Injection Moulding Simulation and Efficient NumericalMethods for the Determinatin of Fiber Orientations by Direct Calculation or Reconstruction of the Orientation Distribution Function

纤维增强提供了短纤维增强热塑性塑料的高强度和刚度。真实的纤维取向动力学数值模拟是实现对有效复合材料性能足够准确预测的必要前提。该项目的主要重点是开发新的有效的数值方法，用于直接计算方向分布函数和生成高度精确的参考解，以验证基于重建技术的闭包近似。所提出的取向分布函数的计算和重构方法将显著提高短纤维增强复合材料力学模拟数值模型的精度。指定的目标将通过以下工作包实现：- Fokker-Plank方程的物理兼容数值方法-并行化和GPU加速- ODF重建的最优控制-实验设置和验证-对机械性能的影响-概率密度分布的传输方程将使用新颖的保正有限元方案，定制的交替方向方法，以及最先进的高性能计算技术。我们将最大限度地利用自己以前在有关问题上的工作成果。重建概率密度函数的精度将通过与福克-普朗克方程的高分辨率数值解的比较来量化。如有必要，将对模型和/或目标函数进行调整，以达到最优控制。在后续的研究中，将通过实验研究来验证取向分布函数的仿真结果。为此，将使用注射成型工艺开发和生成不同形状的试样。不同的形状产生了不同的流动条件。通过分析不同形状试样的纤维取向，可以在更大范围的边界条件下验证模拟结果。制作的样品的纤维取向将与模拟的取向分布函数进行比较。利用数值计算的ODF和实验测量的纤维取向进行机械结构模拟。通过比较，可以看出更精确的ODF对力学模拟的影响。力学模拟预报质量的提高也将通过适当的实验分析来评价。

Fiber reinforcement provides the high strength and stiffness of short fiber reinforced thermoplastics. Realistic numerical modeling of the fiber orientation dynamics is an essential prerequisite for achieving a sufficiently accurate prediction of the effective composite properties. The main focus of this project is on the development of new efficient numerical methods for direct calculation of orientation distribution functions and generation of highly accurate reference solutions for validation of closure approximations based on reconstruction techniques. The proposed approaches to calculation and reconstruction of orientation distribution functions will significantly improve the accuracy of numerical models for mechanical simulation of short fiber reinforced composites.The specified goals will be achieved by following work packages:- Physics-compatible numerical methods for the Fokker-Plank equation- Parallelization and GPU acceleration - Optimal control for reconstruction of ODF - Experimental set-up and validation- Effect on mechanical propertiesTransport equations for the probability density distribution will be solved using novel positivity-preserving finite element schemes, tailor-made alternating direction methods, and state-of-the-art high-performance computing techniques. The results of previous own work on related problems will be utilized to the greatest extent possible. The accuracy of reconstructed probability density functions will be quantified by comparisons to high-resolution numerical solutions of the Fokker-Planck equation. Adjustments of the model and/or of the objective functional for the optimal control will be performed if necessary. In the sequel, simulation results for orientation distribution functions will be validated by experimental studies. To that end, specimen of different shapes will be developed and generated using the injection molding process. The different shapes induce defined-varying flow conditions. Analyzing the fiber orientation of the specimens with different shapes makes it possible to validate the simulation results for a wide range of boundary conditions. The fiber orientation of the produced specimens will be compared to the simulated orientation distribution functions. Mechanical structure simulations will be performed with the numerically calculated ODF and the experimentally measured fiber orientation. Comparing them will show the effect of the more accurate ODF on the mechanical simulations. The enhanced forecast quality of mechanical simulations will also be evaluated by appropriate experimental analysis.