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Multi-physically programmable tubular origami metamaterials: Exploitable nexus of geometry, folding mechanics and stimuli-responsive physics
Abstract and Figures
Metamaterials and metastructures developed based on tubular origami-inspired structural forms can leverage the convolution of geometry, crease mechanics and stimuli-responsive physics to provide unique mechanical and functional properties, including geometric efficiency and compactness, deployability and reconfigurability, structural integration ability in complex shapes, stiffness and strength modulation, constitutive programming and deformation mode coupling, high specific energy absorption, multi-stability and programmable dynamic behaviour, leading to diverse applications in the field of mechanical, robotics, space, electronic devices and communication, biomedical, and architecture. With stupendous advancement over the last decade in computational and manufacturing capabilities to realize complex crease architectures along with on-demand programmability through coupling folding-driven mechanics with stimuli-responsive physics of electrical or magnetic fields, temperature, light, controlled chemical reactions and pneumatic actuation, the field of origami-inspired mechanical metamaterials has been attracting wide attention due to immense potential of achieving unprecedented multi-physical and multi-functional attributes that are typically not attainable in naturally-occurring materials or traditional structures. In this article, we endeavour to review the developments reported in relevant literature concerning mechanical and multi-physical property modulation of tubular origami metamaterials, highlighting the broad-spectrum potential in innovative applications across the length scales along with critically analysing the emerging trends, challenges and potential future research landscape.
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Metamaterials with multimodal deformation mechanisms resemble machines1,2, especially when endowed with autonomous functionality. A representative architected assembly, with tunable chirality, converts linear motion into rotation³. These chiral metamaterials with a machine-like dual modality have potential use in areas such as wave manipulation⁴, optical activity related to circular polarization⁵ and chiral active fluids⁶. However, the dual motions are essentially coupled and cannot be independently controlled. Moreover, they are restricted to small deformation, that is, strain ≤2%, which limits their applications. Here we establish modular chiral metamaterials, consisting of auxetic planar tessellations and origami-inspired columnar arrays, with decoupled actuation. Under single-degree-of-freedom actuation, the assembly twists between 0° and 90°, contracts in-plane up to 25% and shrinks out-of-plane more than 50%. Using experiments and simulations, we show that the deformation of the assembly involves in-plane twist and contraction dominated by the rotating-square tessellations and out-of-plane shrinkage dominated by the tubular Kresling origami arrays. Moreover, we demonstrate two distinct actuation conditions: twist with free translation and linear displacement with free rotation. Our metamaterial is built on a highly modular assembly, which enables reprogrammable instability, local chirality control, tunable loading capacity and scalability. Our concept provides routes towards multimodal, multistable and reprogrammable machines, with applications in robotic transformers, thermoregulation, mechanical memories in hysteresis loops, non-commutative state transition and plug-and-play functional assemblies for energy absorption and information encryption.
Maxwell lattices are periodic frameworks characterized by a balance between the number of kinematic variables and constraints in each unit cell, attracting attention as a source of topological mechanical metamaterials. In particular, one-dimensional (1D) Maxwell lattices maintain a constant number of degrees of freedom (DOFs) as the number of unit cells increases, offering advantages in the design and control of their kinematics. Here, we construct a 1D Maxwell lattice with tunable DOFs, termed the Maxwell origami tube, by closing a triangulated origami tessellation, which is a 2D Maxwell lattice. In topological mechanics, the infinitesimal deformation modes of uniformly configured Maxwell lattices are classified into edge and bulk modes. Unlike conventional 1-DOF 1D Maxwell lattices, multi-DOF 1D Maxwell lattices exhibit a mixture of DOFs corresponding to edge and bulk modes, which we term eDOFs and bDOFs. This paper investigates how the eDOFs and bDOFs of the Maxwell origami tube depend on the crease patterns and folded states using a discrete dynamical system model. We find that ground states with zero and nonzero bDOFs can coexist within a single crease pattern. Additionally, in states with nonzero bDOF, the ratio of bDOF to total DOF decreases as the total DOF increases. In contrast, we present another origami tube with a constant DOF of 2, which represents the first overconstrained lattice to exhibit nonuniform bulk modes. This work highlights the versatility of Maxwell lattices and provides a theoretical foundation for designing novel mechanical metamaterials.
Published by the American Physical Society 2025
Kresling origami-based metamaterials have gained significant attention lately due to their mechanical advantages like deployability, energy manipulation and absorption, vibration control and tailorable constitutive behavior. While previous investigations have primarily focused on kinematics and statics, as most engineering applications experience dynamic conditions, few recent studies have examined the dynamic performance including transient and linear vibration. In this paper, we computationally investigate the nonlinear dynamics of Kresling origami in an expanded design space through the introduction of conical architecture. The conical Kresling origami module (CKOM) leads to a highly nonlinear behavior, originating from the geometrical constraints. This makes the dynamic behavior under specific natures of external disturbance more complex and chaotic, while programmable as a function of the geometrical features. CKOM provides an excellent support system and better stability at period-n attractor, which means that the system behaves in the same pattern after n-period of oscillation. It is further noted that the CKOM system is an elastically foldable truss-like idealized structure, which often exhibits interesting static behavior like bi-stability. Programmability in the expanded design space of conicity and other geometrical parametric features of the Kresling tubular origami would lead to widespread applications including spacecraft, aircraft wings, robotics, vehicles, and various deployable structures across the length scales.
Metamaterials with bandgap properties have been widely studied and applied in the attenuation of surface and bulk waves propagating in the soil. However, most of the studies consider soil as the isotropic medium and ignore the general anisotropy property from the practical point of view. In this work, we consider the transversely isotropic constitutive model of soil and propose a cross-like metamaterial consisting of concrete inclusion and rubber coating to achieve broadband attenuation for omnidirectional bulk waves. The proposed cross-like metamaterials have more and wider bandgaps compared to circle and square metamaterials, and they have better wave attenuation performance in transversely isotropic soil with higher degrees of anisotropy. The transmission spectra of cross-like metamaterials demonstrate the wave attenuation effect of bandgaps. Furthermore, we build the full-scale transmission model considering the subway tunnel condition and demonstrate the practical wave attenuation performance of cross-like metamaterials in frequency and time domains. We also find that a larger depth of the metamaterial region will enhance wave attenuation in the bandgaps while considering rubber viscosity can enhance wave attenuation in the overall frequency ranges. The variations of omnidirectional bandgaps with rubber thickness, geometric parameters, and hollow concrete sizes are discussed. This study presents an appropriate way to design metamaterials for broadband omnidirectional bulk wave attenuation in transversely isotropic soil, which can be easily extended to other anisotropic media.
Magnetically actuated miniature origami crawlers are capable of robust locomotion in confined environments but are limited to passive functionalities. Here, we propose a bistable origami crawler that can shape-morph to access two separate regimes of folding degrees of freedom that are separated by an energy barrier. Using the modified bistable V-fold origami crease pattern as the fundamental unit of the crawler, we incorporated internal permanent magnets to enable untethered shape-morphing. By modulating the orientation of the external magnetic field, the crawler can reconfigure between an undeployed locomotion state and a deployed load-bearing state. In the undeployed state, the crawler can deform to enable out-of-plane crawling for robust bi-directional locomotion and navigation in confined environments based on friction anisotropy. In the deployed state, the crawler can execute microneedle insertion in confined environments. Through this work, we demonstrated the advantage of incorporating bistability into origami mechanisms to expand their capabilities in space-constraint applications.
Kresling origami structure has attracted significant interest for achieving extraordinary mechanical properties. In this study, we proposed a new strategy to develop 3D-printable Kresling-embedded honeycombs (KEHs) based mechanical metamaterials and achieve optimized mechanical energy absorption capability. By exploiting the twisted deformation modes and boundary constraints, various KEH reinforced metamaterials were designed, where their deformation behaviors and energy absorption properties were investigated using finite element analysis and quasi-static compression tests. Effects of orientation twisting angle, boundary constraint and crease tilting angle on the deformation behaviors of these KEH reinforced metamaterials were studied to optimize their energy absorption properties. Finally, deformation behaviors and energy absorption properties of KEH reinforced metamaterials incorporated of KEH arrays in both 2D structure and 3D structures were studied. Both experimental and simulation results showed that the proposed KEH reinforced metamaterials achieved much more stable compression behaviors and higher energy absorption capabilities than those of the traditional honeycomb structures. This study provides a novel KEH reinforcement strategy for 3D printed metamaterials with optimized energy absorption capabilities to dramatically expand their practical applications.
Mashrabiya are oriel windows characteristic of Islamic architectural tradition that were historically integrated into buildings located in places with arid climates. The present paper formulates a novel design approach to Mashrabiya systems, by employing origami modules equipped with photovoltaic cells. The examined oriel window is able to complement the main traditional functions of a Mashrabiya with solar energy harvesting. A primary folding motion of the origami modules designed to tessellate its surface permits the sunlight to pass through the system in a controlled way. A secondary tilting folding motion of the photovoltaic cells placed on these modules lets the system harvest solar energy and produce electric power. The paper illustrates the architectural and mechanical design of the examined Mashrabiya window, as well as its energy harvesting properties, using both numerical and experimental methods.
Origami structures have been widely applied for various engineering applications due to their extraordinary mechanical properties. However, the relationship between in-plane rotating coupling and energy absorption of these Origami structures is seldom studied previously. The study proposes a design strategy that utilizes identical-twin rotation (i.e. simultaneous rotation with the same chirality) and fraternal-twin rotation (i.e. simultaneous rotation with the opposite chirality) of Kresling metamaterials to achieve multimodal rotation coupling and enhanced energy absorption. Deformation mode and energy absorption properties of 3D-printed Kresling metamaterials have been studied using both quasi-static compression tests and finite element analysis. Furthermore, effects of polygon units and their connections to 2D and 3D arrangements, which generate 4 × 4 arrays and 2 × 2 × 2 arrays, have been investigated to identify the optimized structures for achieving ultra-high energy absorption of chiral Kresling metamaterials. Results showed that rotating coupling of chiral identical twins in multimodal Kresling metamaterials possesses diverse deformation patterns and ultra-high energy absorption. This study provides a novel strategy to optimize structural designs and mechanical properties of the Kresling metamaterials.
Soft robots often draw inspiration from nature to navigate different environments. Although the inching motion and crawling motion of caterpillars have been widely studied in the design of soft robots, the steering motion with local bending control remains challenging. To address this challenge, we explore modular origami units which constitute building blocks for mimicking the segmented caterpillar body. Based on this concept, we report a modular soft Kresling origami crawling robot enabled by electrothermal actuation. A compact and lightweight Kresling structure is designed, fabricated, and characterized with integrated thermal bimorph actuators consisting of liquid crystal elastomer and polyimide layers. With the modular design and reprogrammable actuation, a multiunit caterpillar-inspired soft robot composed of both active units and passive units is developed for bidirectional locomotion and steering locomotion with precise curvature control. We demonstrate the modular design of the Kresling origami robot with an active robotic module picking up cargo and assembling with another robotic module to achieve a steering function. The concept of modular soft robots can provide insight into future soft robots that can grow, repair, and enhance functionality.
Emerging nano-kirigami/origami technology enables the flexible transformations of 2D planar patterns into exquisite 3D structures in situ and has aroused great interest in the areas of nanophotonics and optoelectronics. This paper briefly reviews some milestone research and breakthrough progresses in nano-kirigami/origami from the aspects of stimuli approaches and application directions. Versatile stimuli for kirigami/origami, including capillary force, residual stress, mechanical force, and irradiation-induced stress, are introduced in the micro/nanoscale region. Appealing optical applications and reconfigurable schemes of nano-kirigami/origami structures are summarized, offering effective routes to realize tunable nanophotonic and optoelectronic devices. Future challenges and promising pathways are also envisioned, including design methods, innovative materials, multi-physics field driving, and reprogrammable devices.
In this study an innovative parameterized water-bomb wheel modeling method based on recursive solving are introduced, significantly reducing the modeling workload compared to traditional methods. A multi-link supporting structure is designed upon the foundation of the water-bomb wheel model. The effectiveness of the supporting structure is verified through simulations and experiments. For robots equipped with this water-bomb wheel featuring the multi-link support, base on the kinematic model of multi-link structure, a mapping algorithm that incorporates parameterized kinematic solutions and IMU-fused parameterized odometry is proposed. Based on this algorithm, SLAM and autonomous navigation experiments are carried out in simulation environment and real environment respectively. Compared with the traditional algorithm, this algorithm the precision of SLAM is enhanced, achieving high-precision SLAM and autonomous navigation with a robot error rate below 5%.
Artificial gravity is a crucial technology to enable long-duration human space flight. However, a kilometer-scale rotating space structure is needed to generate artificial grav- ity at rotation rates that can be tolerated comfortably by crew. Constructing such a structure with current technology would require many launches and significant in-space assembly. This work presents HERDS, High-Expansion-Ratio Deployable Structures, a hierarchical expansion mechanism that can deploy a kilometer-scale structure from a single launch. HERDS lever- ages a hierarchical combination of a Kresling mechanism and a pop-up extending truss (PET), a novel variant of the scissor mechanism. We show that HERDS designs achieve 4-11x better beam member aspect ratios than non-hierarchical Kresling or scissor mechanisms, resulting in a stiffer deployed structure. Furthermore, HERDS designs are shown in simulation to satisfy the necessary loading and structural constraints for supporting the Lunar Gateway mission with a factor of safety greater than 1.5 using existing launch vehicles. Our modeling and analysis is validated on a 1/10 scale prototype with a 50x expansion ratio.
Active origami capable of precise deployment control, enabling on-demand modulation of its properties, is highly desirable in multi-scenario and multi-task applications. While 4D printing with shape memory composites holds great promise to realize such active origami, it still faces challenges such as low load-bearing capacity and limited transformable states. Here, we report a fabrication-design-actuation method of precisely controlled electrothermal origami with excellent mechanical performance and spatiotemporal controllability, utilizing 4D printing of continuous fiber-reinforced composites. The incorporation of continuous carbon fibers empowers electrothermal origami with a controllable actuation process via Joule heating, increased actuation force through improved heat conduction, and enhanced mechanical properties as a result of reinforcement. By modeling the multi-physical and highly nonlinear deploying process, we attain precise control over the active origami, allowing it to be reconfigured and locked into any desired configuration by manipulating activation parameters. Furthermore, we showcase the versatility of electrothermal origami by constructing reconfigurable robots, customizable architected materials, and programmable wings, which broadens the practical engineering applications of origami.
Owing to the architected void-filled low-density configurations, metamaterials are prone to defects during the complex manufacturing process, or damages under operational conditions. Recently mechanical cloaking has been proposed to shield the effect of such disorders in terms of homogenized mechanical responses. The major drawback in these studies are that the damage location should be known a priori, and the cloak is designed around that damaged zone before manufacturing. Such postulation does not allow unsupervised damage resilience during the manufacturing and service life of metamaterials by active reconfiguration of the stress field depending on the random and unpredictable evolution of damage. Here, we propose a radically different approach by introducing piezoelectric lattices where the effect of random appearance of any single or multiple disorders and damages with complex shapes, sizes and distributions can be shielded through active multi-physically controlled cloaks by voltage-dependent modulation of the stress fields within the cloaking region. Notably, this can be achieved without breaking periodicity and any additional material in the cloaking region unlike earlier studies concerning mechanical cloaks. The proposed active class of elastic metamaterials will bring a step-change in the on-demand mechanical performance of critically important structural components and unsupervised damage resilience for enhanced durability and sustainability.
This article is part of the theme issue ‘Current developments in elastic and acoustic metamaterials science (Part 1)’.
Structures inspired by the Kresling origami pattern have recently emerged as a foundation for building functional engineering systems with versatile characteristics that target niche applications spanning different technological fields. Their light weight, deployability, modularity, and customizability are a few of the key characteristics that continue to drive their implementation in robotics, aerospace structures, metamaterial and sensor design, switching, actuation, energy harvesting and absorption, and wireless communications, among many other examples. This work aims to perform a systematic review of the literature to assess the potential of the Kresling origami springs as a structural component for engineering design keeping three objectives in mind: (i) facilitating future research by summarizing and categorizing the current literature, (ii) identifying the current shortcomings and voids, and (iii) proposing directions for future research to fill those voids.
Soft grippers due to their highly compliant material and self-adaptive structures attract more attention to safe and versatile grasping tasks compared to traditional rigid grippers. However, those flexible characteristics limit the strength and the manipulation capacity of soft grippers. In this paper, we introduce a hybrid-driven gripper design utilizing origami finger structures, to offer adjustable finger stiffness and variable grasping range. This gripper is actuated via pneumatic and cables, which allows the origami structure to be controlled precisely for contraction and extension, thus achieving different finger lengths and stiffness by adjusting the cable lengths and the input pressure. A kinematic model of the origami finger is further developed, enabling precise control of its bending angle for effective grasping of diverse objects and facilitating in-hand manipulation. Our proposed design method enriches the field of soft grippers, offering a simple yet effective approach to achieve safe, powerful, and highly adaptive grasping and in-hand manipulation capabilities.
This paper presents an electromagnetic energy harvester based on a unique nonlinear Kresling origami-inspired structure. By introducing the equilibrium shift phenomenon, reversible nonlinearity (i.e. mixed softening-hardening behavior) empowers the proposed harvester to work in a broad frequency band, confirmed by both simulation using a dynamic model and experimentation. The prototyped device can produce the open-circuit root mean square (RMS) voltage from 0.09 V to 0.20 V in the reversibly nonlinear response region in (6.19 Hz, 9.63 Hz) and a maximum output power of 0.4956 mW at an optimum load of 18.1 Ω under the excitation of 1.1 g. Moreover, detailed research further reveals that the design parameters of Kresling origami-inspired structure and electrical and mechanical loads influence reversible nonlinearity. Increasing the tip mass and γ 0 in the M2 region of the design map strengthens the softening behavior, and enlarging the electrical load enhances the hardening behavior. The findings from this work deepen the understanding of the nonlinear behavior of Kresling origami, unveils the great potential of origami structure in energy harvesting and offers a new method to realize broadband vibration energy harvesters.
In this work, we have presented a soft encapsulating gripper for gentle grasps. This was enabled by a series of soft origami patterns, such as the Yoshimura pattern, which was directly printed on fabric. The proposed gripper features a deformable body that enables safe interaction with its surroundings, gentle grasps of delicate and fragile objects, and encapsulated structures allowing for noninvasive enclosing. The gripper was fabricated by a direct 3D printing of soft materials on fabric. This allowed for the stiffness adjustment of gripper components and a simple fabrication process. We evaluated the grasping performance of the proposed gripper with several delicate and ultra-gentle objects. It was concluded that the proposed gripper could manipulate delicate objects from fruits to silicone jellyfishes and, therefore, have considerable potential for use as improved soft encapsulating grippers in agriculture and engineering fields.
The potential of ingestible medical devices can be greatly enhanced through the use of smart structures made from stimuli-responsive materials. While hydration is a convenient stimulus for inducing shape changes in biomaterials, finding robust materials that can achieve rapid actuation, facile manufacturability, and biocompatibility suitable for ingestible medical devices poses practical challenges. Hydration is a convenient stimulus to induce shape changes in smart biomaterials; however, there are many practical challenges to identifying materials that can achieve rapid actuation and facile manufacturability while satisfying constraints associated with biocompatibility requirements and mechanical properties that are suitable for ingestible medical devices. Herein, we illustrate the formulation and processability of a moisture-responsive genipin-crosslinked gelatin bioplastic system, which can be processed into complex three-dimensional shapes. Mechanical characterization of bioplastic samples showed Young's Modulus values as high as 1845 MPa and toughness values up to 52 MJ/m3, using only food-safe ingredients. Custom molds and UV-laser processing enabled the fabrication of centimeter-scale structures with over 150 independent actuating joints. These self-actuating structures soften and unfold in response to surrounding moisture, eliminating the need for additional stimuli or actuating elements.
Traditionally lattice materials are made of a network of beams in two and three dimensions with majority of the lattice volume being void space. Recently researchers have started exploring ways to exploit this void space for multi-physical property modulation of lattices such as global mechanical behaviour including different elastic moduli, wave propagation, vibration, impact and acoustic features. The elastic moduli are of crucial importance to ensure the structural viability of various multi-functional devices and systems where a space-filled lattice material could potentially be used. Here we develop closed-form analytical expressions for the effective elastic moduli of space- filled lattices based on an exact stiffness matrix approach coupled with the unit cell method, wherein transcendental shape functions are used to obtain exact solutions of the underlying differential equation. This can be viewed as an accurate multi-material based generalization of the classical formulae for elastic moduli of honeycombs. Numerical results show that the effective in-plane elastic moduli can increase by orders of magnitude with a relatively lower infill stiffness (10\%).This gives an exceptional opportunity to engineer multi-material lattices with optimal specific stiffness along with characterizing the mechanical properties of a multitude of lattice-like artificial and naturally occurring structural forms with space filling.
Origami bellows are formed by folding flat sheets into closed cylindrical structures along predefined creases. As the bellows unfold, the volume of the origami structure will change significantly, offering potential for use as inflatable deployable structures. This paper presents a geometric study of the volume of multi-stable Miura-ori and Kresling bellows, focusing on their application as deployable space habitats. Such habitats would be compactly stowed during launch, before expanding once in orbit. The internal volume ratio between different deployed states is investigated across the geometric design space. As a case study, the SpaceX Falcon 9 payload fairing is chosen for the transportation of space habitats. The stowed volume and effective deployed volume of the origami space habitats are calculated to enable comparison with conventional habitat designs. Optimal designs for the deployment of Miura-ori and Kresling patterned tubular space habitats are obtained using particle swarm optimisation (PSO) techniques. Configurations with significant volume expansion can be found in both patterns, with the Miura-ori patterns achieving higher volume expansion due to their additional radial deployment. A multi-objective PSO (MOPSO) is adopted to identify trade-offs between volumetric deployment and radial expansion ratios for the Miura-ori pattern.
Applying tessellated origami patterns to the design of mechanical materials can enhance properties such as strength-to-weight ratio and impact absorption ability. Another advantage is the predictability of the deformation mechanics since origami materials typically deform through the folding and unfolding of their creases. This work focuses on creating 4D printed flexible tubular origami based on three different origami patterns: the accordion, the Kresling and the Yoshimura origami patterns, fabricated with a flexible polylactic acid (PLA) filament with heat-activated shape memory effect. The shape memory characteristics of the self-unfolding structures were then harnessed at 60°C, 75°C and 90°C. Due to differences in the folding patterns of each origami design, significant differences in behaviour were observed during shape programming and actuation. Among the three patterns, the accordion proved to be the most effective for actuation as the overall structure can be compressed following the folding crease lines. In comparison, the Kresling pattern exhibited cracking at crease locations during deformation, while the Yoshimura pattern buckled and did not fold as expected at the crease lines. To demonstrate a potential application, an accordion-patterned origami 4D printed tube for use in hand rehabilitation devices was designed and tested as a proof-of-concept prototype incorporating self-unfolding origami.
Kresling pattern origami is known for its bistable property, as confirmed by the truss model used to analyze its dynamics. However, our theoretical research and folding experiments reveal that the Kresling pattern origami possesses three stable states during folding motion, with the third state exhibiting high stiffness. These represent exciting new achievements for origami research. Here, Kresling pattern origami is studied using the geometric definitions of triangulated cylindrical origami and triangulated conical origami, and the truss model is corrected based on the proposed tristable property and an established mathematical model of the third stable state. Analysis of the energy landscapes obtained from the corrected truss model reveals various properties of the Kresling pattern origami that confirm its tristable property. In addition, origami-inspired structures are created that exhibit excellent deployability, collapsibility, load-bearing capacity, and multistability. Thereafter, the high stiffness of the third stable state is validated experimentally. These studies can provide new content for constructing multistable metamaterials and improving the load-bearing capacity of deployable structures.
Mechanical metamaterials are engineered materials with unconventional mechanical behavior that originates from artificially programmed microstructures along with intrinsic material properties. With tremendous advancement in computational and manufacturing capabilities to realize complex microstructures over the last decade, the field of mechanical metamaterials has been attracting wide attention due to immense possibilities of achieving unprecedented multi-physical properties which are not attainable in naturally-occurring materials. One of the rapidly emerging trends in this field is to couple the mechanics of material behavior and the unit cell architecture with different other multi-physical aspects such as electrical or magnetic fields, and stimuli like temperature, light or chemical reactions to expand the scope of actively programming on-demand mechanical responses. In this article, we aim to abridge outcomes of the relevant literature concerning mechanical and multi-physical property modulation of metamaterials focusing on the emerging trend of bi-level design, and subsequently highlight the broad-spectrum potential of mechanical metamaterials in their critical engineering applications. The evolving trends, challenges and future roadmaps have been critically analyzed here involving the notions of real-time reconfigurability and functionality programming, 4D printing, nano-scale metamaterials, artificial intelligence and machine learning, multi-physical origami/kirigami, living matter, soft and conformal metamaterials, manufacturing complex microstructures, service-life effects and scalability.
Origami and kirigami have become foundations for programmable sheet materials that fold along flexible creases. However, since they are originated from folded paper that allows no in‐plane sheet deformation, they suffer from limited folding energy arising from narrow creases, and large varieties of crease patterns are completely non‐foldable due to over‐constraint. Herein, a new strategy that breaks the limitations of the conventional crease‐induced folding kinematics by leveraging a folding effect from in‐plane shear deformation of the sheet is reported, and it is referred to as shearigami. It is shown that shearigami extends the realm of foldable structures to include the strictly non‐foldable origami patterns such as degree‐3 vertices, and the sheet‐stored self‐folding energy outperforms the crease‐stored energy by a potentially two orders of magnitude. Shearigami also inherits the mathematical framework of paper folding and provides a unified view that regards origami and kirigami as two special cases. Herein, self‐folding shearigami models are experimentally demonstrated based on previously non‐foldable patterns, including artificial muscles with rapid shear‐induced extension. The way is paved toward active structures and architectured materials with design freedom and self‐folding capabilities beyond origami and kirigami.
Fully soft bistable mechanisms have shown extensive applications ranging from soft robotics, wearable devices, and medical tools, to energy harvesting. However, the lack of design and fabrication methods that are easy and potentially scalable limits their further adoption into mainstream applications. Herein, a top–down planar approach is presented by introducing Kirigami‐inspired engineering combined with a pre‐stretching process. Using this method, Kirigami‐Pre‐stretched Substrate‐Kirigami trilayered precursors are created in a planar manner; upon release, the strain mismatch—due to the pre‐stretching of substrate—between layers will induce an out‐of‐plane buckling to achieve targeted 3D bistable structures. By combining experimental characterization, analytical modeling, and finite element simulation, the effect of the pattern size of Kirigami layers and pre‐stretching on the geometry and stability of resulting 3D composites is explored. In addition, methods to realize soft bistable structures with arbitrary shapes and soft composites with multistable configurations are investigated, which may encourage further applications. This method is demonstrated by using bistable soft Kirigami composites to construct two soft machines: (i) a bistable soft gripper that can gently grasp delicate objects with different shapes and sizes and (ii) a flytrap‐inspired robot that can autonomously detect and capture objects.
In recent decades, origami has been explored to aid in the design of engineering structures. These structures span multiple scales and have been demonstrated to be used towards various areas such as aerospace, metamaterial, biomedical, robotics, and architectural applications. Conventionally, origami or deployable structures have been actuated by hands, motors, or pneumatic actuators, which can result in heavy or bulky structures. On the other hand, active materials, which reconfigure in response to external stimulus, eliminate the need for external mechanical loads and bulky actuation systems. Thus, in recent years, active materials incorporated with deployable structures have shown promise for remote actuation of light weight, programmable origami. In this review, active materials such as shape memory polymers and alloys, hydrogels, liquid crystal elastomers, magnetic soft materials, and covalent adaptable network polymers, their actuation mechanisms, as well as how they have been utilized for active origami and where these structures are applicable is discussed. Additionally, the state‐of‐the‐art fabrication methods to construct active origami are highlighted. The existing structural modeling strategies for origami, the constitutive models used to describe active materials, and the largest challenges and future directions for active origami research are summarized.
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Robots are increasingly integral across various sectors due to their efficiency and superior capabilities, which enable performance beyond human potential. However, the development of robotic systems often conflicts with the sustainable development goals set by the United Nations, as they generate considerable nondegradable waste and organic/inorganic pollutants throughout their life cycle. In this paper, we introduce a dual closed-loop robotic system that integrates biodegradable, sustainable materials such as plasticized cellulose films and NaCl-infused ionic conductive gelatin organogels. These materials undergo a closed-loop ecological cycle from processing to biodegradation, contributing to new growth, while the self-sensing, origami-based robot supports a seamless human-in-the-loop teleoperation system. This innovative approach represents a paradigm shift in the application of soft robotic systems, offering a path toward a more sustainable future by aligning advanced robotic functionalities with environmental stewardship.
Multifunctional materials attract extensive attention for simultaneously satisfying diverse engineering applications, such as protection against mechanical and vibratory intrusions. Here, the mechanical responses and wave attenuation of multi-functional metamaterials at various elastoplastic are custom-designed. An elegant kiri/origami metamaterial is proposed, offering widely tunable mechanical responses and broadband wave attenuation in ultra low-frequencies. The incomparable compression-twist of kresling origami and the prominent local-resonance of kirigami split-rings promote efficient elastic wave polarization and plastic hinges, providing comprehensive protection from elastic to plastic. Kirigami split-rings highlight a fabrication-friendly approach of forming local resonators.Experiments and analyses confirm the reliability and superiority. Leveraging a machine learning-aided framework, optimal and anticipated individual properties and custom multi-performances are achieved for wave attenuation, energy absorption, plateau fluctuations, deformation triggering forces, and load-bearing/plateau forces under various impact levels. The machine learning-aided framework enables rapid multi-objective prediction and customization end-to-end without requiring prior knowledge. This work holds significant potential for the development and application of multi-functional, multi-physical field and multi-scale metamaterials.
Shear non-reciprocity, implying unequal shear forces in opposite shear directions, can be achieved by arranging structures asymmetrically. However, the non-reciprocal Poynting effect, i.e., unequal normal stresses induced by the same shear displacements to the left and right, has not been fully explored. We discover the non-reciprocal Poynting effect using a generalized directional truss model. Inspired by this discovery, the cylindrical lattice metamaterials constructed from antisymmetric curled microstructures are employed as a case study to generate the non-reciprocal Poynting effect. We develop a design framework that integrates digital generation, finite deformation theory, finite element modeling, and three-dimensional (3D) printing to program the non-reciprocal Poynting effect. Applications such as bionic Poynting effect matching, wave energy converter, and unidirectional motion limitation are demonstrated. This framework allows the one-to-one mapping between the torque and normal forces, paving the way for designing soft devices with precise force transmission capabilities.
Origami structures have the advantages of foldability and adjustability, with applications spanning numerous engineering fields. However, there remains a dearth of intelligent and convenient methods that can effectively tackle both potential energy prediction and design problems on origami structures. This study proposes a novel physics-informed neural network (PINN) to predict and design potential energy curves of Kresling origami structures without labelled data. A sorting operation is coupled into the PINN, ensuring the prediction correctness. The accuracy of the potential energy curves predicted by the PINN is demonstrated through comparison with a reference and the exhaustive method. A prediction only takes less than one second and the precision of the PINN significantly surpasses that of the exhaustive method, proving the extremely high efficiency and credibility of the PINN. Furthermore, two design cases for Kresling origami structures, matching a target potential energy curve and a set of target potential energy points, are performed. The designed structures meet the expectations and each design takes a few seconds, showing the efficiency and applicability of the PINN in inverse design. The presented physics-driven approach without labelled data offers an innovative tool with learning ability to predict and design. It also provides a valuable reference for the force and stiffness design of Kresling origami structures. In addition, the code of the PINN is shared online.
This study proposes a multi-scale composite lattice-origami metamaterial (MCLOM) to achieve excellent bandgap characteristics and energy absorption capacities. The MCLOMs are constructed by considering the high impedance mismatch of lattice structures, the spatial deformability of origami structures, and the tunability of the components in multi-scale composite materials. Firstly, elastic wave propagation characteristics are analyzed in the Bloch wave framework, revealing the realization of complete bandgaps and their generation mechanism by mode shape analysis and transmission spectrum. Subsequently, an optimization framework integrating the particle swarm optimization (PSO) algorithm is developed to maximize the first bandgap’s bandwidth by adjusting various component parameters. Under optimal distribution, the proposed metamaterials achieve remarkable improvements of 289% and 271% in the design objectives of two lattice-origami metamaterials with 90∘ dihedral angle compared to the initial distribution. It can be demonstrated that non-uniform distributions of multi-scale composite materials are dramatically effective for broadband wave attenuation. Additionally, while striving to widen the bandgap, the energy absorption capacities of structures are also crucial. The effect of the distribution of multi-scale composite materials with the optimal bandgap on the energy absorption performance is investigated. The results reveal that the optimal distribution of the lattice-origami metamaterials yields notable improvements of 48.26% and 34.86% under low-velocity impact, and 37.41% and 25.19% under medium-velocity impact. This work presents innovative concepts and approaches for devising and implementing novel dual-functional metamaterials, undoubtedly propelling the continual progress of material science and engineering technology in the times ahead.
Mechanical Metamaterials (MMs) are artificially designed structures with extraordinary properties that are dependent on micro architectures and spatial tessellations of unit cells, rather than constitutive compositions. They have demonstrated promising and attractive application potentials in practical engineering. Recently, how to rationally design novel MMs and discover their multifunctional behaviors has received tremendous discussions with rapid progress, particularly in the last ten years with an enormous increase of publications and citations. Herein, we present a comprehensive overview of considerable advances of MMs, including critical focuses at different scales, forward and inverse design mechanisms with optimization formulations, micro architectures of unit cells, and their spatial tessellations in discovering novel MMs and future prospects. The implications in clarifying the four focuses at levels from the global to the physical in MMs are highlighted, that is, unique structures designed for unique functions, unique micro unit cells placed in unique locations, unique micro unit cells designed for unique properties and unique micro unit cells evaluated by unique mechanisms. We examine the inverse designs of MMs with intrinsic mechanisms of structure-property driven characteristics to achieve unprecedented behaviors, which are involved into material designs and multiscale designs. The former primarily optimizes micro architectures to explore novel MMs, and the latter focuses on micro architectures and spatial tessellations to promote multifunctional applications of MMs in engineering. Finally, we propose several promising research topics with serious challenges in design formulations, micro architectures, spatial tessellations and industrial applications.
Introducing origami patterns to the thin-walled tubes has been proven to effectively enhance the energy-absorbing capacity. However, the energy-absorbing capacity improved by pattern design alone has reached the ceiling and is difficult to improve further. In the present study, we provided a brand new technical route to solve this problem. We firstly designed a pre-folded thin-walled tube with uniform structure as the reference structure. We then made the wall thickness of the reference structure unhomogenized. Keeping the total mass of the tube unchanged, we thickened the wall thickness of the local region with relatively large plastic deformation, at the same time thinned the wall thickness of the local region with relatively small plastic deformation. Such non-uniform design makes the overall deformation of the thin-wall tube more harmonize, not only significantly increasing the specific energy absorption (SEA), but also decreasing the peak crushing force (PCF), achieving a superior combination of SEA and PCF.
We investigate the reconfigurability and tunability of the tessellation of Tachi-Miura Polyhedron (TMP), an origami-based cellular structure composed of bellows-like unit cells. Lattice-based three-dimensional mechanical metamaterials have recently received significant scientific interest due to their superior and unique mechanical performance compared to conventional materials. However, it is often challenging to achieve tunability and reconfigurability from these metamaterials, since their geometry and functionality tend to be pre-determined in the design and fabrication stage. Here, we utilize TMP's highly versatile phase-transforming and tessellating capabilities to design reconfigurable metamaterial architecture with tunable mechanical properties. The theoretical analyses and experiments with heat processing discover the wide range of the in-situ tunability of the metamaterial – specifically orders of magnitude change in effective density, Young's modulus, and Poisson's ratio – after its fabrication within the elastic deformation regime. We also witness a rather unique behavior of the inverse correlation between effective density and stiffness. This mechanical platform paves the way to design the metamaterial that can actively adapt to various external environments.
As an art of paper folding, origami has been widely explored by artists for centuries. Only in recent decades has it gained attention from mathematicians and engineers for its complex geometry and rich mechanical properties. The surge of origami-inspired metamaterials has opened a new window for designing materials and structures. Typically, to build origami structures, a sheet of material is folded according to the creaselines that are marked with compliant mechanisms. However, despite their importance in origami fabrication, such compliant mechanisms have been relatively unexplored in the setting of origami metamaterials. In this study, we explore the relationship between the design parameters of compliant mechanisms and origami mechanical properties. In particular, we employ single hinge crease and Kresling origami, representative examples of rigid and non-rigid origami units, fabricated using a double-stitch perforation compliant mechanism design. We conduct axial compression tests using different crease parameters and fit the result into the bar-hinge origami model consisting of axial and torsional springs. We extract the relationship between the spring coefficients and crease parameters using Gaussian process regression. Our result shows that the change in the crease parameter contributes significantly to each spring element in a very different manner, which suggests the fine tunability of the compliant mechanisms depending on the mode of deformation. In particular, the spring stiffness varies with the crease parameter differently for rigid and non-rigid origami, even when the same crease parameter is tuned. Furthermore, we report that the qualitative static response of the Kresling origami can be tuned between monostable and bistable, or linear and nonlinear, by only changing the crease parameter while keeping the same fold pattern geometry. We believe that our compiled result proffers a library and guidelines for choosing compliant mechanisms for the creases of origami mechanical metamaterials.
Inflatable space capsules can be compactly folded to a small volume during launch and then deployed in space to create a large enclosed place for astronauts and equipment. Current inflatable space capsules are usually made of soft composite materials and need to be rigidized after deployment, but the rigidization techniques to date cannot meet the requirements of high stiffness and low thermal expansion simultaneously. The study on cylindrical transformable volume structures based on metals is also limited due to the large in-plane deformation during manufacturing and deployment. Here, we propose a novel inflatable metallic cylinder based on the Kresling origami pattern which has a large deployment ratio and high stiffness without rigidization. The folding and deployment process of the cylinder with varying geometric parameters and inflation rates are investigated through numerical simulation that is validated by experiments, from which the deformation process, maximum plastic strain, and the deployment ratio are unveiled. The results show that the maximum plastic strain reduces with the increase in the total number of creases in the cylinder and their transition arc radius, but a large number of creases will lead to a lower deployment ratio. To achieve a deployment ratio of 3.35 which is comparable with those of the state-of-the-art inflatable space capsules, the maximum plastic strain is kept below 0.18. This proposed metallic origami cylinder thus shows great potentials in the application of space capsules.
