Buckling of ultrastretchable kirigami metastructures for mechanical programmability and energy harvesting

Metastructures based on kirigami (the Japanese art of paper folding and cutting) have great potential for applications in stretchable electronics, bioprobes, and controllable optical and thermal devices. However, a theoretical framework for understanding the physics of their buckling behavior and to facilitate the search for ultrahigh stretchability has yet to be developed. Here, we present such a framework based on an energy approach. Closed-form analytical solutions and scaling laws are obtained for some key mechanical quantities, including flexibility, normalized flexibility, critical buckling strain, maximum tensile strain, elastic stretchability, normalized stretchability, and out-of-plane stiffness. Both experiments and numerical calculations are performed to validate the accuracy and scalability of the theoretical model. Systematic analyses of key mechanical quantities reveal how it is possible to bridge the gap between kirigami design by experience and by mechanically guided design, as well as how various dimensionless geometric parameters can be used to regulate buckling responses. Illustrative applications show that the ability to predict and tune the mechanical programmability of the proposed theoretical framework enables stable electromechanical conversion and programmable electromechanical kirigami with domino-like buckling. This work provides a foundation for further research and can also aid in the design of kirigami for use in programmable metastructures and metamaterials and energy harvesting. (C) 2021 Elsevier Ltd. All rights reserved.