Geometry and materials: rigidity, flexibility and scaling in some problems from materials science (B03)

• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 539309657

The objective of this project is to investigate prototypical models in shape-memory alloys which display a dichotomy between rigidity and flexibility within the geometrically nonlinear theory of elasticity. We seek to identify critical regularity thresholds in this transition by studying scaling laws in the singular perturbation parameter for models involving an elastic and a surface energy contribution. To this end, we adopt a geometric perspective and explore quantitative rigidity results arising from the multi-well nature of the Cauchy-Green tensors. A particular emphasis will be on the investigation of the highly nonlinear compatibility conditions.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1720: Analysis of criticality: from complex phenomena to models and estimates
• Applicant Institution: Rheinische Friedrich-Wilhelms-Universität Bonn
• Project Heads: Professor Dr. Stefan Müller, since 7/2025; Professorin Dr. Angkana Rüland, since 7/2025