Soft network materials with isotropic negative Poisson's ratios over large strains

Customized surface adhesive and wettability properties of conformal electronic devices

Conformal and body-adaptive electronics have revolutionized the way we interact with technology, ushering in a new era of wearable devices that can seamlessly integrate with our daily lives. However, the inherent mismatch between artificially synthesized materials and biological tissues (caused by irregular skin fold, skin hair, sweat, and skin grease) needs to be addressed, which can be realized using body-adaptive electronics by rational design of their surface adhesive and wettability properties. Over the past few decades, various approaches have been developed to enhance the conformability and adaptability of bioelectronics by (i) increasing flexibility and reducing device thickness, (ii) improving the adhesion and wettability between bioelectronics and biological interfaces, and (iii) refining the integration process with biological systems. Successful development of a conformal and body-adaptive electronic device requires comprehensive consideration of all three aspects. This review starts with the design strategies of conformal electronics with different surface adhesive and wettability properties. A series of conformal and body-adaptive electronics used in the human body under both dry and wet conditions are systematically discussed. Finally, the current challenges and critical perspectives are summarized, focusing on promising directions such as telemedicine, mobile health, point-of-care diagnostics, and human-machine interface applications.

Suppressing torsional buckling in auxetic meta-shells

Take a thin cylindrical shell and twist it; it will buckle immediately. Such unavoidable torsional buckling can lead to systemic failure, for example by disrupting the blood flow through arteries. In this study, we prevent this torsional buckling instability using a combination of auxeticity and orthotropy in cylindrical metamaterial shells with a holey pattern. When the principal axes of the orthotropic meta-shell are relatively aligned with that of the compressive component of the applied stress during twisting, the meta-shell uniformly shrinks in the radial direction as a result of a local buckling instability. This shrinkage coincides with a softening-stiffening transition that leads to ordered stacking of unit cells along the compressive component of the applied stress. These transitions due to local instabilities circumvent the usual torsional instability even under a large twist angle. This study highlights the potential of tailoring anisotropy and programming instabilities in metamaterials, with potential applications in designing mechanical elements for soft robotics, biomechanics or fluidics. As an example of such applications, we demonstrate soft torsional compressor for generating pulsatile flows through a torsion release mechanism.

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.

3D Tiled Auxetic Metamaterial: A New Family of Mechanical Metamaterial with High Resilience and Mechanical Hysteresis

For artificial materials, desired properties often conflict. For example, engineering materials often achieve high energy dissipation by sacrificing resilience and vice versa, or desired auxeticity by losing their isotropy, which limits their performance and applications. To solve these conflicts, a strategy is proposed to create novel mechanical metamaterial via 3D space filling tiles with engaging key-channel pairs, exemplified via auxetic 3D keyed-octahedron-cuboctahedron metamaterials. This metamaterial shows high resilience while achieving large mechanical hysteresis synergistically under large compressive strain. Especially, this metamaterial exhibits ideal isotropy approaching the theoretical limit of isotropic Poisson's ratio, -1, as rarely seen in existing 3D mechanical metamaterials. In addition, the new class of metamaterials provides wide tunability on mechanical properties and behaviors, including an unusual coupled auxeticity and twisting behavior under normal compression. The designing methodology is illustrated by the integral of numerical modeling, theoretical analysis, and experimental characterization. The new mechanical metamaterials have broad applications in actuators and dampers, soft robotics, biomedical materials, and engineering materials/systems for energy dissipation.

Flexible Energy Storage Devices to Power the Future

The field of flexible electronics is a crucial driver of technological advancement, with a strong connection to human life and a unique role in various areas such as wearable devices and healthcare. Consequently, there is an urgent demand for flexible energy storage devices (FESDs) to cater to the energy storage needs of various forms of flexible products. FESDs can be classified into three categories based on spatial dimension, all of which share the features of excellent electrochemical performance, reliable safety, and superb flexibility. In this review, the application scenarios of FESDs are introduced and the main representative devices applied in disparate fields are summarized first. More specifically, it focuses on three types of FESDs in matched application scenarios from both structural and material aspects. Finally, the challenges that hinder the practical application of FESDs and the views on current barriers are presented.

Omnidirectional Configuration of Stretchable Strain Sensor Enabled by the Strain Engineering with Chiral Auxetic Metamaterial

An electromechanical interface plays a pivotal role in determining the performance of a stretchable strain sensor. The intrinsic mechanical property of the elastomer substrate prevents the efficient modulation of the electromechanical interface, which limits the further evolution of a stretchable strain sensor. In this study, a chiral auxetic metamaterial (CAM) is incorporated into the elastomer substrate of a stretchable strain sensor to override the deformation behavior of the pristine device and regulate the device performance. The tunable isotropic Poisson's ratio (from 0.37 to -0.25) achieved by the combination of CAM and elastomer substrate endows the stretchable strain sensor with significantly enhanced sensitivity (53-fold improvement) and excellent omnidirectional sensing ability. The regulation mechanism associated with crack propagation on the deformed substrate is also revealed with finite element simulations and experiments. The demonstration of on-body monitoring of human physiological signals and a smart training assistant for trampoline gymnastics with the CAM-incorporated strain sensor further illustrates the benefits of omnidirectionally enhanced performance.

Auxetic Kirigami Metamaterials upon Large Stretching

Auxetic kirigami metamaterials (KMs) attain negative Poisson's ratios with periodic slender cuts on thin sheets. The existing thin auxetic KMs forfeit auxeticity under large tensions because their auxeticity mainly arises from in-plane deformation, but out-of-plane buckling could arise to cause large deviations, and thicker KMs would suffer from stress failure. This paper proposes a novel family of KMs that can realize and retain auxeticity for up to 0.50 applied strains by fully exploiting out-of-plane buckling in the design model. Numerical and experimental results show that the designed KMs possess unique properties that are not exhibited by existing KMs, including a wide range of negative Poisson's ratios with designable variation modes under different applied strains, sheet thickness-insensitive auxeticity, and excellent shape recoverability. A potential application is exemplified with a scenario that they are designed as a stretchable display without image distortions under large tensions. The proposed auxetic KMs open new opportunities for the design of specific functional devices in areas of compliant robotics, bio-medical devices, and flexible electronics.

Dual-Phase Inspired Soft Electronic Sensors with Programmable and Tunable Mechanical Properties

Wearable and stretchable sensors are important components to strictly monitor the behavior and health of humans and attract extensive attention. However, traditional sensors are designed with pure horseshoes or chiral metamaterials, which restrict the biological tissue engineer applications due to their narrow regulation ranges of the elastic modulus and the poorly adjustable Poisson's ratio. Inspired by the biological spiral microstructure, a dual-phase metamaterial (chiral-horseshoes) is designed and fabricated in this work, which possesses wide and programmable mechanical properties by tailoring the geometrical parameters. Experimental, numerical, and theoretical studies are conducted, which reveal that the designed microstructures can reproduce mechanical properties of most natural animals such as frogs, snakes, and rabbits skin. Furthermore, a flexible strain sensor with the gauge factor reaching 2 under 35% strain is fabricated, which indicates that the dual-phase metamaterials have a stable monitoring ability and can be potentially applied in the electronic skin. Finally, the flexible strain sensor is attached on the human skin, and it can successfully monitor the physiological behavior signals under various actions. In addition, the dual-phase metamaterial could combine with artificial intelligence algorithms to fabricate a flexible stretchable display. The dual-phase metamaterial with negative Poisson's ratio could decrease the lateral shrinkage and image distortion during the stretching process. This study offers a strategy for designing the flexible strain sensors with programmable, tunable mechanical properties, and the fabricated soft and high-precision wearable strain sensor can accurately monitor the skin signals under different human motions and potentially be applied for flexible display.

Designing Hierarchical Soft Network Materials with Developable Lattice Nodes for High Stretchability

Soft network materials (SNMs) represent one of the best candidates for the substrates and the encapsulation layers of stretchable inorganic electronics, because they are capable of precisely customizing the J-shaped stress-strain curves of biological tissues. Although a variety of microstructures and topologies have been exploited to adjust the nonlinear stress-strain responses of SNMs, the stretchability of most SNMs is hard to exceed 100%. Designing novel high-strength SNMs with much larger stretchability (e.g., >200%) than existing SNMs and conventional elastomers remains a challenge. This paper develops a class of hierarchical soft network materials (HSNMs) with developable lattice nodes, which can significantly improve the stretchability of SNMs without any loss of strength. The effects of geometric parameters, lattice topologies, and loading directions on the mechanical properties of HSNMs are systematically discussed by experiments and numerical simulations. The proposed node design strategy for SNMs is also proved to be widely applicable to different constituent materials, including polymers and metals.

The rise of mechanical metamaterials: Auxetic constructs for skin wound healing

Auxetic materials are known for their unique ability to expand/contract in multiple directions when stretched/compressed. In other words, they exhibit a negative Poisson's ratio, which is usually positive for most of materials. This behavior appears in some biological tissues such as human skin, where it promotes wound healing by providing an enhanced mechanical support and facilitating cell migration. Skin tissue engineering has been a growing research topic in recent years, largely thanks to the rapid development of 3D printing techniques and technologies. The combination of computational studies with rapid manufacturing and tailored designs presents a huge potential for the future of personalized medicine. Overall, this review article provides a comprehensive overview of the current state of research on auxetic constructs for skin healing applications, highlighting the potential of auxetics as a promising treatment option for skin wounds. The article also identifies gaps in the current knowledge and suggests areas for future research. In particular, we discuss the designs, materials, manufacturing techniques, and also the computational and experimental studies on this topic.

Flexible Metamaterial Electronics

Over the last decade, extensive efforts have been made on utilizing advanced materials and structures to improve the properties and functionalities of flexible electronics. While the conventional ways are approaching their natural limits, a revolutionary strategy, namely metamaterials, is emerging toward engineering structural materials to break the existing fetters. Metamaterials exhibit supernatural physical behaviors, in aspects of mechanical, optical, thermal, acoustic, and electronic properties that are inaccessible in natural materials, such as tunable stiffness or Poisson's ratio, manipulating electromagnetic or elastic waves, and topological and programmable morphability. These salient merits motivate metamaterials as a brand-new research direction and have inspired extensive innovative applications in flexible electronics. Here, such a groundbreaking interdisciplinary field is first coined as "flexible metamaterial electronics," focusing on enhancing and innovating functionalities of flexible electronics via the design of metamaterials. Herein, the latest progress and trends in this infant field are reviewed while highlighting their potential value. First, a brief overview starts with introducing the combination of metamaterials and flexible electronics. Then, the developed applications are discussed, such as self-adaptive deformability, ultrahigh sensitivity, and multidisciplinary functionality, followed by the discussion of potential prospects. Finally, the challenges and opportunities facing flexible metamaterial electronics to advance this cutting-edge field are summarized.

An Innovative Auxetic Honeycomb Sandwich Tube: Fabrication and Mechanical Properties

In this study, based on the free-rolling mechanism of the auxetic honeycomb, a honeycomb cylindrical shell was successfully prepared to overcome the fracture problem of the hexagonal honeycomb during rolling. Auxetic honeycomb sandwich tubes (AHSTs) with a variable Poisson’s ratio were fabricated by molding and bonding. A Poisson’s ratio model of the auxetic honeycomb core was developed based on the strain increment ratio of the deformed honeycomb and validated using computed tomography (CT). Four failure modes (progressive stable fold mode I, unstable local buckling mode II, transverse shearing mode III, and mid-length collapse mode IV) of the AHST were summarized by comparing the deformation behavior and force–displacement curves with different geometric parameters. When the aspect ratio R is greater than 3, the AHST will be more easily damaged in instability (Mode IV). Static compression tests showed that the peak force (PF) and crushing force efficiency (CFE) of the AHST were higher than those of the CFRP thin-walled tube of the same diameter by 78% and 115%, respectively. Therefore, the AHST has excellent mechanical properties and it is feasible to use the auxetic honeycomb as a core for sandwich structures.

Toughened Hydrogels for 3D Printing of Soft Auxetic Structures

Materials with negative Poisson's ratio have attracted considerable attention and offered high potential applications as biomedical devices due to their ability to expand in every direction when stretched. Although negative Poisson's ratio has been obtained in various base materials such as metals and polymers, there are very limited works on hydrogels due to their intrinsic brittleness. Herein, we report the use of methacrylated cellulose nanocrystals (CNCMAs) as a macro-cross-linking agent in poly(2-hydroxyethyl methacrylate) (pHEMA) hydrogels for 3D printing of auxetic structures. Our developed CNCMA-pHEMA hydrogels exhibit significant improvements in mechanical properties, which is attributed to the coexistence of multiple chemical and physical interactions between the pHEMA and CNCMAs. Structures printed by using CNCMA-pHEMA hydrogels show auxetic behavior with greatly enhanced toughness and stretchability compared to the hydrogel with a traditional cross-linking agent. Such strong and tough auxetic hydrogels would contribute toward establishing advanced flexible implantable devices such as biodegradable oesophageal self-expandable stents.

Design and evaluation of 3D-printed auxetic structures coated by CWPU/graphene as strain sensor

A strain sensor characterized by elasticity has recently been studied in various ways to be applied to monitoring humans or robots. Here, 4 types of 3D-printed auxetic lattice structures using thermoplastic polyurethane as raw material were characterized: truss and honeycomb with positive Poisson's ratio and chiral truss and re-entrant with negative Poisson's ratio. Each structure was fabricated as a flexible and stable strain sensor by coating graphene through a dip-coating process. The fabricated auxetic structures have excellent strength, flexibility, and electrical conductivity desirable for a strain sensor and detect a constant change in resistance at a given strain. The 3D-printed auxetic lattice 4 type structures coated with CWPU/Graphene suggest potential applications of multifunctional strain sensors under deformation.

Regenerating dynamic organs using biomimetic patches

The regeneration of dynamic organs remains challenging because they are intrinsically anisotropic and undergo large volumetric deformation during normal or pathological function. This hampers the durability and applicability of regenerative medicine approaches. To address the challenges of organ dynamics, a new class of patches have emerged with anisotropic and auxetic properties that mimic native tissue biomechanics and accommodate volumetric deformation. Here, we outline the critical design, materials, and processing considerations for achieving optimal patch biomechanics according to target pathology and summarize recent advances in biomimetic patches for dynamic organ regeneration. Furthermore, we discuss the challenges and opportunities which, if overcome, would open up new applications in organ regeneration and expedite the clinical translation of patch-based therapeutics.

A programmable and skin temperature-activated electromechanical synergistic dressing for effective wound healing

Mechanical regulation and electric stimulation hold great promise in skin tissue engineering for manipulating wound healing. However, the complexity of equipment operation and stimulation implementation remains an ongoing challenge in clinical applications. Here, we propose a programmable and skin temperature-activated electromechanical synergistic wound dressing composed of a shape memory alloy-based mechanical metamaterial for wound contraction and an antibacterial electret thin film for electric field generation. This strategy is successfully demonstrated on rats to achieve effective wound healing in as short as 4 and 8 days for linear and circular wounds, respectively, with a statistically significant over 50% improvement in wound closure rate versus the blank control group. The optimally designed electromechanical synergistic stimulation could regulate the wound microenvironment to accelerate healing metabolism, promote wound closure, and inhibit infection. This work provided an effective wound healing strategy in the context of a programmable temperature-responsive, battery-free electromechanical synergistic biomedical device.

Materials for Smart Soft Actuator Systems

In contrast to conventional hard actuators, soft actuators offer many vivid advantages, such as improved flexibility, adaptability, and reconfigurability, which are intrinsic to living systems. These properties make them particularly promising for different applications, including soft electronics, surgery, drug delivery, artificial organs, or prosthesis. The additional degree of freedom for soft actuatoric devices can be provided through the use of intelligent materials, which are able to change their structure, macroscopic properties, and shape under the influence of external signals. The use of such intelligent materials allows a substantial reduction of a device's size, which enables a number of applications that cannot be realized by externally powered systems. This review aims to provide an overview of the properties of intelligent synthetic and living/natural materials used for the fabrication of soft robotic devices. We discuss basic physical/chemical properties of the main kinds of materials (elastomers, gels, shape memory polymers and gels, liquid crystalline elastomers, semicrystalline ferroelectric polymers, gels and hydrogels, other swelling polymers, materials with volume change during melting/crystallization, materials with tunable mechanical properties, and living and naturally derived materials), how they are related to actuation and soft robotic application, and effects of micro/macro structures on shape transformation, fabrication methods, and we highlight selected applications.

4D Printing of Bioinspired Absorbable Left Atrial Appendage Occluders: A Proof-of-Concept Study

The significant mismatch of mechanical properties between the implanted medical device and biological tissue is prone to cause wear and even perforation. In addition, the limited biocompatibility and nondegradability of commercial Nitinol-based occlusion devices can easily lead to other serious complications, such as allergy and corrosion. The present study aims to develop a 4D printed patient-specific absorbable left atrial appendage occluder (LAAO) that can match the deformation of left atrial appendage (LAA) tissue to reduce complications. The desirable bioinspired network is explored by iterative optimization to mimic the stress-strain curve of LAA tissue and LAAOs are designed based on the optimal network. In vitro degradation tests are carried out to evaluate the effects of degradation on mechanical properties. In addition, 48 weeks of long-term subcutaneous implantation of the occluder shows favorable biocompatibility, and the 20-cycle compression test demonstrates outstanding durability of LAAO. Besides, a rapid, complete, and remote-controlled 4D transformation process of LAAO is achieved under the trigger of the magnetic field. The deployment of the LAAO in an isolated swine heart initially exhibits its feasibility for transcatheter LAA occlusion. To the best of our knowledge, this is the first demonstration of the 4D printed LAA occlusion device. It is worth noting that the bioinspired design concept is not only applicable to occlusion devices, but also to many other implantable medical devices, which is conducive to reducing complications, and a broad range of appealing application prospects can be foreseen.

The 3D-Printed Honeycomb Metamaterials Tubes with Tunable Negative Poisson's Ratio for High-Performance Static and Dynamic Mechanical Properties

The synthesized understanding of the mechanical properties of negative Poisson’s ratio (NPR) convex–concave honeycomb tubes (CCHTs) under quasi-static and dynamic compression loads is of great significance for their multifunctional applications in mechanical, aerospace, aircraft, and biomedical fields. In this paper, the quasi-static and dynamic compression tests of three kinds of 3D-printed NPR convex–concave honeycomb tubes are carried out. The sinusoidal honeycomb wall with equal mass is used to replace the cell wall structure of the conventional square honeycomb tube (CSHT). The influence of geometric morphology on the elastic modulus, peak force, energy absorption, and damage mode of the tube was discussed. The experimental results show that the NPR, peak force, failure mode, and energy absorption of CCHTs can be adjusted by changing the geometric topology of the sinusoidal element. Through the reasonable design of NPR, compared with the equal mass CSHTs, CCHTs could have the comprehensive advantages of relatively high stiffness and strength, enhanced energy absorption, and damage resistance. The results of this paper are expected to be meaningful for the optimization design of tubular structures widely used in mechanical, aerospace, vehicle, biomedical engineering, etc.

Two-dimensional arsenene polymorph beyond the auxetic foam: high mechanical sensitivity and large, negative NPR

Single-layer δ-As and γ-P have unique atomic arrangement, which belong to the Pmc21 and Pbcm space groups, respectively. Because of the coupling hinge structure, the physical properties of the two materials have obvious anisotropy. In this paper, we report the mechanical properties of the single-layer δ-As and γ-P. That is, their inherent negative Poisson ratio (NPR) is -0.708 and -0.226, respectively. Surprisingly, the absolute value of the NPR of δ-As is approximately 26.2 times greater than that of single-layer black phosphorus (the NPR of single-layer black phosphorus is -0.027), and remains invariant at a certain strain range. Thus, single-layer δ-As will have huge potential applications in nanosensors and electronic wearable devices due to its invariant and large, negative NPR.

Factors affecting the negative Poisson's ratio of black phosphorus and black arsenic: electronic effects

Negative Poisson's ratio (NPR) materials (when stretched longitudinally, the thickness of these materials increases along the lateral direction) are widely used in engineering because of their good resistance to shear, denting, and fracture. Observance of a negative Poisson's ratio (NPR) in two-dimensional (2D) single-layer materials presently has two explanations. The first, from mechanical principles, is that it derives from the presence of a special structure (hinge structure), such as in single-layer black phosphorus (BP) or black arsenic (β-As). The second, from electronic effects, is that it derives from (non-hinge-like) planar honeycomb structures and transition-metal dichalcogenides, MX2. Through first-principle calculations, we show that 2D single-layer materials with a hinge structure also have distinct electronic effects, similar to those observed from 2D planar honeycomb materials. Under strain, electronic effects of Px orbitals lead to the inherent NPR of the 2D single-layer material with a hinge structure. We discuss the influencing factors of the hinge structure on the NPR and demonstrate that the electronic effects inside the hinge structure are the fundamental factor in determining the inherent NPR.

An Overview of Additive Manufacturing of Polymers and Associated Composites

Additive manufacturing is rapidly evolving and opening new possibilities for many industries. This article gives an overview of the current status of additive manufacturing with polymers and polymer composites. Various types of reinforcements in polymers and architectured cellular material printing including the auxetic metamaterials and the triply periodic minimal surface structures are discussed. Finally, applications, current challenges, and future directions are highlighted here.

Tensegrity Modelling and the High Toughness of Spider Dragline Silk

This work establishes a tensegrity model of spider dragline silk. Tensegrity systems are ubiquitous in nature, being able to capture the mechanics of biological shapes through simple and effective modes of deformation via extension and contraction. Guided by quantitative microstructural characterization via air plasma etching and low voltage scanning electron microscopy, we report that this model is able to capture experimentally observed phenomena such as the Poisson effect, tensile stress-strain response, and fibre toughness. This is achieved by accounting for spider silks' hierarchical organization into microfibrils with radially variable properties. Each fibril is described as a chain of polypeptide tensegrity units formed by crystalline granules operating under compression, which are connected to each other by amorphous links acting under tension. Our results demonstrate, for the first time, that a radial variability in the ductility of tensegrity chains is responsible for high fibre toughness, a defining and desirable feature of spider silk. Based on this model, a discussion about the use of graded tensegrity structures for the optimal design of next-generation biomimetic fibres is presented.

Numerical Investigation of Auxetic Textured Soft Strain Gauge for Monitoring Animal Skin

Recent advances in hyperelastic materials and self-sensing sensor designs have enabled the creation of dense compliant sensor networks for the cost-effective monitoring of structures. The authors have proposed a sensing skin based on soft polymer composites by developing soft elastomeric capacitor (SEC) technology that transduces geometric variations into a measurable change in capacitance. A limitation of the technology is in its low gauge factor and lack of sensing directionality. In this paper, we propose a corrugated SEC through surface texture, which provides improvements in its performance by significantly decreasing its transverse Poisson's ratio, and thus improving its sensing directionality and gauge factor. We investigate patterns inspired by auxetic structures for enhanced unidirectional strain monitoring. Numerical models are constructed and validated to evaluate the performance of textured SECs, and to study their performance at monitoring strain on animal skin. Results show that the auxetic patterns can yield a significant increase in the overall gauge factor and decrease the stress experienced by the animal skin, with the re-entrant hexagonal honeycomb pattern outperforming all of the other patterns.

Mechanically-Guided Structural Designs in Stretchable Inorganic Electronics

Over the past decade, the area of stretchable inorganic electronics has evolved very rapidly, in part because the results have opened up a series of unprecedented applications with broad interest and potential for impact, especially in bio-integrated systems. Low modulus mechanics and the ability to accommodate extreme mechanical deformations, especially high levels of stretching, represent key defining characteristics. Most existing studies exploit structural material designs to achieve these properties, through the integration of hard inorganic electronic components configured into strategic 2D/3D geometries onto patterned soft substrates. The diverse structural geometries developed for stretchable inorganic electronics are summarized, covering the designs of functional devices and soft substrates, with a focus on fundamental principles, design approaches, and system demonstrations. Strategies that allow spatial integration of 3D stretchable device layouts are also highlighted. Finally, perspectives on the remaining challenges and open opportunities are provided.

Toward Imperfection-Insensitive Soft Network Materials for Applications in Stretchable Electronics

Development of stretchable devices with mechanical responses that mimic those of biological tissues/organs is of particular importance for the long-term biointegration, as the discomfort induced by the mechanical mismatch can be minimized. Recent works have established the bioinspired designs of soft network materials that can precisely reproduce the unconventional J-shaped stress-strain curves of human skin at different regions. Existing studies mostly focused on the design, fabrication, and modeling of perfect soft network materials. When utilized as the substrates of biointegrated electronics, the soft network designs, however, often need to incorporate deterministic holes, a type of imperfection, to accommodate hard, inorganic electronic components. Understanding of the effect of hole imperfections on the mechanical properties of soft network materials is thereby essential in practical applications. This paper presents a combined experimental and computational study of the stretchability and elastic modulus of imperfect soft network materials consisting of circular holes with a variety of diameters. Both the size and location of the circular-hole imperfections are shown to have profound influences on the stretchability. Based on these results, design guidelines of imperfection-insensitive network materials are introduced. For the imperfections that result in an evident reduction of stretchability, an effective reinforcement approach is presented by enlarging the width of horseshoe microstructures at strategic locations, which can enhance the stretchability considerably. A stretchable and imperfection-insensitive integrated device with a light-emitting diode embedded in the network material serves a demonstrative application.

3D Printing of Auxetic Metamaterials with Digitally Reprogrammable Shape

Two-dimensional lattice structures with specific geometric features have been reported to have a negative Poisson's ratio, termed as auxetic metamaterials, that is, stretching-induced expansion in the transversal direction. In this paper, we designed a novel auxetic metamaterial; by utilizing the shape memory effect of the constituent materials, the in-plane moduli and Poisson's ratios can be continuously tailored. During deformation, the curved meshes ensure the rotation of the mesh joints to achieve auxetics. The rotations of these mesh joints are governed by the mesh curvature, which continuously changes during deformation. Because of the shape memory effect, the mesh curvature after printing can be programmed, which can be used to tune the rotation of the mesh joints and the mechanical properties of auxetic metamaterial structures, including Poisson's ratios, moduli, and fracture strains. Using the finite element method, the deformation of these auxetic meshes was analyzed. Finally, we designed and fabricated gradient/digital patterns and cylindrical shells and used the auxetics and shape memory effects to reshape the printed structures.

Geometric Mechanics of Origami Patterns Exhibiting Poisson's Ratio Switch by Breaking Mountain and Valley Assignment

Exploring the configurational space of specific origami patterns [e.g., Miura-ori (flat surface with parallelogram crease patterns), eggbox] has led to notable advances in science and technology. To augment the origami design space, we present a pattern, named "Morph," which combines the features of its parent patterns. We introduce a four-vertex origami cell that morphs continuously between a Miura mode and an eggbox mode, forming an homotopy class of configurations. This is achieved by changing the mountain and valley assignment of one of the creases, leading to a smooth switch through a wide range of negative and positive Poisson's ratios. We present elegant analytical expressions of Poisson's ratios for both in-plane stretching and out-of-plane bending and find that they are equal in magnitude and opposite in sign. Further, we show that by combining compatible unit cells in each of the aforementioned modes through kinematic bifurcation, we can create hybrid origami patterns that display unique properties, such as topological mode locking and tunable switching of Poisson's ratio.

Shape-morphing architected sheets with non-periodic cut patterns

We investigate the out-of-plane shape morphing capability of single-material elastic sheets with architected cut patterns that result in arrays of tiles connected by flexible hinges. We demonstrate that a non-periodic cut pattern can cause a sheet to buckle into three-dimensional shapes, such as domes or patterns of wrinkles, when pulled at specific boundary points. These global buckling modes are observed in experiments and rationalized by an in-plane kinematic analysis that highlights the role of the geometric frustration arising from non-periodicity. The study focuses on elastic sheets, and is later extended to elastic-plastic materials to achieve shape retention. Our work illustrates a scalable route towards the fabrication of three-dimensional objects with nonzero Gaussian curvature from initially-flat sheets.