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。纤维取向动力学的真实数值模拟是实现有效复合材料性能的足够准确的预测的必要前提。该项目的主要重点是开发新的高效数值方法，用于直接计算方向分布函数，并生成高精度的参考解，用于基于重建技术的闭合近似验证。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，具体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-简化和GPU加速-ODF重建的最佳控制-实验设置和验证-对机械性能的影响将使用新的正性求解概率密度分布的传输方程-保留有限元方案，量身定制的交替方向方法，以及最先进的高性能计算技术。将尽可能利用自己以前就有关问题所作工作的结果。重建的概率密度函数的准确性将通过与福克-普朗克方程的高分辨率数值解的比较来量化。如果需要，将执行模型和/或目标泛函的调整以用于最优控制。在后续的实验研究中，取向分布函数的模拟结果将得到验证。为此，将使用注塑工艺开发和生成不同形状的样品。不同的形状引起确定的变化的流动条件。通过分析不同形状试件的纤维取向，可以验证各种边界条件下的模拟结果。将所生产试样的纤维取向与模拟取向分布函数进行比较。机械结构模拟将与数值计算的ODF和实验测量的纤维取向。比较它们将显示更精确的ODF对力学模拟的影响。还将通过适当的实验分析来评估机械模拟的增强预测质量。

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.