Shaping curved surfaces using origami.

In order to understand the full range of equilibrium shapes and mechanical response of origami-based metamaterials, one is led to take into account both the geometrical constraints induced by the crease network and the elasticity of the material. A model example for this is a shell formed by an accordion-like origami, made from a single elastic sheet decorated by a series of parallel creases, crossed by a central longitudinal crease. Surprisingly, while the imprinted crease network does not have a geodesic curvature, the emergent three-dimensional structure is characterized by an effective curvature along the central line. We craft these patterns and scan them using a structured-light 3D-scanner. Our study captures the exotic zoology of face deformations that appear due to kinematic constraints imposed by the crease network, ranging from simple bending to ribbon-like behavior, as confirmed by FEM simulations.