Inverse Design of Kirigami through Shape Programming of Rotating Units

Kirigami metamaterials have enabled a plethora of morphing patterns across art and engineering. However, the inverse design of kirigami for complex shapes remains a puzzle that so far cannot be solved without relying on complex numerical methods. Here, we present a purely geometric design method to overcome the reliance on sophisticated numerical algorithms and showcase how to leverage it for three distinct types of morphing targets, i.e., the contracted shape, the deployed shape, and the internal trajectories of the rotating units in kirigami specimens. Our results unveil the fundamental relations between the kirigami deformation and the shape of its rotating units and enable us to establish the underpinning physics through theoretical investigations validated via numerical simulations. This work brings ground-rule insights into morphing matter with rotating units and offers an intuitive, firsthand geometric route for the swift design of complex kirigami.