3D soft metamaterials with negative Poisson's ratio

Acoustic metamaterials for remote manipulation of large objects in water

Acoustic metamaterials have recently been applied to assist in the remote manipulation of objects in air, showing remarkable potential to alleviate the constraints of non-metamaterial-based acoustic manipulation methods in terms of object size and the force degree of freedom. To extend this approach to underwater manipulation, in this work, we develop a new type of underwater acoustic metamaterial based on a metal-resin composite, offering submillimeter scale feature resolution and high acoustic impedance contrast with water. By designing the surface patterns of the metamaterial, we demonstrate the remote acoustic manipulation of in-water large objects (>20 wavelengths) with 3D translational and rotational degrees of freedom. We then proposed two methods, surface pattern superimposition and frequency multiplexing, to integrate different manipulation forces within a single metamaterial patch. Additionally, we demonstrate more examples of complex object manipulation using multiple metamaterial patches and transducers, such as multi-object, multi-path, non-invasive, and 3D underwater manipulation. Our metamaterial-assisted remote underwater acoustic manipulation will have broad applications in underwater robot actuation, vehicle transportation, manufacturing, drug delivery and minimally invasive surgery.

Tribological metamaterial: how feathers reduce drag and friction through hidden energy dissipation structures

The lateral moving resistance of a liquid droplet on a solid surface generally increases with velocity and is dominated by the non-viscous wetting line friction. Many superhydrophobic man-made and biological surfaces have minimal, nevertheless speed-sensitive, water droplet friction, limiting their potential to reduce drag at high speeds in natural situations. Using an in situ surface force apparatus, we demonstrated low and remarkably speed-insensitive (over 300-fold) water bridge sliding friction on a goose feather vane. Detailed analyses suggest a dominant, hidden energy dissipation channel probably related to the deformation and elastic recovery of feather's characteristic metamaterial-like structure, which also results in feather's speed insensitive (from 0.1 to 1 mm s-1) ultra-low dry sliding friction coefficient observed in this study (approx. 0.07). The new insights gained have the potential to motivate novel approaches to the design of all-weather and speed-insensitive low-friction surfaces with practical applications in aviation and lubrication technology.

4D Printed Shape Memory Polyimide Composite Aerogels with High Recovery Stress for Load Driving

Shape memory polyimide aerogels with lightweight, high-temperature resistance, and excellent shape memory performance are ideal materials for intelligent structural components of aerospace. However, their low recovery stress has been a significant barrier to their practical use, particularly in driving structural deformations. Herein, we have prepared a 4D printed shape memory polyimide/polyimide nanofiber (PI/PIF) composite aerogel with high recovery stress and excellent shape memory performance for load driving at high temperatures. The PIF enhances ink printability and mechanical properties, allowing for the design of PI/PIF aerogels with double-curve macrostructures by 3D printing technology. During the shape programming process, double-curve macrostructures can absorb elastic strain energy to enhance recovery stress. Consequently, the printed PI/PIF aerogels exhibit a low density (0.09 g cm-3) and a high specific recovery stress (2.8 N mm kg-1) and can drive the deformation of 10 times their own weight. The proposed aerogel is expected to expand the application of lightweight shape memory materials for driving components in aerospace.

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

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

Sign-Switchable Poisson's Ratio Design for Bimodal Strain-to-Electrical Signal Transducing Device

Stretchable electronic devices that conduct strain-related electronic performances have drawn extensive attention, functioning as mechanical sensors, actuators, and stretchable conductors. Although strain-insensitive or strain-responsive nature is well-achieved separately, it remains challenging to combine these two characteristics in one single device, which will offer versatile adaptability in various working situations. Herein, a hybrid material with sign-switchable Poisson's ratio (SSPR) is developed by combining a phase-change gel based reentrantreentrant honeycomb pattern and a polydimethylsiloxane film. The phase-change gel featuring thermally-regulated Young's modulus enables the hybrid material to switch between negative and positive Poisson's ratios. After integrating with a pre-stretched silver nanowires film, the obtained stretchable device performs bimodal strain-to-electrical signal transducing (Bi-SET) functions, in which the SSPR-dominated strain-resistance response switches between strain-dependent and strain-insensitive behaviors. As a proof of concept, a mode-switchable grasping system is constructed using a Bi-SET device-based controller, enabling the adaptation of grasping behaviors to various target objects.

3D polycatenated architected materials

Architected materials derive their properties from the geometric arrangement of their internal structural elements. Their designs rely on continuous networks of members to control the global mechanical behavior of the bulk. In this study, we introduce a class of materials that consist of discrete concatenated rings or cage particles interlocked in three-dimensional networks, forming polycatenated architected materials (PAMs). We propose a general design framework that translates arbitrary crystalline networks into particle concatenations and geometries. In response to small external loads, PAMs behave like non-Newtonian fluids, showing both shear-thinning and shear-thickening responses, which can be controlled by their catenation topologies. At larger strains, PAMs behave like lattices and foams, with a nonlinear stress-strain relation. At microscale, we demonstrate that PAMs can change their shapes in response to applied electrostatic charges. The distinctive properties of PAMs pave the path for developing stimuli-responsive materials, energy-absorbing systems, and morphing architectures.

Unlocking Auxetic Behavior in Recyclable Thermosetting Foams Enabled by Dynamic Disulfide Cross-linking Strategy

Auxetic foams with a negative Poisson's ratio (NPR) have attracted considerable attention in material engineering due to their outstanding performance in seismic and energy absorption. Nevertheless, thermoplastic auxetic foams are compromised by weak non-covalent crosslinking that diminishes the mechanical strength and durability of foams. Conversely, thermosetting foams with chemical crosslinking, although mechanically robust, face challenges in elaborating auxetic structure and in achieving recyclability. Herein, an alternative approach is proposed to tackle this dilemma by incorporating dynamic disulfide bonds into the polymer network for preparing a thermosetting polyurethane foam with covalent adaptable network. By leveraging the unidirectional multi-effect compression technique, the topological network reorganization of foam is induced, transforming the initial circular open-cell structure into a re-entrant cell structure. This structural transformation endows the foam with stable NPR capability, achieving a minimum Poisson's ratio value of -0.4 within 30% compressive strain. Benefiting from its reinforced network structure, the foam also demonstrates high compressive strength (6.47 MPa) and tensile strength (1.67 MPa). Furthermore, it is recyclable and can be recompressed into thermosetting films. This work offers a straightforward approach to making auxetic thermosetting foams with good mechanical and recyclable properties, which is interesting for the development of high-performance auxetic materials.

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

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

Blueprints of Architected Materials: A Guide to Metamaterial Design for Tissue Engineering

Mechanical metamaterials are rationally designed structures engineered to exhibit extraordinary properties, often surpassing those of their constituent materials. The geometry of metamaterials' building blocks, referred to as unit cells, plays an essential role in determining their macroscopic mechanical behavior. Due to their hierarchical design and remarkable properties, metamaterials hold significant potential for tissue engineering; however their implementation in the field remains limited. The major challenge hindering the broader use of metamaterials lies in the complexity of unit cell design and fabrication. To address this gap, a comprehensive guide is presented detailing the design principles of well-established metamaterials. The essential unit cell geometric parameters and design constraints, as well as their influence on mechanical behavior, are summarized highlighting essential points for effective fabrication. Moreover, the potential integration of artificial intelligence techniques is explored in meta-biomaterial design for patient- and application-specific design. Furthermore, a comprehensive overview of current applications of mechanical metamaterials is provided in tissue engineering, categorized by tissue type, thereby showcasing the versatility of different designs in matching the mechanical properties of the target tissue. This review aims to provide a valuable resource for tissue engineering researchers and aid in the broader use of metamaterials in the field.

Toward mechanical proprioception in autonomously reconfigurable kirigami-inspired mechanical systems

Mechanical metamaterials have recently been exploited as an interesting platform for information storing, retrieval and processing, analogous to electronic devices. In this work, we describe the design and fabrication a two-dimensional (2D) multistable metamaterial consisting of building blocks that can be switched between two distinct stable phases, and which are capable of storing binary information analogous to digital bits. By changing the spatial distribution of the phases, we can achieve a variety of different configurations and tunable mechanical properties (both static and dynamic). Moreover, we demonstrate the ability to determine the phase distribution via simple probing of the dynamic properties, to which we refer as mechanical proprioception. Finally, as a simple demonstration of feasibility, we illustrate a strategy for building autonomous kirigami systems that can receive inputs from their environment. This work could bring new insights for the design of mechanical metamaterials with information processing and computing functionalities. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Harnessing plasticity in sequential metamaterials for ideal shock absorption

Mechanical metamaterials exhibit interesting properties such as high stiffness at low density1-3, enhanced energy absorption3,4, shape morphing5-7, sequential deformations8-11, auxeticity12-14 and robust waveguiding15,16. Until now, metamaterial design has primarily relied on geometry, and materials nonlinearities such as viscoelasticity, fracture and plasticity have been largely left out of the design rationale. In fact, plastic deformations have been traditionally seen as a failure mode and thereby carefully avoided1,3,17,18. Here we embrace plasticity instead and discover a delicate balance between plasticity and buckling instability, which we term 'yield buckling'. We exploit yield buckling to design metamaterials that buckle sequentially in an arbitrary large sequence of steps whilst keeping a load-bearing capacity. We make use of sequential yield buckling to create metamaterials that combine stiffness and dissipation-two properties that are usually incompatible-and that can be used several times. Hence, our metamaterials exhibit superior shock-absorption performance. Our findings add plasticity to the metamaterial toolbox and make mechanical metamaterials a burgeoning technology with serious potential for mass production.

Microstructure-Reconfigured Graphene Oxide Aerogel Metamaterials for Ultrarobust Directional Sensing at Human-Machine Interfaces

Graphene aerogels hold huge promise for the development of high-performance pressure sensors for future human-machine interfaces due to their ordered microstructure and conductive network. However, their application is hindered by the limited strain sensing range caused by the intrinsic stiffness of the porous microstructure. Herein, an anisotropic cross-linked chitosan and reduced graphene oxide (CCS-rGO) aerogel metamaterial is realized by reconfiguring the microstructure from a honeycomb to a buckling structure at the dedicated cross-section plane. The reconfigured CCS-rGO aerogel shows directional hyperelasticity with extraordinary durability (no obvious structural damage after 20 000 cycles at a directional compressive strain of ≤0.7). The CCS-rGO aerogel pressure sensor exhibits an ultrahigh sensitivity of 121.45 kPa-1, an unprecedented sensing range, and robust mechanical and electrical performance. The aerogel sensors are demonstrated to monitor human motions, control robotic hands, and even integrate into a flexible keyboard to play music, which opens a wide application potential in future human-machine interfaces.

On the role of geometric phase in the dynamics of elastic waveguides

The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of geometric phase, which is an additional phase factor occurring in dynamical systems, holds the same meaning across different fields of application, its use and interpretation can acquire important nuances specific to the system of interest. In recent years, the development of quantum topological materials and its extension to classical mechanical systems have renewed the interest in the concept of geometric phase. This review revisits the concept of geometric phase and discusses, by means of either established or original results, its critical role in the design and dynamic behaviour of elastic waveguides. Concepts of differential geometry and topology are put forward to provide a theoretical understanding of the geometric phase and its connection to the physical properties of the system. Then, the concept of geometric phase is applied to different types of elastic waveguides to explain how either topologically trivial or non-trivial behaviour can emerge based on the geometric features of the waveguide. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Auxetic Biomedical Metamaterials for Orthopedic Surgery Applications: A Comprehensive Review

Poisson's ratio in auxetic materials shifts from typically positive to negative, causing lateral expansion during axial tension. This scale-independent characteristic, originating from tailored architectures, exhibits specific physical properties, including energy adsorption, shear resistance, and fracture resistance. These metamaterials demonstrate exotic mechanical properties with potential applications in several engineering fields, but biomedical applications seem to be one of the most relevant, with an increasing number of articles published in recent years, which present opportunities ranging from cellular repair to organ reconstruction with outstanding mechanical performance, mechanical conduction, and biological activity compared with traditional biomedical metamaterials. Therefore, focusing on understanding the potential of these structures and promoting theoretical and experimental investigations into the benefits of their unique mechanical properties is necessary for achieving high-performance biomedical applications. Considering the demand for advanced biomaterial implants in surgical technology and the profound advancement of additive manufacturing technology that are particularly relevant to fabricating complex and customizable auxetic mechanical metamaterials, this review focuses on the fundamental geometric configuration and unique physical properties of negative Poisson's ratio materials, then categorizes and summarizes auxetic material applications across some surgical departments, revealing efficacy in joint surgery, spinal surgery, trauma surgery, and sports medicine contexts. Additionally, it emphasizes the substantial potential of auxetic materials as innovative biomedical solutions in orthopedics and demonstrates the significant potential for comprehensive surgical application in the future.

Hard- and Soft-Coded Strain Stiffening in Metamaterials via Out-of-Plane Buckling Using Highly Entangled Active Hydrogel Elements

Metamaterials show elaborate mechanical behavior such as strain stiffening, which stems from their unit cell design. However, the stiffening response is typically programmed in the design step and cannot be adapted postmanufacturing. Here, we show hydrogel metamaterials with highly programmable strain-stiffening responses by exploiting the out-of-plane buckling of integrated pH-switchable hydrogel actuators. The stiffening upon reaching a certain extension stems from the initially buckled active hydrogel beams. At low strain, the beams do not contribute to the mechanical response under tension until they straighten with a resulting step-function increase in stiffness. In the hydrogel actuator design, the acrylic acid concentration hard-codes the configuration of the metamaterial and range of possible stiffening onsets, while the pH soft-codes the exact stiffening onset point after fabrication. The utilization of out-of-plane buckling to realize subsequent stiffening without the need to deform the passive structure extends the application of hydrogel actuators in mechanical metamaterials. Our concept of out-of-plane buckled active elements that stiffen only under tension enables strain-stiffening metamaterials with high programmability before and after fabrication.

Direction-dependent bending resistance of 3D printed bio-inspired composites with asymmetric 3D articulated tiles

Inspired by the protective armors in nature, composites with asymmetric 3D articulated tiles attached to a soft layer are designed and fabricated via a multi-material 3D printer. The bending resistance of the new designs are characterized via three-point bending experiments. Bending rigidity, strength, and final deflection of the designs are quantified and compared when loaded in two different in-plane and two different out-of-plane directions. It is found that in general, the designs with articulated tiles show direction-dependent bending behaviors with significantly increased bending rigidity, strength, and deflection to final failure in certain loading directions, as is attributed to the asymmetric tile articulation (asymmetric about the mid-plane of tiles) and an interesting sliding-induced auxetic effect. Analytical, numerical, and experimental analyses are conducted to unveil the underlying mechanisms.

Additive Manufacturing-Enabled Advanced Design and Process Strategies for Multi-Functional Lattice Structures

The properties of each lattice structure are a function of four basic lattice factors, namely the morphology of the unit cell, its tessellation, relative density, and the material properties. The recent advancements in additive manufacturing (AM) have facilitated the easy manipulation of these factors to obtain desired functionalities. This review attempts to expound on several such strategies to manipulate these lattice factors. Several design-based grading strategies, such as functional grading, with respect to size and density manipulation, multi-morphology, and spatial arrangement strategies, have been discussed and their link to the natural occurrences are highlighted. Furthermore, special emphasis is given to the recently designed tessellation strategies to deliver multi-functional lattice responses. Each tessellation on its own acts as a novel material, thereby tuning the required properties. The subsequent section explores various material processing techniques with respect to multi-material AM to achieve multi-functional properties. The sequential combination of multiple materials generates novel properties that a single material cannot achieve. The last section explores the scope for combining the design and process strategies to obtain unique lattice structures capable of catering to advanced requirements. In addition, the future role of artificial intelligence and machine learning in developing function-specific lattice properties is highlighted.

Hydrogel-Reactive-Microenvironment Powering Reconfiguration of Polymer Architectures

Reconfiguration of architected structures has great significance for achieving new topologies and functions of engineering materials. Existing reconfigurable strategies have been reported, including approaches based on heat, mechanical instability, swelling, origami/kirigami designs, and electromagnetic actuation. However, these approaches mainly involve physical interactions between the host materials and the relevant stimuli. Herein, a novel, easy-manipulated, and controllable reconfiguration strategy for polymer architectures is proposed by using a chemical reaction of host material within a hydrogel reactive microenvironment. 3D printed polycaprolactone (PCL) lattices transformed in an aqueous polyacrylamide (PAAm) hydrogel precursor solution, in which ultraviolet (UV) light triggered heterogeneous grafting polymerization between PCL and AAm. In situ microscopy shows that PCL beams go through volumetric expansion and cooperative buckling, resulting in transformation of PCL lattices into sinusoidal patterns. The transformation process can be tuned easily and patterned through the adjustment of the PCL beam diameter, unit cell width, and UV light on-off state. Controlling domain formation is achieved by using UV masks. This framework enables the design, fabrication, and programming of architected materials and inspires the development of novel 4D printing approaches.

Reduced stress propagation leads to increased mechanical failure resistance in auxetic materials

Materials with a negative Poisson ratio have the counterintuitive property of expanding laterally when they are stretched longitudinally. They are accordingly termed auxetic, from the Greek auxesis meaning to increase. Experimental studies have demonstrated auxetic materials to have superior material properties, compared with conventional ones. These include synclastic curvature, increased acoustic absorption, increased resilience to material fatigue, and increased resistance to mechanical failure. Until now, the latter observations have remained poorly understood theoretically. With this motivation, the contributions of this work are twofold. First, we elucidate analytically the way in which stress propagates spatially across a material following a localized plastic failure event, finding a significantly reduced stress propagation in auxetic materials compared with conventional ones. In this way, a plastic failure event occurring in one part of a material has a reduced tendency to trigger knock-on plastic events in neighboring regions. Second, via the numerical simulation of a lattice elastoplastic model, we demonstrate a key consequence of this reduced stress propagation to be an increased resistance to mechanical failure. This is seen not only via an increase in the externally measured yield strain, but also via a decreased tendency for plastic damage to percolate internally across a sample in catastrophic system-spanning clusters.

Decoupling particle-impact dissipation mechanisms in 3D architected materials

Ultralight architected materials enabled by advanced manufacturing processes have achieved density-normalized strength and stiffness properties that are inaccessible to bulk materials. However, the majority of this work has focused on static loading and elastic-wave propagation. Fundamental understanding of the mechanical behavior of architected materials under large-deformation dynamic conditions remains limited, due to the complexity of mechanical responses and shortcomings of characterization methods. Here, we present a microscale suspended-plate impact testing framework for three-dimensional micro-architected materials, where supersonic microparticles to velocities of up to 850 m/s are accelerated against a substrate-decoupled architected material to quantify its energy dissipation characteristics. Using ultra-high-speed imaging, we perform in situ quantification of the impact energetics on two types of architected materials as well as their constituent nonarchitected monolithic polymer, indicating a 47% or greater increase in mass-normalized energy dissipation under a given impact condition through use of architecture. Post-mortem characterization, supported by a series of quasi-static experiments and high-fidelity simulations, shed light on two coupled mechanisms of energy dissipation: material compaction and particle-induced fracture. Together, experiments and simulations indicate that architecture-specific resistance to compaction and fracture can explain a difference in dynamic impact response across architectures. We complement our experimental and numerical efforts with dimensional analysis which provides a predictive framework for kinetic-energy absorption as a function of material parameters and impact conditions. We envision that enhanced understanding of energy dissipation mechanisms in architected materials will serve to define design considerations toward the creation of lightweight impact-mitigating materials for protective applications.

Stretchable and negative-Poisson-ratio porous metamaterials

Highly stretchable porous materials are promising for flexible electronics but their fabrication is a great challenge. Herein, several kinds of highly stretchable conductive porous elastomers with low or negative Poisson's ratios are achieved by uniaxial, biaxial, and triaxial hot-pressing strategies. The reduced graphene oxide/polymer nanocomposite elastomers with folded porous structures obtained by uniaxial hot pressing exhibit high stretchability up to 1200% strain. Furthermore, the meta-elastomers with reentrant porous structures combining high biaxial (or triaxial) stretchability and negative Poisson's ratios are achieved by biaxial (or triaxial) hot pressing. The resulting elastomer-based wearable strain sensors exhibit an ultrawide response range (0-1200%). The materials can be applied for smart thermal management and electromagnetic interference shielding, which are achieved by regulating the porous microstructures via stretching. This work provides a versatile strategy to highly stretchable and negative-Poisson-ratio porous materials with promising features for various applications such as flexible electronics, thermal management, electromagnetic shielding, and energy storage.

Electrochemically Responsive 3D Nanoarchitectures

Responsive nanomaterials are being developed to create new unique functionalities such as switchable colors and adhesive properties or other programmable features in response to external stimuli. While many existing examples rely on changes in temperature, humidity, or pH, this study aims to explore an alternative approach relying on simple electric input signals. More specifically, 3D electrochromic architected microstructures are developed using carbon nanotube-Tin (Sn) composites that can be reconfigured by lithiating Sn with low power electric input (≈50 nanowatts). These microstructures have a continuous, regulated, and non-volatile actuation determined by the extent of the electrochemical lithiation process. In addition, this proposed fabrication process relies only on batch lithographic techniques, enabling the parallel production of thousands of 3D microstructures. Structures with a 30-97% change in open-end area upon actuation are demonstrated and the importance of geometric factors in the response and structural integrity of 3D architected microstructures during electrochemical actuation is highlighted.

A Novel 3D-Printed Negative-Stiffness Lattice Structure with Internal Resonance Characteristics and Tunable Bandgap Properties

The bandgap tuning potential offered by negative-stiffness lattice structures, characterized by their unique mechanical properties, represents a promising and burgeoning field. The potential of large deformations in lattice structures to transition between stable configurations is explored in this study. This transformation offers a novel method for modifying the frequency range of elastic wave attenuation, simultaneously absorbing energy and effectively generating diverse bandgap ranges. In this paper, an enhanced lattice structure is introduced, building upon the foundation of the normal negative-stiffness lattice structures. The research examined the behavior of the suggested negative-stiffness lattice structures when subjected to uniaxial compression. This included analyzing the dispersion spectra and bandgaps across different states of deformation. It also delved into the effects of geometric parameter changes on bandgap properties. Furthermore, the findings highlight that the normal negative-stiffness lattice structure demonstrates restricted capabilities in attenuating vibrations. In contrast, notable performance improvements are displayed by the improved negative-stiffness lattice structure, featuring distinct energy band structures and variable bandgap ranges in response to differing deformation states. This highlights the feasibility of bandgap tuning through the deformation of negatively stiffened structures. Finally, the overall metamaterial structure is simulated using a unit cell finite element dynamic model, and its vibration transmission properties and frequency response patterns are analyzed. A fresh perspective on the research and design of negative-stiffness lattice structures, particularly focusing on their bandgap tuning capabilities, is offered in this study.

Unifying the design space and optimizing linear and nonlinear truss metamaterials by generative modeling

The rise of machine learning has fueled the discovery of new materials and, especially, metamaterials-truss lattices being their most prominent class. While their tailorable properties have been explored extensively, the design of truss-based metamaterials has remained highly limited and often heuristic, due to the vast, discrete design space and the lack of a comprehensive parameterization. We here present a graph-based deep learning generative framework, which combines a variational autoencoder and a property predictor, to construct a reduced, continuous latent representation covering an enormous range of trusses. This unified latent space allows for the fast generation of new designs through simple operations (e.g., traversing the latent space or interpolating between structures). We further demonstrate an optimization framework for the inverse design of trusses with customized mechanical properties in both the linear and nonlinear regimes, including designs exhibiting exceptionally stiff, auxetic, pentamode-like, and tailored nonlinear behaviors. This generative model can predict manufacturable (and counter-intuitive) designs with extreme target properties beyond the training domain.

Exploration of truss metamaterials with graph based generative modeling

Optimisation tasks in the inverse design of metamaterials with machine learning were limited due to the representations of generative models. Here the author comments a recent publication in Nature Communications which generates a latent space representation that unlocks non-linear optimisations.

Deep Learning in Mechanical Metamaterials: From Prediction and Generation to Inverse Design

Mechanical metamaterials are meticulously designed structures with exceptional mechanical properties determined by their microstructures and constituent materials. Tailoring their material and geometric distribution unlocks the potential to achieve unprecedented bulk properties and functions. However, current mechanical metamaterial design considerably relies on experienced designers' inspiration through trial and error, while investigating their mechanical properties and responses entails time-consuming mechanical testing or computationally expensive simulations. Nevertheless, recent advancements in deep learning have revolutionized the design process of mechanical metamaterials, enabling property prediction and geometry generation without prior knowledge. Furthermore, deep generative models can transform conventional forward design into inverse design. Many recent studies on the implementation of deep learning in mechanical metamaterials are highly specialized, and their pros and cons may not be immediately evident. This critical review provides a comprehensive overview of the capabilities of deep learning in property prediction, geometry generation, and inverse design of mechanical metamaterials. Additionally, this review highlights the potential of leveraging deep learning to create universally applicable datasets, intelligently designed metamaterials, and material intelligence. This article is expected to be valuable not only to researchers working on mechanical metamaterials but also those in the field of materials informatics.

Dynamic diagnosis of metamaterials through laser-induced vibrational signatures

Mechanical metamaterials at the microscale exhibit exotic static properties owing to their engineered building blocks1-4, but their dynamic properties have remained substantially less explored. Their design principles can target frequency-dependent properties5-7 and resilience under high-strain-rate deformation8,9, making them versatile materials for applications in lightweight impact resistance10-12, acoustic waveguiding7,13 or vibration damping14,15. However, accessing dynamic properties at small scales has remained a challenge owing to low-throughput and destructive characterization8,16,17 or lack of existing testing protocols. Here we demonstrate a high-throughput, non-contact framework that uses MHz-wave-propagation signatures within a metamaterial to non-destructively extract dynamic linear properties, omnidirectional elastic information, damping properties and defect quantification. Using rod-like tessellations of microscopic metamaterials, we report up to 94% direction-dependent and rate-dependent dynamic stiffening at strain rates approaching 102 s-1, as well as damping properties three times higher than their constituent materials. We also show that frequency shifts in the vibrational response allow for characterization of invisible defects within the metamaterials and that selective probing allows for the construction of experimental elastic surfaces, which were previously only possible computationally. Our work provides a route for accelerated data-driven discovery of materials and microdevices for dynamic applications such as protective structures, medical ultrasound or vibration isolation.

Mechanical metamaterials and beyond

Mechanical metamaterials enable the creation of structural materials with unprecedented mechanical properties. However, thus far, research on mechanical metamaterials has focused on passive mechanical metamaterials and the tunability of their mechanical properties. Deep integration of multifunctionality, sensing, electrical actuation, information processing, and advancing data-driven designs are grand challenges in the mechanical metamaterials community that could lead to truly intelligent mechanical metamaterials. In this perspective, we provide an overview of mechanical metamaterials within and beyond their classical mechanical functionalities. We discuss various aspects of data-driven approaches for inverse design and optimization of multifunctional mechanical metamaterials. Our aim is to provide new roadmaps for design and discovery of next-generation active and responsive mechanical metamaterials that can interact with the surrounding environment and adapt to various conditions while inheriting all outstanding mechanical features of classical mechanical metamaterials. Next, we deliberate the emerging mechanical metamaterials with specific functionalities to design informative and scientific intelligent devices. We highlight open challenges ahead of mechanical metamaterial systems at the component and integration levels and their transition into the domain of application beyond their mechanical capabilities.

Stiffening and dynamics of a two-dimensional active elastic solid

This work deals with the mechanical properties and dynamics of an active elastic solid defined as a two-dimensional network of active stochastic particles interacting by nonlinear hard springs. By proposing a discrete model, it is numerically found that when activity in the system is turned on, the active solid stiffens as a function of propulsion forces, thus deviating from equilibrium mechanics. To understand this effect a minimal stochastic model is offered, and a physical explanation based on spatial symmetry-breaking is put forward. In addition, the dynamics of the active solid in the absence of an external stress is also studied. From this, three main features are observed to emerge, namely, a collective behavior within the active solid, a time-density fluctuation, and oscillating dynamics of the internal stresses towards a steady state.

Unleashing the Power of Artificial Intelligence in Materials Design

The integration of artificial intelligence (AI) algorithms in materials design is revolutionizing the field of materials engineering thanks to their power to predict material properties, design de novo materials with enhanced features, and discover new mechanisms beyond intuition. In addition, they can be used to infer complex design principles and identify high-quality candidates more rapidly than trial-and-error experimentation. From this perspective, herein we describe how these tools can enable the acceleration and enrichment of each stage of the discovery cycle of novel materials with optimized properties. We begin by outlining the state-of-the-art AI models in materials design, including machine learning (ML), deep learning, and materials informatics tools. These methodologies enable the extraction of meaningful information from vast amounts of data, enabling researchers to uncover complex correlations and patterns within material properties, structures, and compositions. Next, a comprehensive overview of AI-driven materials design is provided and its potential future prospects are highlighted. By leveraging such AI algorithms, researchers can efficiently search and analyze databases containing a wide range of material properties, enabling the identification of promising candidates for specific applications. This capability has profound implications across various industries, from drug development to energy storage, where materials performance is crucial. Ultimately, AI-based approaches are poised to revolutionize our understanding and design of materials, ushering in a new era of accelerated innovation and advancement.

Chevron-beam-based nonlinearity-tunable elastic metamaterial

In this work, we proposed a chevron-beam-based nonlinearity-tunable elastic metamaterial capable of tuning the nonlinear parameters. Instead of enhancing or suppressing nonlinear phenomena or slightly tuning nonlinearities, the proposed metamaterial directly tunes its nonlinear parameters, allowing much broader manipulation of nonlinear phenomena. Based on the underlying physics, we discovered that the nonlinear parameters of the chevron-beam-based metamaterial are determined by the initial angle. To identify the change in the nonlinear parameters according to the initial angle, we derived an analytical model of the proposed metamaterial to calculate the nonlinear parameters. Based on the analytical model, the actual chevron-beam-based metamaterial is designed. We show that the proposed metamaterial enables nonlinear parameter control and harmonic tuning by numerical methods.

Bioinspired Construction of Annulus Fibrosus Implants with a Negative Poisson's Ratio for Intervertebral Disc Repair and Restraining Disc Herniation

Inspired by the negative Poisson's ratio (NPR) effects of the annulus fibrosus (AF) in intervertebral discs (IVDs), we designed a re-entrant honeycomb model and then 3D printed it into a poly(ε-caprolactone) (PCL) scaffold with NPR effects, which was followed by in situ polymerization of polypyrrole (PPy), thus constructing a PPy-coated NPR-structured PCL scaffold (-vPCL-PPy) to be used as the AF implant for the treatment of lumbar herniated discs. Mechanical testing and finite element (FE) simulation indicated that the NPR composite implant could sustain axial spine loading and resist nucleus pulposus (NP) swelling while displaying uniform stress diffusion under NP swelling and contraction. More interestingly, the NPR-structured composite scaffold could also apply a reacting force to restrain NP herniation owing to the NPR effect. In addition, the in vitro biological assessment and in vivo implantation demonstrated that the NPR composite scaffold exhibited good biocompatibility and exerted the ability to restore the physiological function of the disc segments.

Engineering zero modes in transformable mechanical metamaterials

In the field of flexible metamaterial design, harnessing zero modes plays a key part in enabling reconfigurable elastic properties of the metamaterial with unconventional characteristics. However, only quantitative enhancement of certain properties succeeds in most cases rather than qualitative transformation of the metamaterials' states or/and functionalities, due to the lack of systematic designs on the corresponding zero modes. Here, we propose a 3D metamaterial with engineered zero modes, and experimentally demonstrate its transformable static and dynamic properties. All seven types of extremal metamaterials ranging from null-mode (solid state) to hexa-mode (near-gaseous state) are reported to be reversibly transformed from one state to another, which is verified by the 3D-printed Thermoplastic Polyurethanes prototypes. Tunable wave manipulations are further investigated in 1D-, 2D- and 3D-systems. Our work sheds lights on the design of flexible mechanical metamaterials, which can be potentially extended from the mechanical to the electro-magnetite, the thermal or other types.

Patient-specific femoral implant design using metamaterials for improving load transfer at proximal-lateral region of the femur

Loading configuration of hip joint creates resultant bending effect on femoral implants. So, the lateral side of femoral implant which is under tension retracts from peri‑implant bone due to positive Poisson's ratio. This retraction of implant leads to load shielding and gap opening in proximal-lateral region, thereby allowing entry of wear particle to implant-bone interface. Retraction of femoral implant can be avoided by introducing auxetic metamaterial to the retracting side. This allows the implant to push peri‑implant bone under tensile condition by virtue of their auxetic (negative Poisson's ratio) nature. To develop such implants, a patient-specific conventional solid implant was first designed based on computed-tomography scan of a patient's femur. Two types of metamaterials (2D: type-1) and (3D: type-2) were employed to design femoral meta-implants. Type-1 and type-2 meta-implants were fabricated using metallic 3D printing method and mechanical compression testing was conducted. Three finite element (FE) models of the femur implanted with solid implant, type-1 meta-implant and type-2 meta-implant were developed and analysed under compression loading. Significant correlation (R² = 0.9821 and R² = 0.9977) was found between the experimental and FE predicted strains of the two meta-implants. In proximal-lateral region of the femur, an increase of 7.1% and 44.1% von-Mises strain was observed when implanted with type-1 and type-2 meta-implant over the solid implant. In this region, bone remodelling analysis revealed 2.5% bone resorption in case of solid implant. While bone apposition of 0.5% and 7.7% was observed in case of type-1 and type-2 meta-implants, respectively. The results of this study indicates that concept of introduction of metamaterial to the lateral side of femoral implant can prove to provide higher osseointegration-friendly environment in the proximal-lateral region of femur.

Entering a New Dimension in Powder Processing for Advanced Ceramics Shaping

Filigree structures can be manufactured via two-photon polymerization (2PP) operating in the regime of nonlinear light absorption. For the first time, it is possible to apply this technique to the powder processing of ceramic structures with a feature size in the range of the critical defect sizes responsible for brittle fracture and, thus, affecting fracture toughness of high-performance ceramics. In this way, tailoring of advanced properties can be achieved already in the shaping process. Traditionally, 2PP relies on transparent polymerizable resins, which are diametrically opposed to the usually completely opaque ceramic resins and slurries. Here a transparent and photocurable suspension of nanoparticles (resin) with very high mass fractions of yttria-stabilized zirconia particles (YSZ) is presented. Due to the extremely well-dispersed nanoparticles, scattering of light can be effectively suppressed at the process-relevant wavelength of 800 nm. Sintered ceramic structures with a resolution of down to 500 nm are obtained. Even at reduced densities of 1-4 g cm^-3 , the resulting compressive strength with 4.5 GPa is equivalent or even exceeding bulk monolithic yttria-stabilized zirconia. A ceramic metamaterial is born, where the mechanical properties of yttria-stabilized zirconia are altered by changing geometrical parameters, and gives access to a new class of ceramic materials.

3D-printed auxetic-structured intervertebral disc implant for potential treatment of lumbar herniated disc

In this study, a novel artificial intervertebral disc implant with modified “Bucklicrystal” structure was designed and 3D printed using thermoplastic polyurethane. The new implant has a unique auxetic structure with building blocks joined “face-to-face”. The accompanied negative Poisson’s ratio enables its excellent energy absorption and stability under compression. The deformation and load distribution behavior of the implant under various loading conditions (bending, torsion, extension and flexion) has been thoroughly evaluated through finite element method. Results show that, compared to natural intervertebral disc and conventional 3D implant, our new implant exhibits more effective stress transfer and attenuation under practical loading conditions. The implant's ability to contract laterally under compression can be potentially used to alleviate the symptoms of lumbar disc herniation. Finally, the biocompatibility of the implant was assessed in vitro and its ability to restore the physiological function of the disc segment was validated in vivo using an animal model.

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Auxetic-structured IVD implant features negative Poisson's ratio (NPR) behavior.

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Modified “Bucklicrystal”structure exhibits better energy absorption and stability.

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The stress effectively and evenly transfers/attenuates in the auxetic implant.

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Auxetic implant potentially alleviates the symptoms of lumbar disc herniation.

Shape Morphing by Topological Patterns and Profiles in Laser-Cut Liquid Crystal Elastomer Kirigami

Programming shape changes in soft materials requires precise control of the directionality and magnitude of their mechanical response. Among ordered soft materials, liquid crystal elastomers (LCEs) exhibit remarkable and programmable shape shifting when their molecular order changes. In this work, we synthesized, remotely programmed, and modeled reversible and complex morphing in monolithic LCE kirigami encoded with predesigned topological patterns in its microstructure. We obtained a rich variety of out-of-plane shape transformations, including auxetic structures and undulating morphologies, by combining different topological microstructures and kirigami geometries. The spatiotemporal shape-shifting behaviors are well recapitulated by elastodynamics simulations, revealing that the complex shape changes arise from integrating the custom-cut geometry with local director profiles defined by topological defects inscribed in the material. Different functionalities, such as a bioinspired fluttering butterfly, a flower bud, dual-rotation light mills, and dual-mode locomotion, are further realized. Our proposed LCE kirigami with topological patterns opens opportunities for the future development of multifunctional devices for soft robotics, flexible electronics, and biomedicine.

Origami Tribo-Metamaterials with Mechanoelectrical Multistability

The emerging mechanical functional metamaterials reported with promising mechanoelectrical characteristics bring increasing attention to structurally functional materials. It is essential to deploy mechanical metamaterials in energy materials for effective triggering and controllable mechanoelectrical response. This study reports origami tribo-metamaterials (OTMs) that design triboelectric materials in the origami-enabled, tubular metamaterials. The octagonal, hexagonal, and conical origami units are deployed as the metamaterial substrates to trigger the triboelectric pairs for mechanoelectrical multistability. For the octagonal OTM configuration with the triboelectric pair of fluorinated ethylene propylene-paper, the peak open-circuit voltage, short-circuit current, and transferred charge are obtained as 206.4 V, 4.66 μA, and 0.38 μC, respectively, and the maximum instantaneous output power density is 0.96 μW/cm² with the load resistance of 20 MΩ. The OTM takes advantage of the origami metamaterials to obtain the multistable force-displacement response as effective stimuli for the triboelectric materials, which leads to tunable mechanoelectrical performance for speed and weight sensing and energy harvesting. The proposed OTM not only offers a strategy to structurally design energy materials to achieve desirable mechanoelectrical response, but also provides a guideline for the applications of mechanical functional metamaterials in practice.

Deep-learning-based inverse design of three-dimensional architected cellular materials with the target porosity and stiffness using voxelized Voronoi lattices

Architected cellular materials are a class of artificial materials with cellular architecture-dependent properties. Typically, designing cellular architectures paves the way to generate architected cellular materials with specific properties. However, most previous studies have primarily focused on a forward design strategy, wherein a geometry is generated using computer-aided design modeling, and its properties are investigated experimentally or via simulations. In this study, we developed an inverse design framework for a disordered architected cellular material (Voronoi lattices) using deep learning. This inverse design framework is a three-dimensional conditional generative adversarial network (3D-CGAN) trained based on supervised learning using a dataset consisting of voxelized Voronoi lattices and their corresponding relative densities and Young's moduli. A well-trained 3D-CGAN adopts variational sampling to generate multiple distinct Voronoi lattices with the target relative density and Young's modulus. Consequently, the mechanical properties of the 3D-CGAN generated Voronoi lattices are validated through uniaxial compression tests and finite element simulations. The inverse design framework demonstrates potential for use in bone implants, where scaffold implants can be automatically generated with the target relative density and Young's modulus.

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.

Kirigami-inspired metamaterials for programming constitutive laws: Mixed-mode multidirectional auxeticity and contact-induced stiffness modulation

Stress-strain constitutive relations and Poisson's ratios are fundamental properties of naturally occurring materials, based on which their mechanical applications can be designed. The lack of tailorability and restricted margin for such critical properties severely limit the bounds of achievable multi-functional engineering designs using conventional materials. Through analytical and numerical analyses, supported by elementary-level physical experiments, we have proposed a kirigami-inspired hybrid metamaterial with programmable deformation-dependent stiffness and mixed-mode multidirectional auxeticity. The metamaterial can transition from a phase of low stiffness to a contact induced phase that brings forth an extensive rise in stiffness. Uniform and graded configurations of multi-layer tessellated material are developed to modulate the constitutive law of the metastructure with augmented programmability in two- and three-dimensional spaces. The proposed metamaterial will lead to extreme lightweight functional designs for impact resistance, shape morphing, multidirectional deformation, vibration and wave propagation control, where the capabilities of intrinsic material can be most optimally exploited.

3D Auxetic Metamaterials with Elastically-Stable Continuous Phase Transition

In solid state physics, phase transitions can influence material functionality and alter their properties. In mechanical metamaterials, structural-phase transitions can be achieved through instability or buckling of certain structural elements. However, these fast transitions in one mechanical parameter typically affect significantly the remaining parameters, hence, limiting their applications. Here, this limitation is addressed by designing a novel 3D mechanical metamaterial that is capable of undergoing a phase transition from positive to negative Poisson's ratio under compression, without significant degradation of Young's modulus (i.e. the phase transition is elastically-stable). The metamaterial is fabricated by two-photon lithography at the micro-scale and its mechanical behavior is assessed experimentally. For another choice of structural parameters, it is then shown that the auxetic behavior of the considered 3D metamaterial class can be maintained over a wide range of applied compressive strain.

Multifunctional PbS2 Monolayer with an In-Plane Negative Poisson Ratio and Photocatalytic Water Splitting Properties

Designing novel multifunctional materials at the nanoscale is vitally important for flexible electronics. Here, we have uncovered a two-dimensional metal dichalcogenide PbS₂ with intriguing negative Poisson ratio behavior and favorable optical and photocatalytic water splitting properties. The calculations indicate that the Poisson ratio of the PbS₂ monolayer is -0.061 along both x and y lattice directions, which is attributed to its unique tetrahedral motif and the ligand field of the local PbS₄ units in the PbS₂ monolayer. The electronic band structures show that the narrow band gap (1.59 eV) of the PbS₂ monolayer could be effectively modulated by strain engineering. Most importantly, the strain-induced tunability of optical absorbance and suitable band edge alignment make the PbS₂ monolayer a promising catalyst for photocatalytic water splitting, which is further confirmed by the reaction free energies. These findings offer an effective avenue for the design and synthesis of a novel optoelectronic functional material.

Programming Multistable Metamaterials to Discover Latent Functionalities

Using multistable mechanical metamaterials to develop deployable structures, electrical devices, and mechanical memories raises two unanswered questions. First, can mechanical instability be programmed to design sensors and memory devices? Second, how can mechanical properties be tuned at the post-fabrication stage via external stimuli? Answering these questions requires a thorough understanding of the snapping sequences and variations of the elastic energy in multistable metamaterials. The mechanics of deformation sequences and continuous force/energy-displacement curves are comprehensively unveiled here. A 1D array, that is chain, of bistable cells is studied to explore instability-induced energy release and snapping sequences under one external mechanical stimulus. This method offers an insight into the programmability of multistable chains, which is exploited to fabricate a mechanical sensor/memory with sampling (analog to digital-A/D) and data reconstruction (digital to analog-D/A) functionalities operating based on the correlation between the deformation sequence and the mechanical input. The findings offer a new paradigm for developing programmable high-capacity read-write mechanical memories regardless of thei size scale. Furthermore, exotic mechanical properties can be tuned by harnessing the attained programmability of multistable chains. In this respect, a transversely multistable mechanical metamaterial with tensegrity-like bistable cells is designed to showcase the tunability of chirality.

Shock-absorbing effect of flooring-adopted mechanical metamaterial technology and its influence on the gait and balance of older adults

Objective

To elucidate the performance of a shock-absorbing floor material with a mechanical metamaterial (MM-flooring) structure and its effect on the gait and balance of older adults.

Methods

The drop-weight impact was applied to evaluate the shock-absorbing performance. The falling weight was adjusted equivalent to the energy exerted on the femur of an older woman when she falls, which was evaluated on the MM-flooring and six other flooring materials.

Nineteen healthy people over the age of 65 years participated in the gait and balance evaluations. The timed up and go and two-step tests were adopted as gait performance tests, and the sway-during-quiet-balance test with force plates and the functional reach test (FRT) were adopted as balance tests. All the participants underwent these tests on the MM-flooring, shock-absorbing mat and rigid flooring.

Results

The shock-absorbing performance test revealed that MM-flooring has sufficient shock-absorbing performance, and suggesting that it may reduce the probability of fractures in the older people when they fall. The results of the gait performance test showed that the participants demonstrated the same gait performance on the MM-flooring and the rigid floor. In the quiet standing test, MM-flooring did not affect the balance function of the participants to the same extent as the rigid floor, compared with the shock-absorbing mat. In the FRT, no significant differences were found for any of the flooring conditions.

Conclusions

MM-flooring has the potential to prevent fractures attributed to falls and does not affect the gait or balance of older adults.

Inverse Design of Mechanical Metamaterials with Target Nonlinear Response via a Neural Accelerated Evolution Strategy

Materials with target nonlinear mechanical response can support the design of innovative soft robots, wearable devices, footwear, and energy-absorbing systems, yet it is challenging to realize them. Here, mechanical metamaterials based on hinged quadrilaterals are used as a platform to realize target nonlinear mechanical responses. It is first shown that by changing the shape of the quadrilaterals, the amount of internal rotations induced by the applied compression can be tuned, and a wide range of mechanical responses is achieved. Next, a neural network is introduced that provides a computationally inexpensive relationship between the parameters describing the geometry and the corresponding stress-strain response. Finally, it is shown that by combining the neural network with an evolution strategy, one can efficiently identify geometries resulting in a wide range of target nonlinear mechanical responses and design optimized energy-absorbing systems, soft robots, and morphing structures.

Discrete symmetries control geometric mechanics in parallelogram-based origami

Geometric compatibility constraints dictate the mechanical response of soft systems that can be utilized for the design of mechanical metamaterials such as the negative Poisson's ratio Miura-ori origami crease pattern. Here, we develop a formalism for linear compatibility that enables explicit investigation of the interplay between geometric symmetries and functionality in origami crease patterns. We apply this formalism to a particular class of periodic crease patterns with unit cells composed of four arbitrary parallelogram faces and establish that their mechanical response is characterized by an anticommuting symmetry. In particular, we show that the modes are eigenstates of this symmetry operator and that these modes are simultaneously diagonalizable with the symmetric strain operator and the antisymmetric curvature operator. This feature reveals that the anticommuting symmetry defines an equivalence class of crease pattern geometries that possess equal and opposite in-plane and out-of-plane Poisson's ratios. Finally, we show that such Poisson's ratios generically change sign as the crease pattern rigidly folds between degenerate ground states and we determine subfamilies that possess strictly negative in-plane or out-of-plane Poisson's ratios throughout all configurations.

Programmable Auxeticity in Hydrogel Metamaterials via Shape-Morphing Unit Cells

Mechanical metamaterials recruit unique mechanical behavior that is unavailable in bulk materials from a periodic unit cell structure with a specific geometry. However, such metamaterials can typically not be reconfigured once manufactured. Herein, the authors introduce shape morphing of a hydrogel metamaterial via spatio-selective integration of responsive actuating elements to reconfigure the mesoscale unit cell geometry to reach programmable auxeticity on the macroscale. Via thermal control, the unit cell angle of a honeycomb structure can be precisely programmed from 68° to 107°. This results in negative, zero, or positive Poisson's ratio under applied tensile strain. The geometrical reconfiguration with resulting programmable auxeticity is predicted and verified by finite element (FE) simulation. This concept of shape-morphing hydrogel metamaterials via the addition of actuating struts into otherwise passive architectures offers a new strategy for reconfigurable metamaterials and extends applications of hydrogels in general. It can be readily extended to other architectures and may find applications in mechanical computing as well as soft robotics.

Broadband Electromagnetic Absorption Effect of Topological Structure Using Carbon Nanotube Based Hybrid Material

The development of microwave absorbing technology raises the demands for all-band absorption. The topological structures expand the frequency range of electromagnetic wave absorption and eliminate the differences caused by scattering in different incident directions. The multi-wall carbon nanotube and carbonyl iron particles were mixed with polylactic polymer to fabricate filaments for fused deposition. The distribution characteristics of the structures using carbonyl iron/carbon nanotube hybrid material for the key absorption frequency band are obtained. The reflectivity of the honeycomb structure in X and Ku bands is verified experimentally through the preparation method of fused deposition modeling 3D printing. With the decrease of the fractal dimension number, the electromagnetic loss performance basically increases. Preliminary research results showed that the topological structure could significantly expand the absorbing frequency range, and the effective frequency band less than −10 dB is 2–40 GHz, which has a clear application potential for radar absorption.