Mechanics of Buckled Kirigami Membranes for Stretchable Interconnects in Island-Bridge Structures

Island-bridge structures incorporated with kirigami membranes emerge as a novel design strategy for flexible/stretchable electronics, taking advantages of large stretchability, high-surface filling ratio and low resistance. However, it is hard to determine the mechanical properties of this design due to its complex geometries and nonlinear deformation configuration, thereby limiting its further applications. In this paper, we present a model for the postbuckling behavior of kirigami membranes through a combination of theoretical modeling, finite element analysis, and experiments. Scaling laws for elastic stretchability are developed, showing good agreement with numerical results and experimental images. Investigations on the critical height of post array are conducted to ensure the boundary condition of the kirigami membranes in the analytical model. These results can serve as design guidelines for kirigami structures and facilitate their applications in flexible/stretchable electronics.