FEM
Variational Methods for Complex Phenomena in Engineering Structures and Materials
Funding period: 2020-2023
Description: Nonlinear bending theories for thin elastic objects have recently attracted considerable attention within mathematical research. One reason for this is the unresolved mathematical issues arising when allowing for large deformations and self-avoidance. The underlying theory is a higher regularity theory, where Geometric Measure Theory (GMT) and the rigorous justification of Kirchhoff’s bending theory have generated interest. This project aims to advance knowledge in this area, focusing on the interaction of curved rod-like objects with shells, and investigates the stability of different numerical methods for this problem.
FEM
Variational Methods for PDEs
Funding period: 2020-2024
Description: Programmatic advances in the precise modeling of elastic materials whose shape can be controlled via external stimuli have created new opportunities for engineering applications. This project focuses on the bending behavior of nematic liquid crystal elastomers, addressing the mathematical challenges related to the design of optimal material configurations, their stability, and robustness under different physical conditions. Our approach integrates variational methods with nonlinear elasticity theory, providing a comprehensive analysis of these materials.
FEM
Non-Smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization
Funding period: 2020-2023
Description: Designing and analyzing numerical methods for shape optimization problems typically requires the handling of non-smooth shapes. This project aims to provide efficient approximation schemes for non-smooth convex shapes with applications in optimal insulation, minimal resistance, and other phenomena. The research explores variational techniques combined with geometric analysis to achieve desired outcomes efficiently.
FEM
Variational Methods for Stochastic PDEs
Funding period: 2018-2021
Description: Spaces of functions of bounded variation provide an attractive framework to describe material interfaces and discontinuities. This project focuses on developing and analyzing efficient numerical schemes for approximating such functions. The reliability and stability of these schemes are essential for predicting material behaviors, especially in cases involving fracture and phase transitions.