Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Kirigami engineering - Nanoscale structures exhibiting a range of controllable 3D configurations



Xu Zhang, Lior Medina, Haogang Cai, Vladimir Aksyuk, Horacio Espinosa, Omar D. Lopez


Kirigami structures provide a promising approach to transform flat films with patterns of cuts into 3D complex structures that are difficult to achieve by conventional fabrication approaches. This work demonstrates that by fine tuning the cutting geometry, distinctive out-of-plane modes can be designed, and that the intrinsic tensile stress of the structural films can be used to deploy the final 3D structures. These instability-induced out-of-plane configurations are separated by a sharp transition characterized by a critical geometric dimension of the structures. Such sharp transition in the design space is an intrinsic property of structures exhibiting buckling phenomena. The thickness dependence of the deployed kirigami structures is investigated and it is observed that their stability and deformed configurations are determined by the ratio between the membrane torsional hinges width and its thickness. Geometrically nonlinear finite element analysis (FEA) accurately predicts the out-of-plane modes measured experimentally, its transition as a function of cut geometry, as well as the stress- strain response of the different configurations. Our findings provide a new degree of freedom to deploy 3D configurations of micro and nanoscale buckling-induced Kirigami structures. The out-of-plane configurations, triggered by an instability, promise great utility in the creation of micro and nanoscale systems that can harness such structural behavior, such as optical scanning micromirrors, novel actuators, and nanorobotics. This is of particular significance as the Kirigami dimensions approach the sub-micrometer scale with thickness in the nanoscale, which would be challenging to achieve with conventional micro-electromechanical system (MEMS) technologies.
Advanced Materials


Kirigami, MEMS, NEMS


Zhang, X. , Medina, L. , Cai, H. , Aksyuk, V. , Espinosa, H. and Lopez, O. (2020), Kirigami engineering - Nanoscale structures exhibiting a range of controllable 3D configurations, Advanced Materials, [online],, (Accessed April 12, 2024)
Created December 22, 2020, Updated October 12, 2021