Forschungsprojekt ::

From auxetic composites to kirigami: A variational analysis of mechanical metamaterials

Projektbeschreibung

This research project serves as the starting point for establishing a lasting research collaboration between the applicant's group at KU and experts from Rutgers. The mathematical focus of this project is the development of innovative methods for the analysis of variational models of mechanical metamaterials – artificially fabricated materials exhibiting mechanical properties that do not occur naturally. Specifically, we analyze metamaterials with a shape-morphing ability that emerges from opening gaps in rotating microstructures. This can, for example, lead to an auxetic response, which means that stretching in one direction gives rise to an elongation in the direction orthogonal to the applied force. Shape-morphing materials have a variety of applications for our society, ranging from shock-absorbent shoes to self-expanding medical stents and soft robotic grippers and deployable space structures.
Combining both groups' complementary knowledge may lead to the solution of some open problems in their respective papers. By carefully adapting the panel deformation constructions in [ZNCTP22, ZNCTP23] and utilizing the PDE governing the macroscopic deformations of kirigami, the homogenization result in [DEK23] for high-contrast checkerboard-type composites could be generalized to include also non-affine macroscopic deformations in the limit model. On the other hand, the KU group's expertise in the calculus of variations can support a full homogenization result via Gamma-convergence for kirigami metamaterials, which is the next step in Tobasco's program.
This project is expected to develop a joint publication in a renowned peer-reviewed journal dedicated to applied analysis. This effort is designed not only to establish a foundation for an enduring interchange of expertise between our research teams but also to explore additional initiatives, including the pursuit of international research funding opportunities, e.g., through the Marie Skłodowska-Curie Actions.