Collaborative Research: Topology of Shapes, Topology of Waves and Their Interplay in Metamaterials Optimization

The design of materials and structures has become increasingly dominated by the adoption of optimization methods, which allow maximizing certain measures of mechanical performance, such as stiffness and energy absorption. Optimization is crucial in engineering applications involving components that are expected to execute complex mechanical operations, such as aerospace systems, biomedical devices and soft robotics.

Together with the fabrication flexibility in additive manufacturing, optimization boosts the opportunities for design by tapping into a nearly unbounded design space. This award supports research with the goal to design structures that can be programmed to display variable levels of material softness and rigidity, allowing them to manage, intelligently, the loads applied by the outside environment.

The advances enabled by this study will affect many technological applications of industrial and societal interest, such as the design of tires space vehicles or operating in hazardous environments, protective equipment that can sustain impacts from projectiles, and soft robotic devices with sensing capabilities. The knowledge will enrich understanding of important concepts in mechanics and optimization, with educational impact on how these topics are taught in the classroom.

Topological metamaterials are systems whose functionalities are controlled and protected by the topology of their phonon bands. They display unconventional elasticity regimes characterized by robustness against defects, damage and randomness. This project is especially concerned with so-called topological polarization, a property of certain lattice materials that manifests as a dichotomy between edges, whereby one edge displays an excess of softness, promoting extreme localization of deformation, while the opposite edge behaves rigidly.

This property enables the design of materials with soft boundaries that can handle asperities and sharp loads, without compromising the global stiffness of the entire structure. The project will investigate polarization through the lens of optimization with a double objective: acquiring a deeper understanding of the mechanistic relations between the geometric features of the materials and the emergent polarization, and designing families of metamaterials with maximized and programmable polarization, beyond the canonical kagome paradigm.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.