Research projects at Saarland University

Towards uncertainty quantification for PDEs on networks

Duration: TBD–TBD
Funding scheme: Research Grants Program (Sachbeihilfe)
Funder: German Research Foundation
Budget: 245,708 €
My role: Principal investigator
Predecessor: Uncertainty quantification for PDEs on hypergraphs

3D printing is becoming ubiquitous in engineering and science. One of the main reasons for such success is its ability to create small structures not producible in any other known way. Typical examples include lightweight but strong materials (resembling, e.g., honeycombs) and artificial tissues. Such materials need to provide specific properties, while production is subject to uncertainties in the printing process. This project grows out of the need for mathematical algorithms to find optimal structures that retain their outstanding properties even in the presence of small errors. Robustness is vital for lightweight materials used to build lighter cars, planes, and rockets that save fuel. Similarly, 3D-printed artificial tissue has to mimic the real human tissue of fire victims to a high degree.

Compared to the most efficient existing approaches, the methodology of this project reduces the cost of an optimization-based product design cycle by orders of magnitude.

The picture shows micro-fiber scaffolds that are one artificial tissue component. It is taken from Mechanical behavior of a soft hydrogel reinforced with three-dimensional printed microfibre scaffolds by Miguel Castilho et al., licensed under CC BY 4.0.