Design–material transition threshold of ribbon kirigami

Abstract

The ribbon kirigami pattern has garnered significant attention over the past decade because of its interesting geometric and mechanical properties such as extreme elongation and high ductility, making it a viable choice for various applications such as developing medical devices and flexible electronics. Despite the promising prospects of this type of morphing structure, its deformation mechanism and sensitivity to materials properties and geometric parameters have remainedlargely unexplored. Here we take a computational approach to studying the deformation process and ductility of a typical ribbon kirigami metastructure. To this end, the deformation process is divided into various stages. We demonstrate the existence of a certain threshold of the process at which the deformation behavior starts to be dominated by the properties of the constituent material, after the initial geometric-design-dominated stages. This turning point, called the design–material transition (DMT) threshold, determines a key limit in the deformation capacity of such metastructures for practical applications. Based on the introduced deformation mechanism, an elongation prediction model is derived for the metastructure, followed by conducting experiments to validate the accuracy of the model. Furthermore, a genetic algorithm and an interior-point method are utilized to develop an efficient algorithm for the optimization of the geometric parameters of the kirigami pattern. We anticipate that the findings of this study open a path to engineering functional kirigami patterns for the design and fabrication of highly ductile shape-shifting structures.