Mathematical Sciences Department Analysis/PDE Seminar: Professor Xuenan Li, Columbia University

Title: Deformations in soft mechanical metamaterials: modeling, analysis, and applications

Abstract: Mechanical metamaterials are synthetic materials that exhibit microscale buckling in response to mechanical deformation. These artificial materials are like elastic composites but sometimes more degenerate since they can deform with almost zero elastic energy. We call such deformations with very small elastic energy mechanisms. In this talk, I will focus mainly on a rich example, the Kagome lattice metamaterial, which has many mechanisms that might seem incompatible with having a meaningful macroscopic energy at first sight. I will discuss our model of the Kagome lattice metamaterial, which allows us to obtain a well-defined effective energy, and further discuss the large-scale elastic behavior. Our macroscopic theory reveals that compressive conformal maps are the only deformations that achieve zero effective energy. If time permits, I will switch from the static point of view of these materials to a dynamic one and discuss how the slowly varying deformations can change wave propagation in these soft mechanical metamaterials.