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1. Kirigami‐Inspired Inflatables with Programmable Shapes

   https://doi.org/10.1002/adma.202001863  

   Jin, Lishuai; Forte, Antonio_Elia; Deng, Bolei; Rafsanjani, Ahmad; Bertoldi, Katia (July 2020, Advanced Materials)

   Abstract Kirigami, the Japanese art of paper cutting, has recently enabled the design of stretchable mechanical metamaterials that can be easily realized by embedding arrays of periodic cuts into an elastic sheet. Here, kirigami principles are exploited to design inflatables that can mimic target shapes upon pressurization. The system comprises a kirigami sheet embedded into an unstructured elastomeric membrane. First, it is shown that the inflated shape can be controlled by tuning the geometric parameters of the kirigami pattern. Then, by applying a simple optimization algorithm, the best parameters that enable the kirigami inflatables to transform into a family of target shapes at a given pressure are identified. Furthermore, thanks to the tessellated nature of the kirigami, it is shown that we can selectively manipulate the parameters of the single units to allow the reproduction of features at different scales and ultimately enable a more accurate mimicking of the target. 

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2. Transverse Wave Propagation Bandgap in a Buckled Kirigami Sheet

   https://doi.org/10.1115/SMASIS2021-68200  

   Khosravi, Hesameddin; Li, Suyi (September 2021, Proceedings of the ASME 2021 Conference on Smart Materials, Adaptive Structures and Intelligent Systems)

   This study examines the transverse elastic wave propagation bandgap in a buckled kirigami sheet. Kirigami — the ancient art of paper cutting — has become a design and fabrication framework for constructing metamaterials, robotics, and mechanical devices of vastly different sizes. For the first time, this study focuses on the wave propagation in a buckled kirigami sheet with uniformly distributed parallel cuts. When we apply an in-plane stretching force that exceeds a critical threshold, this kirigami sheet buckles and generates an out-of-plane, periodic deformation pattern that can change the propagation direction of passing waves. That is, waves entering the buckled Kirigami unit cells through its longitudinal direction can turn to the out-of-plane direction. As a result, the stretched kirigami sheet shows wave propagation band gaps in specific frequency ranges. This study formulates an analytical model to analyze the correlation between such propagation bandgap and the kirigami geometry. This model first simplifies the complex shape of buckled kirigami by introducing “virtual” folds and flat facets in between them. Then it incorporates the plane wave expansion method (PWE) to calculate the dispersion relationship, which shows that the periodic nature of the buckled kirigami sheet is sufficient to create Bragg scattering propagation bandgap. This study’s results could open up new dynamic functionalities of kirigami as a versatile and multi-functional structural system. 

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3. Kirigami enhances film adhesion

   https://doi.org/10.1039/c7sm02338c  

   Zhao, Ruike; Lin, Shaoting; Yuk, Hyunwoo; Zhao, Xuanhe (January 2018, Soft Matter)

   Structures of thin films bonded on substrates have been used in technologies as diverse as flexible electronics, soft robotics, bio-inspired adhesives, thermal-barrier coatings, medical bandages, wearable devices and living devices. The current paradigm for maintaining adhesion of films on substrates is to make the films thinner, and more compliant and adhesive, but these requirements can compromise the function or fabrication of film–substrate structures. For example, there are limits on how thin, compliant and adhesive epidermal electronic devices can be fabricated and still function reliably. Here we report a new paradigm that enhances adhesion of films on substrates via designing rational kirigami cuts in the films without changing the thickness, rigidity or adhesiveness of the films. We find that the effective enhancement of adhesion by kirigami is due to (i) the shear-lag effect of the film segments; (ii) partial debonding at the film segments’ edges; and (iii) compatibility of kirigami films with inhomogeneous deformation of substrates. While kirigami has been widely used to program thin sheets with desirable shapes and mechanical properties, fabricate electronics with enhanced stretchability and design the assembly of three-dimensional microstructures, this paper gives the first systematic study on kirigami enhancing film adhesion. We further demonstrate novel applications including a kirigami bandage, a kirigami heat pad and printed kirigami electronics. 

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4. Programmable active kirigami metasheets with more freedom of actuation

   https://doi.org/10.1073/pnas.1906435116  

   Tang, Yichao; Li, Yanbin; Hong, Yaoye; Yang, Shu; Yin, Jie (December 2019, Proceedings of the National Academy of Sciences)

   Kirigami (cutting and/or folding) offers a promising strategy to reconfigure metamaterials. Conventionally, kirigami metamaterials are often composed of passive cut unit cells to be reconfigured under mechanical forces. The constituent stimuli-responsive materials in active kirigami metamaterials instead will enable potential mechanical properties and functionality, arising from the active control of cut unit cells. However, the planar features of hinges in conventional kirigami structures significantly constrain the degrees of freedom (DOFs) in both deformation and actuation of the cut units. To release both constraints, here, we demonstrate a universal design of implementing folds to reconstruct sole-cuts–based metamaterials. We show that the supplemented folds not only enrich the structural reconfiguration beyond sole cuts but also enable more DOFs in actuating the kirigami metasheets into 3 dimensions (3D) in response to environmental temperature. Utilizing the multi-DOF in deformation of unit cells, we demonstrate that planar metasheets with the same cut design can self-fold into programmable 3D kirigami metastructures with distinct mechanical properties. Last, we demonstrate potential applications of programmable kirigami machines and easy-turning soft robots. 

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5. Cross-sections of doubly curved sheets as confined elastica

   https://doi.org/10.1073/pnas.2216786120  

   He, Mengfei; Démery, Vincent; Paulsen, Joseph D. (March 2023, Proceedings of the National Academy of Sciences)

   Although thin films are typically manufactured in planar sheets or rolls, they are often forced into three-dimensional (3D) shapes, producing a plethora of structures across multiple length scales. To understand this complex response, previous studies have either focused on the overall gross shape or the small-scale buckling that decorates it. A geometric model, which considers the sheet as inextensible yet free to compress, has been shown to capture the gross shape of the sheet. However, the precise meaning of such predictions, and how the gross shape constrains the fine features, remains unclear. Here, we study a thin-membraned balloon as a prototypical system that involves a doubly curved gross shape with large amplitude undulations. By probing its side profiles and horizontal cross-sections, we discover that the mean behavior of the film is the physical observable that is predicted by the geometric model, even when the buckled structures atop it are large. We then propose a minimal model for the horizontal cross-sections of the balloon, as independent elastic filaments subjected to an effective pinning potential around the mean shape. Despite the simplicity of our model, it reproduces a broad range of phenomena seen in the experiments, from how the morphology changes with pressure to the detailed shape of the wrinkles and folds. Our results establish a route to combine global and local features consistently over an enclosed surface, which could aid the design of inflatable structures, or provide insight into biological patterns. 

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