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

Lightweight 3D Hierarchical Metamaterial Microlattices

Hierarchical auxetic metamaterials are a class of materials which are characterized by a multi-tiered architecture and have the capability of exhibiting enhanced mechanical properties in comparison to their single-geometry counterparts. In this work, three distinct new classes of hierarchical auxetic metamaterials designed by incorporating cubic crystal lattice geometries, namely, Body-Centred Cubic (BCC), Face-Centred Cubic (FCC) and Tetrahedral Cubic (TC) are proposed into 3D rotating cube structures. Through the introduction of hierarchy, these relatively dense mechanical metamaterials are rendered lightweight, through a volume fraction reduction of over 90% in the majority of cases from their full-block (FB) counterparts, while retaining their original auxetic capabilities. These systems are also demonstrated to possess the ability to exhibit a wide range of stiffnesses and Poisson's ratios, including giant negative values, as well as superior stiffness/density ratios making them ideal for implementation in lightweight applications. Furthermore, a two-photon lithography 3D-printer is used to fabricate these new lattice structures at the microscale and test them in-situ. The results obtained provide clear and comprehensive evidence of the improvement imparted through the introduction of hierarchy and the advantages of using this method to design lightweight 3D rotating unit auxetic structures.

Multi-Physical Lattice Metamaterials Enabled by Additive Manufacturing: Design Principles, Interaction Mechanisms, and Multifunctional Applications

Lattice metamaterials emerge as advanced architected materials with superior physical properties and significant potential for lightweight applications. Recent developments in additive manufacturing (AM) techniques facilitate the manufacturing of lattice metamaterials with intricate microarchitectures and promote their applications in multi-physical scenarios. Previous reviews on lattice metamaterials have largely focused on a specific/single physical field, with limited discussion on their multi-physical properties, interaction mechanisms, and multifunctional applications. Accordingly, this article critically reviews the design principles, structure-mechanism-property relationships, interaction mechanisms, and multifunctional applications of multi-physical lattice metamaterials enabled by AM techniques. First, lattice metamaterials are categorized into homogeneous lattices, inhomogeneous lattices, and other forms, whose design principles and AM processes are critically discussed, including the benefits and drawbacks of different AM techniques for fabricating different types of lattices. Subsequently, the structure-mechanism-property relationships and interaction mechanisms of lattice metamaterials in a range of physical fields, including mechanical, acoustic, electromagnetic/optical, and thermal disciplines, are summarized to reveal critical design principles. Moreover, the multifunctional applications of lattice metamaterials, such as sound absorbers, insulators, and manipulators, sensors, actuators, and soft robots, thermal management, invisible cloaks, and biomedical implants, are enumerated. These design principles and structure-mechanism-property relationships provide effective design guidelines for lattice metamaterials in multifunctional applications.

Kirigami-Inspired Stretchable Piezoelectret Sensor for Analysis and Assessment of Parkinson's Tremor

Human muscle activity contains rich information that can reflect human movement patterns and conditions of diseases or physical abnormalities. Flexible pressure sensors enable the assessment of muscle tremors in Parkinson's disease (PD) through Force Myography (FMG). Here, an easily fabricated, ultra-sensitive, and stretchable piezoelectret pressure sensor is presented. Utilizing an effective integration of Kirigami structure and piezoelectret air gap, the sensor achieved a dynamic sensitivity of ≈725 pC/N (@5 Hz), measurement repeatability of <2.5%, measurement hysteresis of <1%, a pressure detection limit of <15 Pa, a response time of ≈2.5 ms, stable output within ±3% over 40 000 cycles, and output decay of <2.5% after 1000 cycles of complex deformation, meeting non-distorted measurement conditions up to 20 Hz. Successful monitoring and assessment of hand muscle tremors are demonstrated. Furthermore, using a 1×3 sensor array enabled tremor localization, achieving a high accuracy rate of 99.5% with machine learning algorithms. Additionally, the sensor facilitated the experimental quantification and assisted scoring of the Movement Disorder Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS), with an accuracy of ≈85%. The sensor demonstrates potential for assisting in the diagnosis and rehabilitation monitoring of Parkinson's disease.

Kirigami-Inspired Three-Dimensional Metamaterials with Programmable Isotropic and Orthotropic Thermal Expansion

Mechanical metamaterials with specifically designed cells can provide unusual thermal expansion properties for diverse applications. Limited by very few available cell topologies and complicated non-linear structural deformation, most existing thermal expansion metamaterials can only achieve orthogonally isotropic negative/zero/positive thermal expansion (NTE/ZTE/PTE) within a mild range, especially the 3D ones. Here, based on one-degree-of-freedom kirigami polyhedrons proposed with a kinematic design strategy, a family of 3D isotropic and orthotropic metamaterials capable of programmable NTE, PTE, and even ZTE over ultra-wide range is developed. Incorporating bi-material strips as creases for isotropic polyhedrons, NTE and PTE metamaterials with coefficients of thermal expansion (CTEs) ranging from -2354.3 to 3006.7 ppm/°C are designed and programmed by the theoretical model. Meanwhile, isotropic ZTE metamaterials are constructed by either homogeneous tessellation of ZTE cells or hybrid tessellation of NTE and PTE cells. Furthermore, by allowing distinct geometric parameters in the three orthogonal directions of the kirigami polyhedrons while preserving the kinematic motion, orthotropic metamaterials, in which each of the three directions can be assigned with an independently programmed NTE, ZTE, or PTE, are also achieved. This study paves a novel pathway for the development of thermal expansion metamaterials with potential applications for space optical systems, MEMS, and so on.

Folding a single high-genus surface into a repertoire of metamaterial functionalities

The concepts of origami and kirigami have often been presented separately. Here, we put forth a synergistic approach-the folded kirigami-in which kirigami assemblies are complemented by means of folding, typical of origami patterns. Besides the emerging patterns themselves, the synergistic approach also leads to topological mechanical metamaterials. While kirigami metamaterials have been fabricated by various methods, such as 3D printing, cutting, casting, and assemblage of building blocks, the "folded kirigami" claim their distinctive properties from the universal folding protocols. For a target kirigami pattern, we design an extended high-genus pattern with appropriate sets of creases and cuts, and proceed to fold it sequentially to yield the cellular structure of a 2D lattice endowed with finite out-of-plane thickness. The strategy combines two features that are generally mutually exclusive in canonical methods: fabrication involving a single piece of material and realization of nearly ideal intercell hinges. We test the approach against a diverse portfolio of triangular and quadrilateral kirigami configurations. We demonstrate a plethora of emerging metamaterial functionalities, including topological phase-switching reconfigurability between polarized and nonpolarized states in kagome kirigami, and availability of nonreciprocal mechanical response in square-rhombus kirigami.

Geometric mechanics of kiri-origami-based bifurcated mechanical metamaterials

We explore a new design strategy of leveraging kinematic bifurcation in creating origami/kirigami-based three-dimensional (3D) hierarchical, reconfigurable, mechanical metamaterials with tunable mechanical responses. We start from constructing three basic, thick, panel-based structural units composed of 4, 6 and 8 rigidly rotatable cubes in close-looped connections. They are modelled, respectively, as 4R, 6R and 8R (R stands for revolute joint) spatial looped kinematic mechanisms, and are used to create a library of reconfigurable hierarchical building blocks that exhibit kinematic bifurcations. We analytically investigate their reconfiguration kinematics and predict the occurrence and locations of kinematic bifurcations through a trial-correction modelling method. These building blocks are tessellated in 3D to create various 3D bifurcated hierarchical mechanical metamaterials that preserve the kinematic bifurcations in their building blocks to reconfigure into different 3D architectures. By combining the kinematics and considering the elastic torsional energy stored in the folds, we develop the geometric mechanics to predict their tunable anisotropic Poisson's ratios and stiffnesses. We find that kinematic bifurcation can significantly effect mechanical responses, including changing the sign of Poisson's ratios from negative to positive beyond bifurcation, tuning the anisotropy, and overcoming the polarity of structural stiffness and enhancing the number of deformation paths with more reconfigured shapes.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

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.