Collaborative Research: Mechanics of Optimal Biomimetic Torene Plates and Shells with Ultra-high Genus

Plates and shells have been used in diverse fields such as civil, mechanical, aeronautical, and marine engineering. A hallmark feature of these structures is their ability to support large loads despite their thin architecture. One such shell structure, responsible for guarding the genome inside our cells, is the nuclear envelope (i.e., the boundary of the nucleus). This structure has a unique geometry comprised of two concentric hollow spherical shells fused at thousands of sites with torus-shaped holes, and exhibits one order of magnitude amplification in flexural stiffness. Inspired by this finding, this study investigates a new class of optimal biomimetic shell structures, termed torenes, comprising concentric shell layers fused with torus-shaped holes. The torene architecture could enable new designs in aircrafts, submarines, and rockets to achieve high resilience in countering extreme natural forces. The discovered principles can guide the design of lightweight prosthetics, and protective gear for defense personnel and athletes to counter high impact loads. The research findings will be disseminated by hands-on pedagogical demonstrations, scientoons (science-based cartoons), virtual mechanics labs, journal publications and guest lectures for high school students. Poised at the interface of mechanics, geometry, and optimization, the research will investigate the mechanical properties and failure mechanisms of plate and shell structures with ultra-high genus. The study will perform finite element analyses to investigate force-deformation response and stability of torene structures under in-plane and out-of-plane loadings. This information will be used to construct proper objective functions and constraints to perform topology optimization of multilayer plates and shells. In particular, numerical optimization will be used to identify topologies that maximize performance of torene structures under different external loads and functional requirements. The study will apply the discovered geometric principles to design and experimentally test 3D torene architectures derived from 2D materials for achieving ultra-flexural stiffness. Overall, the work will disentangle the roles of differential geometry and associated geometric parameters in modulating the strength and stability of a new class of topological structures. This approach allows an investigation of structures at different length scales leading to the determination of scaling laws and scaling invariance. 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.