Rapid kirigami simulation using the bar & hinge approach

Abstract

Kirigami, the art of cutting sheets, offers unique characteristics such as shape morphing, stretchability, and adaptability, with applications in deployable and reconfigurable structures. While Finite Element (FE) approaches are widely used to analyze kirigami structures, they are computationally intensive and prone to convergence issues. On the other hand, existing simplified and theoretical models for evaluating kirigami are typically restricted to specific designs and analytical scenarios. This paper proposes a generalized, computationally efficient reduced-order model based on the bar and hinge approach for analyzing any kirigami system. The model represents the entire kirigami structure using truss bars, bending hinges, and torsional springs, capturing both the deformation and internal forces of the system. We derive stiffness expressions for kirigami structures that experience stretching and out-of-plane bending deformations, as well as for structures that experience only in-plane stretching and rotations. The accuracy and robustness of the model are validated through comparisons with FE analysis and experimental data on both single-cut kirigami designs and more complex designs with multiple cuts. Our results demonstrate less than 5% difference in deformation predictions and achieve at least a tenfold computational speedup compared to FE simulations. Additionally, we demonstrate the model's capabilities through simulating complex scenarios, including kirigami-skinned crawlers, high-throughput property-space exploration, and in-plane kirigami-inspired metamaterials. These examples demonstrate computational capabilities that enable large-deformation structural simulations and high-throughput design exploration beyond the practical limits of conventional FE methods.