Mechanics of Curved Crease Origami: One-Degree-of-Freedom Mechanisms, Distributed Actuation by Spontaneous Curvature, and Cross-Talk Between Multiple Folds

Origami morphing, obtained with patches of piecewise smooth isometries separated by straight fold lines, is an exquisite art that has already received considerable attention in the mathematics and mechanics literature. Curved fold lines, leading to curved creases and curved pleated structures, introduce the additional complexity of mechanical coupling between the folds. This coupling can be exploited to obtain morphing structures with more robust folding pathways. We discuss one-degree-of-freedom mechanisms and folds actuated by spontaneous curvature (as in the case of hygromorphic multilayered composites), com- paring the purely geometric approach to two approaches based on the mechanics of active shells and of active three-dimensional solids. Moreover, we discuss the cooperativity of mul- tiple folds and demonstrate the energetic advantage of synchronous folding over sequential folding.