Pop-up kirigami for stiff, dome-like structures

Abstract

In architecture and engineering, surfaces with positive Gaussian curvature such as domes are used for their high stiffness-to-weight ratios and efficiency in enclosing a volume. These curved shapes are difficult to create due to time-consuming or scale-limited processes. In recent years, origami and kirigami have risen as viable routes for the rapid fabrication of complex surfaces from flat sheets; however, these methods typically lead to systems that are overly flexible due to their high number of degrees of freedom. In this paper, we present a design for a pop-up kirigami system that achieves symmetric, positive Gaussian curvature by taking advantage of an internal infinitesimal mechanism. The system is fabricated from flat sheets using a hexagonal pattern, and the sheets remain flat locally as the system deforms into a dome-like shape. We investigate the internal mechanism and deformation modes of the system, revealing the flexible mode that creates dome-like curvature. We discuss geometric variations of the system and illustrate the possible shapes that result from changing the initial pattern parameters. Finally, we demonstrate the high stiffness of the system that arises from restricting its one flexible mode in its final, dome-like shape. The proposed pop-up kirigami system offers a method for fabricating dome-like surfaces with potential applications as deployable enclosures, concave reflectors, and more.