Size-dependent properties of Miura-ori tessellations

We investigate the size-dependent behavior of Miura-ori-based origami tessellations by changing the number of origami unit cells. For large tessellations, the Miura-ori sheet generally exhibits a negative in-plane Poisson's ratio, whereas if the size of the Miura-ori tessellations becomes small, the transition between positive and negative Poisson's ratio emerges in the middle of the folding process. Here, we show that such a transitioning point, i.e., zero Poisson's ratio, yields a kinematic locking state. We also experimentally demonstrate the tunable locking behavior altered by tessellation sizes. Extending the analysis to three-dimensional origami tessellations, we find that the direction of kinematic locking changes depending on the tessellation size. Varying tessellation size thus enables control over both the onset and the direction of locking in origami metamaterials.