The objective of this work is to develop and investigate interpolation methods for fourth-order fiber orientation tensors. The developed methods aim to minimize information loss during mapping in the virtual manufacturing process for fiber-reinforced composites. The strategy of decomposing features that describe tensor shape and orientation, followed by separate interpolation, has been found to be a suitable approach for interpolating second-order fiber orientation tensors. Thus, in this work, decomposition-based approaches are also applied to fourth-order fiber orientation tensors. The decomposition of orthotropic fourth-order tensors into shape- and orientation-describing features with respect to three-dimensional space is presented. Various proposals for shape interpolation are described and evaluated. The developed interpolation methods are then applied to the numerical solution of a continuous problem from fluid mechanics. The continuous solution is used to generate data for the associated discrete problem and to evaluate the interpolation results of the different methods. The evaluation results demonstrate that the proposed interpolation methods are clearly superior to the conventional interpolation methods. Separating shape- and orientation-describing features with respect to three-dimensional space also proves to be useful for fourth-order tensors. The developed methods can significantly reduce the loss of information during mapping in virtual manufacturing process chains.

中文翻译：

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虚拟复合材料制造背景下正交各向异性四阶纤维取向张量的插值方法


这项工作的目的是开发和研究四阶纤维取向张量的插值方法。所开发的方法旨在最大限度地减少纤维增强复合材料虚拟制造过程中映射过程中的信息丢失。分解描述张量形状和方向的特征，然后进行单独插值的策略已被发现是插值二阶纤维方向张量的合适方法。因此，在这项工作中，基于分解的方法也应用于四阶纤维取向张量。提出了将正交各向异性四阶张量分解为三维空间的形状和方向描述特征。描述和评估了形状插值的各种建议。然后将开发的插值方法应用于流体力学连续问题的数值求解。连续解用于生成相关离散问题的数据并评估不同方法的插值结果。评估结果表明，所提出的插值方法明显优于传统的插值方法。事实证明，相对于三维空间分离形状和方向描述特征对于四阶张量也很有用。所开发的方法可以显着减少虚拟制造流程链中映射过程中的信息丢失。