An Applied PhD at the Fraunhofer ITWM

My name is Stephan Wackerle and I am a PhD student in a cooperation between the Department for Flow and Material Simulation (SMS) at the Fraunhofer Institute for industrial Mathematics (ITWM) and the Technical University of Kaiserslautern. This cooperation is a great opportunity to gain already whilst the PhD-studies a lot of insights into the work-flow between industrial partners and the scientific world.

The Fraunhofer Institute provides an ideal platform as an organization with many industrial partners and customers, which is why it is predestined for the applied part of the PhD-studies. While, on the other hand there is a remarkable benefit of the direct connection and access to the university for the theoretical part.

The subject of my personal PhD-research is directly induced by industrial projects, or actually a behavior we deal with every day: Under some conditions textiles may wrinkle. There are situations where this is wanted (curtains, dresses, …) and some where it is not (machine entries, seat upholstery, …). For me the second case is more interesting and the longterm goal is to minimize or even inhibit such a wrinkling behavior. However, because of its complexity this topic splits into two main parts: first the mathematical treatment of the textile on its own and secondly the minimization of the wrinkling amplitude.

The first part deals with the textile as a complex structure of single fibers, which can for example be knitted, crotched or woven. Imaginably, this ends up in vast amount of fibers and even more conditions b
etween them (e.g. contact conditions). This makes every simulation prohibitively costly and honestly no one wants to deal with such complex problems. Additionally, this gives an unnecessary resolution of the textile. In other words: you may see some wrinkles of a large textile without seeing the single small fibers. So the way out of this dilemma is the technique of homogenization. By using the periodic pattern of a textile it is possible to derive a homogeneous plate with effective characteristics coming from the internal microscopic properties of the fibers, their structure and further conditions. Consequently, once the micro-structure is hidden in some attributes of a representative macroscopic model, the further work with the textile is tremendously simplified.

In particular, this is perfect for the second part of my research: the optimization of the wrinkling. But how to decide when wrinkles appear and how to inhibit them? The wrinkles are an effect of a plate under some specific forces applied to it. So we have to solve a partial differential equation (PDE) for the elasticity system for our representative plate. This computation results in some wrinkles, but everything leading to this behavior is hidden inside the PDE. Seeing that, it is clear that the method of choice is the optimization with PDE- constraints, which uses some objective function to optimize, in our case e.g. the wrinkling amplitude, subject to the response of the plate coming from step one. Of course this is additionally limited by the a priori chosen design space, which may for example require that the single fibers have an admissible cross-section, neither too small nor too big. In fact, this kind of optimization is similar to the usual one, but in the context of infinite dimensional spaces, where everything is a bit more involved but also more interesting.

For me this PhD in the cooperation is a great opportunity to see multiple aspects of the scientific work, and although a PhD may have some challenging times, I am happy and grateful to work here with a lot of colleagues and supervisors in a supportive and friendly atmosphere.

For more information please contact Stephan Wackerle (stephan.wackerle@itwm.fraunhofer.de)