Non-intrusive calculation of homogenized material properties for non-periodic and non-linear microstructures (DAAD scholarship)

Fiber-reinforced materials are important in industrial areas with high lightweight design requirements. However, the very heterogeneous structure of such materials makes their simulation cumbersome: Fully resolving microstructures is computationally expensive or even impossible, which is why homogenization approaches are used. These approaches replace heterogeneous materials by piecewise homogeneous ones. In applied mathematics, a different approach to homogenization has become popular in recent years: Instead of computing homogenized material properties, the basis functions of a finite element method are suitably adjusted to better fit to the microstructure. The advantage of such methods is that they work under minimal assumptions on the microstructure. Their drawback is that they are intrusive: They change the basis functions, which makes the implementation of such strategies into available legacy code very complicated. In this project, we will start from mathematically justified intrusive strategies and adjust them suitably to obtain a non-intrusive method that shall then be implemented into available code. Moreover, we will also cover non-linear material properties, where appropriate linearization strategies are required. ... mehrFinally, we will compare simulation results with practical experiments to assess the quality of the novel strategy. Here, the Institute for Applied Materials (IAM) will provide additional support.
- special requirements:
* solid background in applied mathematics
* knowledge of the finite element method and its theoretical investigation
* basic programming skills (in any programming language)
* interest in working in an interdisciplinary environment