The Kagome lattice as a mechanism-based mechanical metamaterial

Data Science Seminar

Xuenan Li (Columbia University)

Abstract

Mechanism-based mechanical metamaterials are synthetic materials that exhibit microscale buckling in response to mechanical deformation. These artificial materials are like elastic composites, but more degenerate, since they can deform with zero elastic energy. We call such deformations with zero elastic energy mechanisms. My research focuses mainly on a rich example, the Kagome lattice metamaterial. This particular material has a huge variety of mechanisms, which might seem incompatible with having a meaningful macroscopic energy at first sight. In this defense, I will discuss the large-scale behavior of the Kagome lattice metamaterial, including the existence of a well-defined effective energy and estimates for it. Our macroscopic theory reveals that compressive conformal maps are the only deformations that achieve zero effective energy. If time permits, I will also discuss the relationship between Guest-Hutchinson modes and periodic mechanisms in lattice systems.