Trapezoid-based Morphing Origami: Theory and Experiment

Origami sheets provide a robust platform for the design of morphable structures whereby the geometry of their underlying crease pattern dictates their capabilities for shape change. While various algorithms exist to determine a crease pattern that fits a target shape, there is no unified framework that classifies origami tessellations based on their large-scale elastic response. In this talk, I expand upon recent work that identified parallelogram-based origami sheets as such a class, characterized by a special relationship between in-plane strain and out-of-plane curvature, to include more generic trapezoidal faces. In addition to capturing the rigid folding motions of a recently-identified family of axisymmetric origami crease patterns, I discuss theoretical and experimental results that enable the characterization of low-energy modes via effective elastic moduli that change nonlinearly as the sheet rigidly folds. This enables us to classify trapezoid-based tessellations based on the relationship between their small scale (intracellular) architecture and their large-scale (intercellular) deformations, thereby aiding the design of morphing origami metamaterials.