Engineering by Cuts: How Kirigami Principle Enables Unique Mechanical Properties and Functionalities

Adaptive hierarchical origami-based metastructures

Shape-morphing capabilities are crucial for enabling multifunctionality in both biological and artificial systems. Various strategies for shape morphing have been proposed for applications in metamaterials and robotics. However, few of these approaches have achieved the ability to seamlessly transform into a multitude of volumetric shapes post-fabrication using a relatively simple actuation and control mechanism. Taking inspiration from thick origami and hierarchies in nature, we present a hierarchical construction method based on polyhedrons to create an extensive library of compact origami metastructures. We show that a single hierarchical origami structure can autonomously adapt to over 103 versatile architectural configurations, achieved with the utilization of fewer than 3 actuation degrees of freedom and employing simple transition kinematics. We uncover the fundamental principles governing theses shape transformation through theoretical models. Furthermore, we also demonstrate the wide-ranging potential applications of these transformable hierarchical structures. These include their uses as untethered and autonomous robotic transformers capable of various gait-shifting and multidirectional locomotion, as well as rapidly self-deployable and self-reconfigurable architecture, exemplifying its scalability up to the meter scale. Lastly, we introduce the concept of multitask reconfigurable and deployable space robots and habitats, showcasing the adaptability and versatility of these metastructures.

Hybrid-Microstructure-Based Soft Network Materials with Independent Tunability of Mechanical Properties over Large Deformations

Introducing auxetic metamaterials into stretchable electronics shows promising prospects for enhancing the performance and innovating the functionalities of various devices, such as stretchable strain sensors. Nevertheless, most existing auxetics fail to meet the requirement of stretchable electronics, which typically include high mechanical flexibility and stable Poisson's ratio over large deformations. Moreover, despite being highly advantageous for application in diverse load-bearing conditions, achieving tunability of J-shaped stress-strain response independent of negative Poisson's ratio remains a significant challenge. This paper introduces a class of hybrid-microstructure-based soft network materials (HMSNMs) consisting of different types of microstructures along the loading and transverse directions. The J-shaped stress-strain curve and nonlinear Poisson's ratio for HMSNMs can be tuned independently of each other. The HMSNM provides much higher strength than the corresponding existing metamaterial while offering a nearly stable negative Poisson's ratio over large strains. Both mechanical properties under infinitesimal and large deformations can be well-tuned by geometric parameters. Fascinating functionalities such as shape programming and stress regulation are achieved by integrating a set of HMSNMs in series/parallel configurations. A stretchable LED-integrated display capable of displaying dynamic images without distortion under uniaxial stretching serves as a demonstrative application.

Engineering Kirigami Frameworks Toward Real-World Applications

The surge in advanced manufacturing techniques has led to a paradigm shift in the realm of material design from developing completely new chemistry to tailoring geometry within existing materials. Kirigami, evolved from a traditional cultural and artistic craft of cutting and folding, has emerged as a powerful framework that endows simple 2D sheets with unique mechanical, thermal, optical, and acoustic properties, as well as shape-shifting capabilities. Given its flexibility, versatility, and ease of fabrication, there are significant efforts in developing kirigami algorithms to create various architectured materials for a wide range of applications. This review summarizes the fundamental mechanisms that govern the transformation of kirigami structures and elucidates how these mechanisms contribute to their distinctive properties, including high stretchability and adaptability, tunable surface topography, programmable shape morphing, and characteristics of bistability and multistability. It then highlights several promising applications enabled by the unique kirigami designs and concludes with an outlook on the future challenges and perspectives of kirigami-inspired metamaterials toward real-world applications.

Highly stretchable graphene kirigami with tunable mechanical properties

In recent years, kirigami techniques have inspired the design of graphene-based nanodevices with exceptional stretchability and ductility. Based on an I-shaped cutting pattern, here we propose a graphene kirigami that exhibits remarkable stretchability and ductility in two independent planar directions along with negative Poisson's ratios. The deformation mechanism underlying the high stretchability of the structure is the flipping and rotation of its cutting ligaments during elongation. Molecular dynamics simulations show that the yield and fracture strains of graphene kirigami can be enhanced by factors of 6 and 10 in the two planar directions. In addition, the mechanical properties of the graphene kirigami can be tuned by altering the cutting geometric parameters as well as incorporating distinct cutting patterns in series. We develop a numerical algorithm to predict the stress-strain response of the series-connected graphene kirigami, and verify its accuracy using appropriate simulations. On this basis, the stress-strain response of the series-connected graphene kirigami can be tuned by altering its geometric parameters and the number of building blocks. This graphene kirigami could be applied to the design and development of next-generation flexible electronics such as stretchable electrodes and strain sensors.

Anisotropic Morphing in Bistable Kirigami through Symmetry Breaking and Geometric Frustration

Shape morphing in bistable kirigami enables remarkable functionalities appealing to a diverse range of applications across the spectrum of length scale. At the core of their shape shifting lies the architecture of their repeating unit, where highly deformable slits and quasi-rigid rotating units often exhibit multiple symmetries that confer isotropic deployment obeying uniform scaling transformation. In this work, symmetry breaking in bistable kirigami is investigated to access geometric frustration and anisotropic morphing, enabling arbitrarily scaled deployment in planar and spatial bistable domains. With an analysis on their symmetry properties complemented by a systematic investigation integrating semi-analytical derivations, numerical simulations, and experiments on elastic kirigami sheets, this work unveils the fundamental relations between slit symmetry, geometric frustration, and anisotropic bistable deployment. Furthermore, asymmetric kirigami units are leveraged in planar and flat-to-3D demonstrations to showcase the pivotal role of shear deformation in achieving target shapes and functions so far unattainable with uniformly stretchable kirigami. The insights provided in this work unveil the role of slit symmetry breaking in controlling the anisotropic bistable deployment of soft kirigami metamaterials, enriching the range of achievable functionalities for applications spanning deployable space structures, wearable technologies, and soft machines.

Physics-aware differentiable design of magnetically actuated kirigami for shape morphing

Shape morphing that transforms morphologies in response to stimuli is crucial for future multifunctional systems. While kirigami holds great promise in enhancing shape-morphing, existing designs primarily focus on kinematics and overlook the underlying physics. This study introduces a differentiable inverse design framework that considers the physical interplay between geometry, materials, and stimuli of active kirigami, made by soft material embedded with magnetic particles, to realize target shape-morphing upon magnetic excitation. We achieve this by combining differentiable kinematics and energy models into a constrained optimization, simultaneously designing the cuts and magnetization orientations to ensure kinematic and physical feasibility. Complex kirigami designs are obtained automatically with unparalleled efficiency, which can be remotely controlled to morph into intricate target shapes and even multiple states. The proposed framework can be extended to accommodate various active systems, bridging geometry and physics to push the frontiers in shape-morphing applications, like flexible electronics and minimally invasive surgery.

Manufacturing of stretchable substrate with biaxial strain control for highly-efficient stretchable solar cells and displays

There has been significant research focused on the development of stretchable materials that can provide a large area with minimal material usage for use in solar cells and displays. However, most materials exhibit perpendicular shrinkage when stretched, which is particularly problematic for polymer-based substrates commonly used in stretchable devices. To address this issue, biaxial strain-controlled substrates have been proposed as a solution to increase device efficiency and conserve material resources. In this study, we present the design and fabrication of a biaxial strain-controlled substrate with a re-entrant honeycomb structure and a negative Poisson's ratio. Using a precisely machined mold with a shape error of less than 0.15%, we successfully fabricated polydimethylsiloxane substrates with a 500 μm thick re-entrant honeycomb structure, resulting in a 19.1% reduction in perpendicular shrinkage. This improvement translates to a potential increase in device efficiency by 9.44% and an 8.60% reduction in material usage for substrate fabrication. We demonstrate that this design and manufacturing method can be applied to the fabrication of efficient stretchable devices, such as solar cells and displays.

Flexible and Stretchable Electrochemical Sensors for Biological Monitoring

The rise of flexible and stretchable electronics has revolutionized biosensor techniques for probing biological systems. Particularly, flexible and stretchable electrochemical sensors (FSECSs) enable the in situ quantification of numerous biochemical molecules in different biological entities owing to their exceptional sensitivity, fast response, and easy miniaturization. Over the past decade, the fabrication and application of FSECSs have significantly progressed. This review highlights key developments in electrode fabrication and FSECSs functionalization. It delves into the electrochemical sensing of various biomarkers, including metabolites, electrolytes, signaling molecules, and neurotransmitters from biological systems, encompassing the outer epidermis, tissues/organs in vitro and in vivo, and living cells. Finally, considering electrode preparation and biological applications, current challenges and future opportunities for FSECSs are discussed.

Effects of Slit Edge Notches on Mechanical Properties of 3D-Printed PA12 Nylon Kirigami Specimens

Kirigami structures, a Japanese paper-cutting art form, has been widely adopted in engineering design, including robotics, biomedicine, energy harvesting, and sensing. This study investigated the effects of slit edge notches on the mechanical properties, particularly the tensile stiffness, of 3D-printed PA12 nylon kirigami specimens. Thirty-five samples were designed with various notch sizes and shapes and printed using a commercial 3D printer with multi-jet fusion (MJF) technique. Finite element analysis (FEA) was employed to determine the mechanical properties of the samples computationally. The results showed that the stiffness of the kirigami samples is positively correlated with the number of edges in the notch shape and quadratically negatively correlated with the notch area of the samples. The mathematical relationship between the stretching tensile stiffness of the samples and their notch area was established and explained from an energy perspective. The relationship established in this study can help fine-tune the stiffness of kirigami-inspired structures without altering the primary parameters of kirigami samples. With the rapid fabrication method (e.g., 3D printing technique), the kirigami samples with suitable mechanical properties can be potentially applied to planar springs for hinge structures or energy-absorbing/harvesting structures. These findings will provide valuable insights into the development and optimization of kirigami-inspired structures for various applications in the future.

Enhanced Rupture Force in a Cut-Dispersed Double-Network Hydrogel

The Kirigami approach is an effective way to realize controllable deformation of intelligent materials via introducing cuts into bulk materials. For materials ranging from ordinary stiff materials such as glass, ceramics, and metals to soft materials, including ordinary hydrogels and elastomers, all of them are all sensitive to the presence of cuts, which usually act as defects to deteriorate mechanical properties. Herein, we study the influence of the cuts on the mechanical properties by introducing "dispersed macro-scale cuts" into a model tough double network (DN) hydrogel (named D-cut gel), which consists of a rigid and brittle first network and a ductile stretchable second network. For comparison, DN gels with "continuous cuts" having the same number of interconnected cuts (named C-cut gel) were chosen. The fracture tests of D-cut gel and C-cut gel with different cut patterns were performed. The fracture observation revealed that crack blunting occurred at each cut tip, and a large wrinkle-like zone was formed where the wrinkles were parallel to the propagation direction of the cut. By utilizing homemade circular polarizing optical systems, we found that introducing dispersed cuts increases the rupture force by homogenizing the stress around the crack tip surrounding every cut, which reduces stress concentration in one certain cut. We believe this work reveals the fracture mechanism of tough soft materials with a kirigami cut structure, which should guide the design of advanced soft and tough materials along this line.