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

• Applicants: Professor Dr. Dmitri Kuzmin; Professor Dr.-Ing. Markus Stommel; Professor Dr. Stefan Turek
• Subject Area: Plastics Engineering ; Mathematics ; Fluid Mechanics
• Term: from 2018 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 401649630

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.

• DFG Programme: Research Grants