Abstract

Fiber orientation tensors (FOT) are widely used to approximate statistical orientation distributions of fibers within fiber-reinforced polymers. The design process of components made of such fiber-reinforced composites is usually accompanied by a virtual process chain. In this virtual process chain, process-induced FOT are computed in a flow simulation and transferred to the structural simulation. Within the structural simulation, effective macroscopic properties are identified based on the averaged information contained in the FOT. Solving the field equations in flow simulations as well as homogenization of effective stiffnesses necessitates the application of a closure scheme, computing higher-order statistical moments based on assumptions. Additionally, non-congruent spatial discretizations require an intermediate mapping operation. This mapping operation is required, if the discretization, i.e., mesh, of the flow simulation differs from the discretization of the structural simulation. The main objective of this work is to give an answer to the question: Does the sequence of closure and mapping influence the achieved results? It will turn out, that the order influences the result, raising the consecutive question: Which order is beneficial? Both questions are addressed by deriving a quantification of the closure-related uncertainty. The two possible sequences, mapping followed by closure and closure followed by mapping, yield strongly different results, with the magnitude of the deviation even exceeding the magnitude of a reference result. Graphical consideration reveals that for both transversely isotropic and planar FOT-input, invalid results occur if the mapping takes place prior to closure. This issue is retrieved by orientation averaging stiffness tensors. As a by-product, we explicitly define for the first time the admissible parameter space of orthotropic fourth-order fiber orientation tensors and define a distance measure in this parameter space.

中文翻译：

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虚拟工艺链中纤维取向张量的平均和闭合

摘要

纤维取向张量 (FOT) 广泛用于近似纤维增强聚合物内纤维的统计取向分布。由这种纤维增强复合材料制成的组件的设计过程通常伴随着虚拟过程链。在这个虚拟工艺链中，工艺引起的 FOT 在流动模拟中计算并转移到结构模拟中。在结构模拟中，根据 FOT 中包含的平均信息来识别有效的宏观属性。求解流动模拟中的场方程以及有效刚度的均质化需要应用闭合方案，根据假设计算高阶统计矩。此外，非全等空间离散化需要中间映射操作。如果流动模拟的离散化（即网格）与结构模拟的离散化不同，则需要此映射操作。这项工作的主要目的是回答以下问题：闭合和映射的顺序是否会影响所取得的结果？事实证明，顺序会影响结果，从而提出连续的问题：哪种顺序是有利的？这两个问题都可以通过对封闭相关的不确定性进行量化来解决。映射后闭合和闭合后映射这两种可能的序列会产生截然不同的结果，偏差的幅度甚至超过参考结果的幅度。图形考虑表明，对于横向各向同性和平面 FOT 输入，如果映射发生在闭合之前，则会出现无效结果。这个问题是通过方向平均刚度张量来检索的。作为副产品，我们首次明确定义了正交各向异性四阶纤维取向张量的可接受参数空间，并在该参数空间中定义了距离度量。