Shape programming by modulating actuation using zigzag patterns

Zigzags structures can be found in a wide variety of fields. For instance, the future leaves of hornbeam are folded in the buds into zigzagging features that deploy as the leaves grow. This natural example has been the source of inspiration to develop origami designs. Here, we present a novel strategy where inextensible thin patches are sealed along zigzag paths to generate complex shape transformation under applied pressure.
We investigate the change in metrics induced by the inflation of these paths and the consequent transformation of the initially flat patches into 3D structures. In particular, we studied in detail the case of asymmetric zigzags, which leads to a rotation of the deformation tensor and widens the routes for reverse-engineering. We finally propose a theoretical model based of zigzagging paths to program the deployment of flat sheets into 3D shapes.