Kirigami surfaces: programmable mechanical response via hierarchical design*

Kirigami - the ancient Japanese art of cutting paper - has recently inspired the design of highly stretchable and morphable mechanical metamaterials that can be easily realized by embedding an array of cuts into a thin sheet. An attractive feature of these systems is that they are manufactured as a simple flat surface with cuts and then exploit elastic instabilities to transform into complex three-dimensional configurations. In this study, we focus on a thin elastic sheet perforated with a hierarchical pattern of cuts and demonstrate that the hierarchy significantly enhances the programmability of the system. In particular, we show that, by tuning the geometric parameters of this hierarchy, not only a variety of different buckling-induced 3D deformation patterns can be triggered, but also the stress-strain response of the surface can be effectively programmed. Finally, we show that when multiple hierarchical surfaces of various geometric patterns are brought together to create one combined heterogenous surface, the mechanical response can be further tuned and complex stress-strain curves can be achieved.