From flat sheets to curved geometries: Origami and kirigami approaches

Transforming flat sheets into three-dimensional structures has emerged as an exciting manufacturing paradigm on a broad range of length scales. Among other advantages, this technique permits the use of functionality-inducing planar processes on flat starting materials, which after shape-shifting, result in a unique combination of macro-scale geometry and surface topography. Fabricating arbitrarily complex three-dimensional geometries requires the ability to change the intrinsic curvature of initially flat structures, while simultaneously limiting material distortion to not disturb the surface features. The centuries-old art forms of origami and kirigami could offer elegant solutions, involving only folding and cutting to transform flat papers into complex geometries. Although such techniques are limited by an inherent developability constraint, the rational design of the crease and cut patterns enables the shape-shifting of (nearly) inextensible sheets into geometries with apparent intrinsic curvature. Here, we review recent origami and kirigami techniques that can be used for this purpose, discuss their underlying mechanisms, and create physical models to demonstrate and compare their feasibility. Moreover, we highlight practical aspects that are relevant in the development of advanced materials with these techniques. Finally, we provide an outlook on future applications that could benefit from origami and kirigami to create intrinsically curved surfaces.     

Kirigami-Based Light-Induced Shape-Morphing and Locomotion

The development of stimuli-responsive soft actuators, a task largely undertaken by material scientists, has become a major driving force in pushing the frontiers of microrobotics. Devices made of soft active materials are oftentimes small in size, remotely and wirelessly powered/controlled, and capable of adapting themselves to unexpected hurdles. However, nowadays most soft microscale robots are rather simple in terms of design and architecture, and it remains a challenge to create complex 3D soft robots with stimuli-responsive properties. Here, it is suggested that kirigami-based techniques can be useful for fabricating complex 3D robotic structures that can be activated with light. External stress fields introduce out-of-plane deformation of kirigami film actuators made of liquid crystal networks. Such 2D-to-3D structural transformations can give rise to mechanical actuation upon light illumination, thus allowing the realization of kirigami-based light-fuelled robotics. A kirigami rolling robot is demonstrated, where a light beam controls the multigait motion and steers the moving direction in 2D. The device is able to navigate along different routes and moves up a ramp with a slope of 6°. The results demonstrate a facile technique to realize complex and flexible 3D structures with light-activated robotic functions.     

Fabrication and Deformation of 3D Multilayered Kirigami Microstructures

Mechanically guided 3D microassembly with controlled compressive buckling represents a promising emerging route to 3D mesostructures in a broad range of advanced materials, including single‐crystalline silicon (Si), of direct relevance to microelectronic devices. During practical applications, the assembled 3D mesostructures and microdevices usually undergo external mechanical loading such as out‐of‐plane compression, which can induce damage in or failure of the structures/devices. Here, the mechanical responses of a few mechanically assembled 3D kirigami mesostructures under flat‐punch compression are studied through combined experiment and finite element analyses. These 3D kirigami mesostructures consisting of a bilayer of Si and SU‐8 epoxy are formed through integration of patterned 2D precursors with a prestretched elastomeric substrate at predefined bonding sites to allow controlled buckling that transforms them into desired 3D configurations. In situ scanning electron microscopy measurement enables detailed studies of the mechanical behavior of these structures. Analysis of the load–displacement curves allows the measurement of the effective stiffness and elastic recovery of various 3D structures. The compression experiments indicate distinct regimes in the compressive force/displacement curves and reveals different geometry‐dependent deformation for the structures. Complementary computational modeling supports the experimental findings and further explains the geometry‐dependent deformation.     

Atomic Layer Deposition for Membranes,Metamaterials, and Mechanisms

Bending and folding techniques such as origami and kirigami enable the scale‐invariant design of 3D structures, metamaterials, and robots from 2D starting materials. These design principles are especially valuable for small systems because most micro‐ and nanofabrication involves lithographic patterning of planar materials. Ultrathin films of inorganic materials serve as an ideal substrate for the fabrication of flexible microsystems because they possess high intrinsic strength, are not susceptible to plasticity, and are easily integrated into microfabrication processes. Here, atomic layer deposition (ALD) is employed to synthesize films down to 2 nm thickness to create membranes, metamaterials, and machines with micrometer‐scale dimensions. Two materials are studied as model systems: ultrathin SiO₂ and Pt. In this thickness limit, ALD films of these materials behave elastically and can be fabricated with fJ‐scale bending stiffnesses. Further, ALD membranes are utilized to design micrometer‐scale mechanical metamaterials and magnetically actuated 3D devices. These results establish thin ALD films as a scalable basis for micrometer‐scale actuators and robotics.     

Kirigami-Design-Enabled Hydrogel Multimorphs with Application as a Multistate Switch

Morphing materials have promising applications in soft robots, intelligent devices, and so forth. Among the various design strategies, kirigami structures are recognized as a powerful tool to obtain sophisticated 3D configurations and unprecedented properties from planar designs on common materials. Here, some kirigami designs are demonstrated for programmable, multistable 3D configurations from composite hydrogel sheets. Via photolithographic polymerization, perforated composite hydrogel sheets are fabricated, in which soft and active hydrogel strips are patterned in stiff and passive hydrogel frames. When immersed in water, the gel strips buckle out of plane due to swelling mismatch. In the kirigami structures, the geometric continuity is disrupted by the introduction of cutouts, and thus the degrees of deformation freedom increases remarkably. Multiple configurations are obtained in a single composite hydrogel by controlling the buckling direction of each strip. Multitier configurations are also obtained by using a hierarchically designed kirigami structure. A multicontact switch of an electric circuit is designed by harnessing the multitier gel configurations. Furthermore, a rotation mode is realized by introducing chirality in the kirigami design. The versatile design of the kirigami structure for programmable deformations should be applicable for other intelligent materials toward promising applications in biomedical devices and flexible electronics.     

From Flatland to Spaceland: Higher Dimensional Patterning with Two‐Dimensional Materials

The creation of three‐dimensional (3D) structures from two‐dimensional (2D) nanomaterial building blocks enables novel chemical, mechanical or physical functionalities that cannot be realized with planar thin films or in bulk materials. Here, we review the use of emerging 2D materials to create complex out‐of‐plane surface topographies and 3D material architectures. We focus on recent approaches that yield periodic textures or patterns, and present four techniques as case studies: (i) wrinkling and crumpling of planar sheets, (ii) encapsulation by crumpled nanosheet shells, (iii) origami folding and kirigami cutting to create programmed curvature, and (iv) 3D printing of 2D material suspensions. Work to date in this field has primarily used graphene and graphene oxide as the 2D building blocks, and we consider how these unconventional approaches may be extended to alternative 2D materials and their heterostructures. Taken together, these emerging patterning and texturing techniques represent an intriguing alternative to conventional materials synthesis and processing methods, and are expected to contribute to the development of new composites, stretchable electronics, energy storage devices, chemical barriers, and biomaterials.     

Atomic origami

Here we summarize recent experimental work in the field of atomic origami: the folding of 3D structures from sheets that are just atoms thick. We highlight current techniques for folding at the microscale and provide scaling arguments as to why some approaches work better than others at small sizes. Finally, we point out that for folding structures made from 2D materials, miniaturization can extend another three orders of magnitude: current state of the art devices are microns in size while, as a platform, atomic membranes should be foldable down to the nanoscale. The ability to scale folding structures over a wide range in size could open diverse applications, from microscopic robots to new interfaces with biology.     

Enabling Robust Self‐Folding Origami by Pre‐Biasing Vertex Buckling Direction

Self‐folding is a powerful approach to fabricate materials with complex 3D forms and advanced properties using planar patterning steps, but suffers from intrinsic limitations in robustness due to the highly bifurcated nature of configuration space around the flat state. Here, a simple mechanism is introduced to achieve robust self‐folding of microscale origami by separating actuation into two discrete steps using different thermally responsive hydrogels. First, the vertices are pre‐biased to move in the desired direction from the flat state by selectively swelling one of the two hydrogels at high temperature. Subsequently, the creases are folded toward their target angles by activating swelling of the second hydrogel upon cooling to room temperature. Since each vertex can be individually programmed to move upward or downward, it is possible to robustly select the desired branch even in multi‐vertex structures with reasonably high complexity. This strategy provides key new principles for designing shaping‐morphing materials that avoid undesired distractor states, expanding their potential applications in areas such as soft robotics, sensors, mechanical metamaterials, and deployable devices.     

Microscale 3D Printing and Tuning of Cellulose Nanocrystals Reinforced Polymer Nanocomposites

The increasing demand for functional materials and an efficient use of sustainable resources makes the search for new material systems an ever growing endeavor. With this respect, architected (meta-)materials attract considerable interest. Their fabrication at the micro- and nanoscale, however, remains a challenge, especially for composites with highly different phases and unmodified reinforcement fillers. This study demonstrates that it is possible to create a non-cytotoxic nanocomposite ink reinforced by a sustainable phase, cellulose nanocrystals (CNCs), to print and tune complex 3D architectures using two-photon polymerization, thus, advancing the state of knowledge toward the microscale. Micro-compression, high-res scanning electron microscopy, (polarised) Raman spectroscopy, and composite modeling are used to study the structure-property relationships. A 100% stiffness increase is observed already at 4.5 wt% CNC while reaching a high photo-polymerization degree of ≈80% for both neat polymers and CNC-composites. Polarized Raman and the Halpin–Tsai composite-model suggest a random CNC orientation within the polymer matrix. The microscale approach can be used to tune arbitrary small scale CNC-reinforced polymer-composites with comparable feature sizes. The new insights pave the way for future applications where the 3D printing of small structures is essential to improve performances of tissue-scaffolds, extend bio-electronics applications or tailor microscale energy-absorption devices.     

Capillary Origami Inspired Fabrication of Complex 3D Hydrogel Constructs

Hydrogels have found broad applications in various engineering and biomedical fields, where the shape and size of hydrogels can profoundly influence their functions. Although numerous methods have been developed to tailor 3D hydrogel structures, it is still challenging to fabricate complex 3D hydrogel constructs. Inspired by the capillary origami phenomenon where surface tension of a droplet on an elastic membrane can induce spontaneous folding of the membrane into 3D structures along with droplet evaporation, a facile strategy is established for the fabrication of complex 3D hydrogel constructs with programmable shapes and sizes by crosslinking hydrogels during the folding process. A mathematical model is further proposed to predict the temporal structure evolution of the folded 3D hydrogel constructs. Using this model, precise control is achieved over the 3D shapes (e.g., pyramid, pentahedron, and cube) and sizes (ranging from hundreds of micrometers to millimeters) through tuning membrane shape, dimensionless parameter of the process (elastocapillary number C_e), and evaporation time. This work would be favorable to multiple areas, such as flexible electronics, tissue regeneration, and drug delivery.     

Hierarchically porous ceramics via direct writing of preceramic polymer-triblock copolymer inks

Hierarchically porous ceramics possess tailored porosity across multiple length scales, giving rise to materials with low density, high specific properties, and multifunctionality. Here, we report a method that combines self-assembly and 3D printing to create ceramic architectures with hierarchical porosity spanning from the nano- to microscale. To programmably define their microscale porosity, an additive manufacturing method, known as direct ink writing, is used to create 3D lattices composed of cylindrical struts. Nanoscale porosity is generated within each strut by block copolymer templating followed by photopolymerization and pyrolysis in a non-oxidative environment, which transforms the preceramic polymer, polycarbosilane, into silicon oxycarbide with a “nanocoral” morphology. The resulting hierarchically porous ceramic lattices exhibit excellent mechanical energy absorption (0.31 MJ/m³), comparable to metal alloy foams. They also possess an order of magnitude lower thermal conductivity (0.087–0.16 W/m⋅K) compared to bulk preceramic polymer-derived ceramics. Prior to pyrolysis, the printed architectures can be manipulated to produce more complex shapes, including lattices with twisted, helical, and overhang features as well as repeated folding to create an origami airplane. By combining self- and directed assembly, our approach opens new avenues for creating hierarchically porous ceramics.     

Light‐Powered Directional Nanofluidic Ion Transport in Kirigami‐Made Asymmetric Photonic‐Ionic Devices

Nacre‐mimetic 2D nanofluidic materials with densely packed sub‐nanometer‐height lamellar channels find widespread applications in water‐, energy‐, and environment‐related aspects by virtue of their scalable fabrication methods and exceptional transport properties. Recently, light‐powered nanofluidic ion transport in synthetic materials gained considerable attention for its remote, noninvasive, and active control of the membrane transport property using the energy of light. Toward practical application, a critical challenge is to overcome the dependence on inhomogeneous or site‐specific light illumination. Here, asymmetric photonic‐ionic devices based on kirigami‐tailored graphene oxide paper are fabricated, and directional nanofluidic ion transport properties therein powered by full‐area light illumination are demonstrated. The in‐plane asymmetry of the graphene oxide paper is essential to the generation of photoelectric driving force under homogeneous illumination. This light‐powered ion transport phenomenon is explained based on a modified carrier diffusion model. In asymmetric nanofluidic structures, enhanced recombination of photoexcited charge carriers at the membrane boundary breaks the electric potential balance in the horizontal direction, and thus drives the ion transport in that direction under symmetric illumination. The kirigami‐based strategy provides a facile and scalable way to fabricate paper‐like photonic‐ionic devices with arbitrary shapes, working as fundamental elements for large‐scale light‐harvesting nanofluidic circuits.     

Assembly and Self‐Assembly of Nanomembrane Materials—From 2D to 3D

Nanoscience and nanotechnology offer great opportunities and challenges in both fundamental research and practical applications, which require precise control of building blocks with micro/nanoscale resolution in both individual and mass‐production ways. The recent and intensive nanotechnology development gives birth to a new focus on nanomembrane materials, which are defined as structures with thickness limited to about one to several hundred nanometers and with much larger (typically at least two orders of magnitude larger, or even macroscopic scale) lateral dimensions. Nanomembranes can be readily processed in an accurate manner and integrated into functional devices and systems. In this Review, a nanotechnology perspective of nanomembranes is provided, with examples of science and applications in semiconductor, metal, insulator, polymer, and composite materials. Assisted assembly of nanomembranes leads to wrinkled/buckled geometries for flexible electronics and stacked structures for applications in photonics and thermoelectrics. Inspired by kirigami/origami, self‐assembled 3D structures are constructed via strain engineering. Many advanced materials have begun to be explored in the format of nanomembranes and extend to biomimetic and 2D materials for various applications. Nanomembranes, as a new type of nanomaterials, allow nanotechnology in a controllable and precise way for practical applications and promise great potential for future nanorelated products.     

3D Hybrid Small Scale Devices

Interfacing nano/microscale elements with biological components in 3D contexts opens new possibilities for mimicry, bionics, and augmentation of organismically and anatomically inspired materials. Abiotic nanoscale elements such as plasmonic nanostructures, piezoelectric ribbons, and thin film semiconductor devices interact with electromagnetic fields to facilitate advanced capabilities such as communication at a distance, digital feedback loops, logic, and memory. Biological components such as proteins, polynucleotides, cells, and organs feature complex chemical synthetic networks that can regulate growth, change shape, adapt, and regenerate. Abiotic and biotic components can be integrated in all three dimensions in a well‐ordered and programmed manner with high tunability, versatility, and resolution to produce radically new materials and hybrid devices such as sensor fabrics, anatomically mimetic microfluidic modules, artificial tissues, smart prostheses, and bionic devices. In this critical Review, applications of small scale devices in 3D hybrid integration, biomicrofluidics, advanced prostheses, and bionic organs are discussed.     

探析剪纸艺术在现代设计中的发展路径

目的研究剪纸艺术对现代设计的启示及其发展。方法对比剪纸艺术与现代设计的相互影响,梳理剪纸艺术在现代设计中的设计要素,从文化与产业的并重、人文与经济的融和、剪纸"时尚化"的演绎3个方面进行研究分析,并在教学及团队研究中作了有益的探索。结论剪纸艺术在现代设计中的发展首先要加强剪纸在文创类产品的开发,其次需推动民间艺术与旅游纪念品的设计与发展,最后通过剪纸"时尚化"的定义,将其衍变为现代"剪纸",成为营造装饰氛围的主力军。剪纸艺术之于现代设计不仅要有情感,而且更要具备一定的功能性与装饰性,其价值才能真正实现。     

Cover Picture: Microsolidics: Fabrication of Three‐Dimensional Metallic Microstructures in Poly(dimethylsiloxane) (Adv. Mater. 5/2007)

Flexible metallic wires embedded in poly(dimethylsiloxane) are produced with microscale dimensions by injecting heated, liquid solder into microfluidic channels and cooling, as reported by George Whitesides and co‐workers on p. 727. This approach is used to fabricate complex, metallic microstructures that are twisted (as shown), rolled, or woven into fabrics. The structures can be rigid or flexible, depending on the type of solder used, and breaks in the metal can be “healed” by reheating the device. This method of fabrication may find applications in flexible electronic circuits, 3D metallic microstructures, and hybrid electronic–microfluidic devices.     

Surface modeling using deformable templates

We present a simple technique to model the structures and behaviors of flexible, elastic objects. We use an imaginary elastic wire frame, which is made of membranous, thin-plate–type material, to model the surface structures of flexible objects. We demonstrate that in computational vision, such a flexible wire frame can be used for visual surface reconstruction with the structured-light sensing technique. In graphic animation, we allow animation sequences to be generated automatically between prespecified key frames, the surface structures of which are described by our flexible mode. Furthermore, we allow collisions of objects' trajectories so that interactions of multiple flexible objects can be simulated. We believe that our technique is widely applicable in many computational vision and graphic animation processes.     

A multiscale virtual element method for the analysis of heterogeneous media

We introduce a novel heterogeneous multiscale method for the elastic analysis of two-dimensional domains with a complex microstructure. To this end, the multiscale finite element method is revisited and originally upgraded by introducing virtual element discretizations at the microscale, hence allowing for generalized polygonal and nonconvex elements. The microscale is upscaled through the numerical evaluation of a set of multiscale basis functions. The solution of the equilibrium equations is performed at the coarse scale at a reduced computational cost. We discuss the computation of the multiscale basis functions and corresponding virtual projection operators. The performance of the method in terms of accuracy and computational efficiency is evaluated through a set of numerical examples.     

Morphable 3D structure for stretchable display

Displays that can be reversibly stretched in their geometrical layout are highly important in various applications. Stretchable displays are commonly demonstrated using two-dimensional (2D) geometries with stretchable rubber substrates and elastic interconnects. However, mechanical stretch induces deterioration of the resolution per unit area and blurs the displayed image, consequently lowering the display quality. In this study, we demonstrate a morphable 3D structure inspired by origami/kirigami to produce stretchable displays that can preserve the original image quality by maintaining the display pixel density under stretching. The morphable 3D display consists of a 7 × 7 micro-light-emitting diode (LED) pixel array integrated on a transparent epoxy structural frame, which can be stretched up to 100% without affecting the performance of the display. The functional 3D system can create important unconventional opportunities for optoelectronic devices.     

Purely Elastic Fluid–Structure Interactions in Microfluidics: Implications for Mucociliary Flows

Fluid–structure interactions lie at the heart of the complex, and often highly coordinated, motions of actively driven microscale biological systems (e.g., translating cilia, flagella, and motile cells). Due to the highly viscoelastic nature of most relevant biological fluids and the small length scales involved, the viscous and inertial forces in such flows are dominated by elasticity. However, elastic effects are often overlooked in studies seeking to address phenomena like the synchronization of beating cilia. In this study, unique microfluidic experiments are presented to demonstrate that inertia‐free viscoelastic flows can lead to highly regular beating of an immersed (passive) flexible structure, herein named “purely‐elastic” fluid–structure interaction. It is also shown how two such flexible structures can achieve an extraordinary degree of synchronization, with a correlation coefficient approaching unity. The synchronization is a result of the generation of localized elastic stresses in the fluid that effectively link the two objects. These purely elastic interactions may be important to consider toward developing a complete understanding of the motions of microscale biological systems.