Geometric Mechanics of Origami Patterns Exhibiting Poisson's Ratio Switch by Breaking Mountain and Valley Assignment

Exploring the configurational space of specific origami patterns [e.g., Miura-ori (flat surface with parallelogram crease patterns), eggbox] has led to notable advances in science and technology. To augment the origami design space, we present a pattern, named "Morph," which combines the features of its parent patterns. We introduce a four-vertex origami cell that morphs continuously between a Miura mode and an eggbox mode, forming an homotopy class of configurations. This is achieved by changing the mountain and valley assignment of one of the creases, leading to a smooth switch through a wide range of negative and positive Poisson's ratios. We present elegant analytical expressions of Poisson's ratios for both in-plane stretching and out-of-plane bending and find that they are equal in magnitude and opposite in sign. Further, we show that by combining compatible unit cells in each of the aforementioned modes through kinematic bifurcation, we can create hybrid origami patterns that display unique properties, such as topological mode locking and tunable switching of Poisson's ratio.