On the Averaging and Closure of Fiber Orientation Tensors in Virtual Process Chains

• DOI: 10.1007/s10659-024-10050-3
• Publication Date: 2024-02-05T13:02:21Z
• Authors: Constantin Krauß; Julian Karl Bauer; Johannes Mitsch; Thomas Böhlke; Luise Kärger
• Keywords: Closure (psychology); Virtual work; Homogenization

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