Virtual production of filaments and fleeces

For many years, the Fraunhofer ITWM has been working to virtualize the production of filaments and fleeces in cooperation with a broad spectrum of industrial clients. This application area, embedded in the field of fluid-structure interactions, offers a multitude of mathematical challenges, since the complexity of the processes renders them unamenable to standard simulation techniques. For numerous key aspects, the Fraunhofer ITWM has developed its own models and tools, so that, today, we can generate simulation-based solutions for our clients' process design and control problems. Here, new modeling approaches, such as turbulent aerodynamic drag models for filament dynamics and stochastic surrogate models for fleece formation, have opened up interesting subject areas for applied mathematics. The contribution in this chapter is based on the Cosserat theory and offers a coherent overview of the models, algorithms, and software building blocks involved. The current state of development is illustrated by means of industrial applications of the spunbond process and the rotational spinning of glass wool.