Space-time finite element methods for production engineering applications

  • Raum-Zeit-Finite-Elemente-Methoden für produktionstechnische Anwendungen

Karyofylli, Violeta; Behr, Marek (Thesis advisor); van Brummelen, Harald (Thesis advisor)

Aachen : RWTH Aachen University (2021)
Dissertation / PhD Thesis

Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2021

Abstract

Virtual product and process development using numerical simulations has evolved and found their way into the industry. In plastics processing and metal fabrication, simulation software delivers enormous benefits to all product development steps in terms of part precision, reliability of the process, costs, and time to market. Numerical computations are also frequently used to predict component properties and their mechanical behavior. Due to constant innovation in materials and processes, there is a high demand for simulation tools utilizing robust numerical techniques that also describe product behavior with improved accuracy. A precise prediction is necessary, especially for processes that only allow a narrow processing window to produce parts of good quality.In most cases, these manufacturing processes are described by complex time-dependent partial differential equations (PDEs). These PDEs are usually discretized in space through the Galerkin or Petrov-Galerkin finite element (FE) method. However, their discretization in time istypically carried out by an explicit or implicit finite difference (FD) scheme. This combination of discretization methods is more conventionally used and easy to implement. However, it does not exhibit the remarkable flexibility of the space-time (ST) FE method when dealing withtopological changes and varying resolution of complex domains both in space and time. This thesis aims to develop a novel discretization technique, which leads to higher simulation accuracy and lower calculation times while fully representing the given phenomena. This pioneering 4D finite element discretization approach is based on simplex space-time (SST)elements, which can deal with a varying refinement of intricate domains in space and time. As a consequence, the efficiency and accuracy of the simulations are increased. This new discretization technique is validated not only with simple benchmark cases from the literature, but also with real complex manufacturing processes, namely the filling stage during injection molding and the droplet formation and detachment during gas metal arc (GMA) welding. These two applications involve complicated multi-phase and phase-transition phenomena, where the evolving interfaces require high flexibility and resolution, both in space and time.Mold filling is an essential stage of injection molding and one of the most common manufacturing processes for producing thermoplastic parts in large quantities. Simulation of the injection molding process and prediction of defects are mandatory for improving product quality. We applied adaptive temporal refinement based on our novel SST discretization to this application for an efficient and accurate capturing of the melt position. The shear-thinning behavior of the melt is also investigated by implementing various material models (i.e., Carreau-WLF). The wetting contact lines are elucidated through the Navier-slip boundary. Finally, a contact model is developed, which sheds light on the hydrophilic and hydrophobic behavior of droplets.In GMA welding, droplets of molten metal detach from the electrode, driven by electromagnetic forces and heating, and impact a weld seam. It is a multi-physics problem and involves the interplay of the molten metal and the shielding gas. Hence, a phase-transition model isdeveloped for computing the melting of the metallic wire. For reducing the dimensionality and the complexity of the dynamics of the droplet formation and detachment during GMA welding, an axisymmetric flat space-time (FST) formulation for two-phase flows with phase transition is developed and validated with various test cases.

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