Session: 13-13-01: Functional Origami and Kirigami-inspired Structures and Materials

Paper Number: 172855

Rapid Kirigami Simulation Using the Bar & Hinge Approach 

Kirigami is the art of cutting and folding sheets. It enables unique characteristics such as shape morphing, stretchability, and adaptability, with applications in deployable structures, building facades, flexible electronics, soft robotics, biomedical devices and more. The mechanical analysis of these structures is primarily performed using Finite Element (FE) Methods, specifically through the use of shell elements. Additionally, some mechanics-based simplified analytical models have been developed to simulate the kinematics of specific kirigami designs. However, FE models are computationally expensive for kirigami simulations, and the existing analytical models are applicable only to very specific tasks or particular kirigami geometries. To this end, we propose a generalized reduced-order model for the rapid analysis of arbitrary kirigami structures based on the bar-and-hinge approach. The bar-and-hinge model is a simplified structural mechanics-based analytical method that captures the deformations and internal forces of thin sheet structures. Previously, this approach has been used to study the kinematic, mechanical, and multi-physical properties of various origami-inspired designs. In this work, we extend the method to simulate a wide range of kirigami configurations. This approach efficiently and effectively captures the two key deformation behaviors in kirigami sheets—namely, stretching and bending. At its core, this method represents the entire sheet surface through a connection of bars and nodes by utilizing two distinct types of elements: a three-dimensional truss bar, which only carries loads along its axis, and a bending hinge, which acts analogously to a rotational spring wrapped around the bar. We introduce a meshing scheme that discretizes the geometry of arbitrary kirigami designs using bars and nodes, and conduct a sensitivity study to understand the impact of different discretization levels. We observe that the meshing scheme has some influence on stiffness; however, even with a coarser mesh, this model can effectively capture the kinematics and stiffness behavior.

The accuracy and robustness of the model are validated through detailed comparisons with FE simulations and with experimental results. We demonstrate these comparisons using both a single-cut kirigami design and more complex structures such as cellular kirigami configurations. Our results reveal more than an order of magnitude improvement in computational efficiency compared to standard FE simulations, while achieving close agreement in terms of deformation behavior and structural stiffness with both experimental results and simulations, as well as with designs reported in the literature. Finally, we highlight the utility of this model by addressing several complex problems involving arbitrary kirigami structures. These include optimizing cut shapes for kirigami-skinned crawlers to achieve desirable frictional properties, performing sequential analyses where loads are applied to already deformed systems, and demonstrating rapid kinematic simulations of randomly generated kirigami configurations. Overall, this modeling framework provides an efficient and generalizable tool for exploring proof-of-concept systems, conducting extensive parametric studies, and performing structural optimization of kirigami-based systems.

Presenting Author: Raj Pradip Khawale University of Michigan - Ann Arbor

Presenting Author Biography: After completing his bachelor’s degree in mechanical engineering from SRM University in 2017, he moved to U.S. to pursue his master’s in mechanical and aerospace engineering from University at Buffalo, New York. In 2019, he began his Ph.D. at the same institution before transferring to Clemson University, South Carolina, with his advisor, Dr. Rahul Rai. He successfully defended his Ph.D. in September 2024, focusing on lattice-based metamaterials and topology optimization. Since then, he has been working with Dr. Evgueni Filipov as a postdoctoral researcher at the University of Michigan–Ann Arbor, where he is developing computational frameworks for designing and analyzing deployable and reconfigurable structures inspired by origami and kirigami principles. His research interests include metastructure design, numerical simulations, data-driven design and manufacturing, and optimization. He has authored over eight peer-reviewed journal articles and a few conference papers.

Authors:

Raj Pradip Khawale University of Michigan - Ann Arbor
Elaheh Mehdizadeh University of Pittsburgh
John Brigham University of Pittsburgh
Dale Clifford California Polytechnic State University
Evgueni Filipov University of Michigan - Ann Arbor