Self-organized complex structures in nature, from hierarchical biopolymers to viral capsids and organisms, offer efficiency, adaptability, robustness, and multifunctionality. How are these structures assembled? Can we understand the fundamental principles behind their formation, and assemble similar structures in the lab using simple inorganic building blocks? What’s the purpose of these complex structures in nature, and can we utilize similar mechanisms to program new functions in metamaterials? In this talk, we will start from the perspective of geometric frustration, to explore answers to these questions. I will discuss our recent work on developing analytic theories based on crystal structures in non-Euclidean space for the self-assembly of nanoparticles into complex structures, mechanical properties of materials in which geometric frustration causes prestress, as well as our ongoing effort in designing topological mechanical metamaterials with and without geometric frustration.
