Mechanism-based 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. The term we use for such deformations with zero elastic energy is mechanisms. This talk 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. 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.

Pizza be served preceding the talk, starting at 12:15.