Invariant and smooth limit of discrete geometry folded from bistable origami leading to multistable metasurfaces.

ABSTRACT: Origami offers an avenue to program three-dimensional shapes via scale-independent and non-destructive fabrication. While such programming has focused on the geometry of a tessellation in a single transient state, here we provide a complete description of folding smooth saddle shapes from concentrically pleated squares. When the offset between square creases of the pattern is uniform, it is known as the pleated hyperbolic paraboloid (hypar) origami. Despite its popularity, much remains unknown about the mechanism that produces such aesthetic shapes. We show that the mathematical limit of the elegant shape folded from concentrically pleated squares, with either uniform or non-uniform (e.g. functionally graded, random) offsets, is invariantly a hyperbolic paraboloid. Using our theoretical mo

SUBMITTER: Liu K 

PROVIDER: S-EPMC6748981 | biostudies-literature | 2019 Sep

REPOSITORIES: biostudies-literature