orientation state. Additionally, the algorithm is capable of generating microstructures for industrial materials, e.g., for a PA66GF35 material with a volume fraction of 19.3% and an aspect ratio of 33. For typical manufacturing processes, short fiber-reinforced composites show a mainly planar fiber arrangement. Therefore, we extend the two-step shaking algorithm of Li et al. [J. Ind. Text. 51(1), pp. 506-530, 2022] for a user-selected rectangular size of the unit cell and periodic boundary conditions. Additionally, the hidden closure structure of the algorithm is uncovered and a precise realization of the fiber orientation state achieved. We examine the representative volume element size for the OCS method, observing representative errors below 2% even for unit cells with edge lengths smaller than the mean fiber length. Additionally, the influence of different closure approximations on the stiffness is investigated. When applied to an industrial PA66GF35 material with sandwich structure, the OCS method demonstrates differences below 2% and 9% for the computed directional Young's moduli E1 and E2 compared to experimental data.

Automated summary

We propose an algorithm, the orientation corrected shaking (OCS) method, for generating short fiber-reinforced microstructures with almost planar fiber orientation. The algorithm achieves high accuracy in terms of volume fraction, fiber length distribution, and fiber orientation state. It can also generate microstructures for industrial materials, such as a PA66GF35 material with a volume fraction of 19.3% and an aspect ratio of 33. We extend the two-step shaking algorithm for a user-selected rectangular size of the unit cell and periodic boundary conditions, and improve the precise realization of the fiber orientation state. The OCS method shows representative errors below 2% and 9% for computed directional Young's moduli E1 and E2, respectively, when applied to an industrial PA66GF35 material with a sandwich structure, compared to experimental data.