In the framework of the project "Fracture Control by Material Optimization" we are investigating mathematical models as well as numerical algorithms to optimize or control crack properties in heterogeneous materials. As control variables can serve, e.g., positions, orientations or shapes of fibers or inclusions in a matrix material. In this context, a big challenge is a lack of continuity, which can, for instance, arise from bifurcations in the crack paths. As a remedy, traditionally strong regularization techniques are applied for the state problem, by which the crack path is computed. Alternatively we suggest a robust optimization setting, in which, in the simplest case, an expected crack property is optimized. First studies have shown that by this the discontinuity issues can be overcome.
However using such robust models, a new challenge appears: in every iteration infinitely many state problems arise. To cope with this, stochastic optimization methods (similar to the stochastic gradient descent method) can be used. In the scope of the project, robust material optimization models in the context of fracture mechanics shall be studied. Moreover, efficient (stochastic) optimization concepts should be developed, which allow for an approximate solution of the optimization problems. Starting from cohesive models, in which the potential crack paths is prescribed, these approaches should be extended to a setting in which a free propagation of the crack path is possible.
The project is an opportunity for a person with strong skills in algorithmic optimization to contribute to a challenging and relevant field in applied mathematics and/or applied mechanics. By the DFG funded research training group FRASCAL (https://www.frascal.research.fau.eu/) the project is embedded in a peer group of young scientists. The candidate will be closely supervised.
The team at FAU.
Our team currently consists of 1 professor, 3 post docs, 8 PhD students with focus in both, applied mathematics as well as computational engineering. Our division has many interdisciplinary collaborations inside FAU and beyond.
What we expect:
• M.Sc. in mathematics or a related subject with strong mathematical orientation (e.g., applied mechanics, computational engineering)
• Requirement 1: Profound knowledge in optimization, numerics and/or analysis
• Requirement 2: Profound knowledge in numerics of partial differential equations or applied mechanics
• Desired: advanced programming skills in Matlab and/or any other scientific language
• Structured and independent working practice, good communication and English skills, ideally German skills
• Time frame: 01/01/2022
• Duration: 3 years
• Funding: Deutsche Forschungsgemeinschaft (DFG) via RTG 2423
The FAU is a member of "The Family in Higher Education Institutions" best practice club and aims to increase the number of women in scientific positions. Female candidates are therefore particularly encouraged to apply. In case of equal qualifications, candidates with disabilities will take precedence.
If you have further questions, you may contact us via email@example.com. Applications should be submitted via e-mail as a single pdf file to Prof. Michael Stingl (firstname.lastname@example.org) and must include:
- informative and concise letter of motivation
- short CV
- master degree including academic transcripts
- letter of recommendation
- statement of research interests