Bifurcation instructed design of multistate machines.

We propose a design paradigm for multistate machines where transitions from one state to another are organized by bifurcations of multiple equilibria of the energy landscape describing the collective interactions of the machine components. This design paradigm is attractive since, near bifurcations, small variations in a few control parameters can result in large changes to the system's state providing an emergent lever mechanism. Further, the topological configuration of transitions between states near such bifurcations ensures robust operation, making the machine less sensitive to fabrication errors and noise. To design such machines, we develop and implement a new efficient algorithm that searches for interactions between the machine components that give rise to energy landscapes with these bifurcation structures. We demonstrate a proof of concept for this approach by designing magnetoelastic machines whose motions are primarily guided by their magnetic energy landscapes and show that by operating near bifurcations we can achieve multiple transition pathways between states. This proof of concept demonstration illustrates the power of this approach, which could be especially useful for soft robotics and at the microscale where typical macroscale designs are difficult to implement.

Mechanical Fourier transform for programmable metamaterials.

Proactively programming materials toward target nonlinear mechanical behaviors is crucial to realize customizable functions for advanced devices and systems, which arouses persistent explorations for rapid and efficient inverse design strategies. Herein, we propose a "mechanical Fourier transform" strategy to program mechanical behaviors of materials by mimicking the concept of Fourier transform. In this strategy, an arbitrary target force-displacement curve is decomposed into multiple cosine curves and a constant curve, each of which is realized by a rationally designed multistable module in an array-structured metamaterial. Various target curves with distinct shapes can be rapidly programmed and reprogrammed through only amplitude modulation on the modules. Two exemplary metamaterials are demonstrated to validate the strategy with a macroscale prototype based on magnet lattice and a microscale prototype based on an etched silicon wafer. This strategy applies to a variety of scales, constituents, and structures, and paves a way for the property programming of materials.

Active metamaterials for realizing odd mass density.

Solids built out of active components have exhibited odd elastic stiffness tensors whose active moduli appear in the antisymmetric part and which give rise to non-Hermitian static and dynamic phenomena. Here, we present a class of active metamaterial featured with an odd mass density tensor whose asymmetric part arises from active and nonconservative forces. The odd mass density is realized using metamaterials with inner resonators connected by asymmetric and programmable feed-forward control on acceleration and active forces along the two perpendicular directions. The active forces produce unbalanced off-diagonal mass density coupling terms, leading to non-Hermiticity. The odd mass is then experimentally validated through a one-dimensional nonsymmetric wave coupling where propagating transverse waves are coupled with longitudinal ones whereas the reverse is forbidden. We reveal that the two-dimensional active metamaterials with the odd mass can perform in either energy-unbroken or energy-broken phases separated by exceptional points along principal directions of the mass density. The odd mass density contributes to the wave anisotropy in the energy-unbroken phase and directional wave energy gain in the energy-broken phase. We also numerically illustrate and experimentally demonstrate the two-dimensional wave propagation phenomena that arise from the odd mass in active solids. Finally, the existence of non-Hermitian skin effect is discussed in which boundaries host an extensive number of localized modes. It is our hope that the emergent concept of the odd mass can open up a new research platform for mechanical non-Hermitian system and pave the ways for developing next-generation wave steering devices.

Realizing the multifunctional metamaterial for fluid flow in a porous medium.

Metamaterials are artificial materials that can achieve unusual properties through unique structures. In particular, their "invisibility" property has attracted enormous attention due to its little or negligible disturbance to the background field that avoids detection. This invisibility feature is not only useful for the optical field, but it is also important for any field manipulation that requires minimum disturbance to the background, such as the flow field manipulation inside the human body. There are several conventional invisible metamaterial designs: a cloak can isolate the influence between the internal and external fields, a concentrator can concentrate the external field to form an intensified internal field, and a rotator can rotate the internal field by a specific angle with respect to the external field. However, a multifunctional invisible device that can continuously tune across all these functions has never been realized due to its challenging requirements on material properties. Inside a porous medium flow, however, we overcome these challenges and realize such a multifunctional metamaterial. Our hydrodynamic device can manipulate both the magnitude and the direction of the internal flow and, at the same time, make negligible disturbance to the external flow. Thus, we integrate the functions of the cloak, concentrator, and rotator within one single hydrodynamic metamaterial, and such metamaterials may find potential applications in biomedical areas such as tissue engineering and drug release.

Inverting the structure-property map of truss metamaterials by deep learning.

Inspired by crystallography, the periodic assembly of trusses into architected materials has enjoyed popularity for more than a decade and produced countless cellular structures with beneficial mechanical properties. Despite the successful and steady enrichment of the truss design space, the inverse design has remained a challenge: While predicting effective truss properties is now commonplace, efficiently identifying architectures that have homogeneous or spatially varying target properties has remained a roadblock to applications from lightweight structures to biomimetic implants. To overcome this gap, we propose a deep-learning framework, which combines neural networks with enforced physical constraints, to predict truss architectures with fully tailored anisotropic stiffness. Trained on millions of unit cells, it covers an enormous design space of topologically distinct truss lattices and accurately identifies architectures matching previously unseen stiffness responses. We demonstrate the application to patient-specific bone implants matching clinical stiffness data, and we discuss the extension to spatially graded cellular structures with locally optimal properties.

Ultrathin Ternary FeCoNi Alloy Nanoarrays in BaTiO3 Matrix for Room-Temperature Multiferroic and Hyperbolic Metamaterial.

Multifunctional vertically aligned nanocomposite (VAN) thin films exhibit considerable potential in diverse fields. Here, a BaTiO3-FeCoNi alloy (BTO-FCN) system featuring an ultrathin ternary FCN alloy nanopillar array embedded in the BTO matrix has been developed with tailorable nanopillar size and interpillar distance. The magnetic alloy nanopillars combined with a ferroelectric oxide matrix present intriguing multifunctionality and coupling properties. The room-temperature magnetic response proves the soft magnet nature of the BTO-FCN films with magnetic anisotropy has been demonstrated. Furthermore, the anisotropic nature of the dielectric-metal alloy VAN renders it an ideal candidate for hyperbolic metamaterial (HMM), and the epsilon-near-zero (ENZ) wavelength, where the real part of permittivity (ε') turns to negative, can be tailored from ∼700 nm to ∼1050 nm. Lastly, room-temperature multiferroicity has been demonstrated via interfacial coupling between the magnetic nanopillars and ferroelectric matrix.

Crack-Deflecting Lattice Metamaterials Inspired by Precipitation Hardening.

Lattice structures, comprising nodes and struts arranged in an array, are renowned for their lightweight and unique mechanical deformation characteristics. Previous studies on lattice structures have revealed that failure often originates from stress concentration points and spreads throughout the material. This results in collapse failure, similar to the accumulation of damage at defects in metallic crystals. Here the precipitation hardening mechanism found in crystalline materials is employed to deflect the initial failure path, through the strategic placement of strengthening units at stress concentration points using the finite element method. Both the mesostructure, inspired by the arrangement of crystals, and the inherent microstructure of the base materials have played crucial roles in shaping the mechanical properties of the macro-lattices. As a result, a groundbreaking multiscale hierarchical design methodology, offering a spectrum of design concepts for engineering materials with desired properties is introduced.

Text-to-Microstructure Generation Using Generative Deep Learning.

Designing novel materials is greatly dependent on understanding the design principles, physical mechanisms, and modeling methods of material microstructures, requiring experienced designers with expertise and several rounds of trial and error. Although recent advances in deep generative networks have enabled the inverse design of material microstructures, most studies involve property-conditional generation and focus on a specific type of structure, resulting in limited generation diversity and poor human-computer interaction. In this study, a pioneering text-to-microstructure deep generative network (Txt2Microstruct-Net) is proposed that enables the generation of 3D material microstructures directly from text prompts without additional optimization procedures. The Txt2Microstruct-Net model is trained on a large microstructure-caption paired dataset that is extensible using the algorithms provided. Moreover, the model is sufficiently flexible to generate different geometric representations, such as voxels and point clouds. The model's performance is also demonstrated in the inverse design of material microstructures and metamaterials. It has promising potential for interactive microstructure design when associated with large language models and could be a user-friendly tool for material design and discovery.

Programmable adhesion through triangular and hierarchical cuts in metamaterial adhesives.

Metamaterial design approaches, which integrate structural elements into material systems, enable the control of uncommon behaviours by decoupling local and global properties. Leveraging this conceptual framework, metamaterial adhesives incorporate nonlinear cut architectures into adhesive films to achieve unique combinations of adhesion capacity, release, and spatial tunability by controlling how cracks propagate forward and in reverse directions during separation. Here, metamaterial adhesive designs are explored with triangular cut features while integrating hierarchical and secondary cut patterns among primary nonlinear cuts. Both cut geometry and secondary cut features tune adhesive force capacity and energy of separation. Importantly, the size and spacing of cut features must be designed around a critical length scale. When secondary cut features are greater than a critical length, cracks can be steered in multiple directions, going both forward and backwards within a primary attachment element. This control over crack dynamics enhances the work of separation by a factor of 1.5, while maintaining the peel force relative to a primary cut. If hierarchical cut features are too small or too compliant, they interact and do not distinctly modify crack behaviour. This work highlights the importance of adhesive length scales and stiffness for crack control and attachment characteristics in adhesive films.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Group-theoretic analysis of symmetry-preserving deployable structures and metamaterials.

Many deployable structures in nature, as well as human-made mechanisms, preserve symmetry as their configurations evolve. Examples in nature include blooming flowers, dilation of the iris within the human eye, viral capsid maturation and molecular and bacterial motors. Engineered examples include opening umbrellas, elongating scissor jacks, variable apertures in cameras, expanding Hoberman spheres and some kinds of morphing origami structures. In these cases, the structures either preserve a discrete symmetry group or are described as an evolution from one discrete symmetry group to another of the same type as the structure deploys. Likewise, elastic metamaterials built from lattice structures can also preserve symmetry type while passively deforming and changing lattice parameters. A mathematical formulation of such transitions/deployments is articulated here. It is shown that if [Formula: see text] is Euclidean space, [Formula: see text] is a continuous group of motions of Euclidean space and [Formula: see text] is the type of the discrete subgroup of [Formula: see text] describing the symmetries of the deploying structure, then the symmetry of the evolving structure can be described by time-dependent subgroups of [Formula: see text] of the form [Formula: see text], where [Formula: see text] is a time-dependent affine transformation. Then, instead of considering the whole structure in [Formula: see text], a 'sector' of it that lives in the orbit space [Formula: see text] can be considered at each instant in time, and instead of considering all motions in [Formula: see text], only representatives from right cosets in the space [Formula: see text] need to be considered. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Wave transmission in quasi-periodic lattices.

Structural lattices with quasi-periodic patterns possess interesting dynamic features that can be exploited to control, localize and redirect propagating waves. In this work, we show that the properties of a large class of quasi-periodic locally resonant systems (approximated as periodic, with arbitrarily large period) can be performed by defining an equivalent discrete system. Several properties of wave propagation can a priori be demonstrated with reference to this system. Results in terms of bulk spectrum, showing the Hofstadter butterfly pattern, and of topological modes are then discussed in detail with reference to a simple example of quasi-periodic lattice. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Current developments in elastic and acoustic metamaterials science.

The concept of metamaterial recently emerged as a new frontier of scientific research, encompassing physics, materials science and engineering. In a broad sense, a metamaterial indicates an engineered material with exotic properties not found in nature, obtained by appropriate architecture either at macro-scale or at micro-/nano-scales. The architecture of metamaterials can be tailored to open unforeseen opportunities for mechanical and acoustic applications, as demonstrated by an impressive and increasing number of studies. Building on this knowledge, this theme issue aims to gather cutting-edge theoretical, computational and experimental studies on elastic and acoustic metamaterials, with the purpose of offering a wide perspective on recent achievements and future challenges. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Current developments in elastic and acoustic metamaterials science.

The concept of metamaterial recently emerged as a new frontier of scientific research, encompassing physics, materials science and engineering. In a broad sense, a metamaterial indicates an engineered material with exotic properties not found in nature, obtained by appropriate architecture either at macro-scale or at micro-/nano-scales. The architecture of metamaterials can be tailored to open unforeseen opportunities for mechanical and acoustic applications, as demonstrated by an impressive and increasing number of studies. Building on this knowledge, this theme issue aims to gather cutting-edge theoretical, computational and experimental studies on elastic and acoustic metamaterials, with the purpose of offering a wide perspective on recent achievements and future challenges.This article is part of the theme issue, 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Design and experimental validation of a finite-size labyrinthine metamaterial for vibro-acoustics: enabling upscaling towards large-scale structures.

In this article, we present the design and experimental validation of a labyrinthine metamaterial for vibro-acoustic applications. Based on a two-dimensional unit cell, different designs of finite-size metamaterial specimens in a sandwich configuration including two plates are proposed. The design phase includes an optimization based on Bloch-Floquet analysis with the aims of maximizing the band gap and extruding the specimens in the third dimension while keeping the absorption properties almost unaffected. By manufacturing and experimentally testing finite-sized specimens, we assess their capacity to mitigate vibrations in vibro-impact tests. The experiments confirm a band gap in the low- to mid-frequency range. Numerical models are employed to validate the experiments and to examine additional vibro-acoustic load cases. The metamaterial's performances are compared with benchmark solutions, usually employed for noise and vibration mitigation, showing a comparable efficacy in the band gap region. To eventually improve the metamaterial's performance, we optimize its interaction with the air and test different types of connections between the metamaterial and the homogeneous plates. This finally leads to metamaterial samples largely exceeding the benchmark performances in the band gap region and reveals the potential of interfaces for performance optimization of composed structures.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Water-tank metabarrier for seismic Rayleigh wave attenuation.

An innovative concept of metabarrier is presented for seismic Rayleigh wave attenuation, which consists of a periodic array of cylindrical water tanks acting as resonant units above the soil surface. A pertinent theoretical framework is developed and implemented in COMSOL Multiphysics. The framework treats the dynamics of the water tank by a well-established three-dimensional linear, pressure-based model for fluid-structure interaction under earthquake excitation, accounting for the flexibility of the tank wall; furthermore, the soil is idealized as a homogeneous and isotropic medium. Floquet-Bloch dispersion analysis of the unit cell demonstrates the presence of relevant band gaps in the low-frequency range below 20 Hz and in the higher frequency range as well. The dispersion analysis is validated by comparison with the frequency-domain analysis of a soil domain with a finite array of water tanks. The band gaps are of interest to attenuate seismic Rayleigh waves and, more generally, Rayleigh waves caused by other ground vibration sources such as road or railway traffic. The water-tank resonant units are readily tunable by varying the water level, which allows changing opening frequencies/widths of the wave attenuation zones. This is a remarkable advantage over alternative seismic metamaterials that, in general, are not designed to be tunable.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Oligomodal metamaterials with multifunctional mechanics.

Mechanical metamaterials are artificial composites that exhibit a wide range of advanced functionalities such as negative Poisson's ratio, shape shifting, topological protection, multistability, extreme strength-to-density ratio, and enhanced energy dissipation. In particular, flexible metamaterials often harness zero-energy deformation modes. To date, such flexible metamaterials have a single property, for example, a single shape change, or are pluripotent, that is, they can have many different responses, but typically require complex actuation protocols. Here, we introduce a class of oligomodal metamaterials that encode a few distinct properties that can be selectively controlled under uniaxial compression. To demonstrate this concept, we introduce a combinatorial design space containing various families of metamaterials. These families include monomodal (i.e., with a single zero-energy deformation mode); oligomodal (i.e., with a constant number of zero-energy deformation modes); and plurimodal (i.e., with many zero-energy deformation modes), whose number increases with system size. We then confirm the multifunctional nature of oligomodal metamaterials using both boundary textures and viscoelasticity. In particular, we realize a metamaterial that has a negative (positive) Poisson's ratio for low (high) compression rate over a finite range of strains. The ability of our oligomodal metamaterials to host multiple mechanical responses within a single structure paves the way toward multifunctional materials and devices.

Complex pathways and memory in compressed corrugated sheets.

The nonlinear response of driven complex materials-disordered magnets, amorphous media, and crumpled sheets-features intricate transition pathways where the system repeatedly hops between metastable states. Such pathways encode memory effects and may allow information processing, yet tools are lacking to experimentally observe and control these pathways, and their full breadth has not been explored. Here we introduce compression of corrugated elastic sheets to precisely observe and manipulate their full, multistep pathways, which are reproducible, robust, and controlled by geometry. We show how manipulation of the boundaries allows us to elicit multiple targeted pathways from a single sample. In all cases, each state in the pathway can be encoded by the binary state of material bits called hysterons, and the strength of their interactions plays a crucial role. In particular, as function of increasing interaction strength, we observe Preisach pathways, expected in systems of independently switching hysterons; scrambled pathways that evidence hitherto unexplored interactions between these material bits; and accumulator pathways which leverage these interactions to perform an elementary computation. Our work opens a route to probe, manipulate, and understand complex pathways, impacting future applications in soft robotics and information processing in materials.

Adaptive plasticity of auxetic Kirigami hydrogel fabricated from anisotropic swelling of cellulose nanofiber film.

Hydrogels are flexible materials that typically accommodate elongation with positive Poisson's ratios. Auxetic property, i.e., the negative Poisson's ratio, of elastic materials can be macroscopically implemented by the structural design of the continuum. We realize it without mold for hydrogel made of cellulose nanofibers (CNFs). The complex structural design of auxetic Kirigami is first implemented on the dry CNF film, i.e., so-called nanopaper, by laser processing, and the CNF hydrogel is formed by dipping the film in liquid water. The CNF films show anisotropic swelling where drastic volumetric change mainly originates from increase in the thickness. This anisotropy makes the design and fabrication of the emergent Kirigami hydrogel straightforward. We characterize the flexibility of this mechanical metamaterial made of hydrogel by cyclic tensile loading starting from the initial end-to-end distance of dry sample. The tensile load at the maximum strain decreases with the increasing number of cycles. Furthermore, the necessary work up to the maximum strain even decreases to the negative value, while the work of restoration to the original end-to-end distance increases from the negative value to the positive. The equilibrium strain where the force changes the sign increases to reach a plateau. This plastic deformation due to the cyclic loading can be regarded as the adaptive response without fracture to the applied dynamic loading input.

Highly anisotropic swelling-based gelation of dry film of cellulose nanofibers enables development of emergent hydrogel Kirigami with auxetic behavior. Furthermore, adaptive response to the iterative loading condition is found.

A Metamaterial-like Structure Design Using Non-uniformly Distributed Dielectric and Conducting Strips to Boost the RF Field Distribution in 7 T MRI.

Metamaterial-based designs in ultra-high field (≥7 T) MRI have the promise of increasing the local magnetic resonance imaging (MRI) signal and potentially even the global efficiency of both the radiofrequency (RF) transmit and receive resonators. A recently proposed metamaterial-like structure-comprised of a high-permittivity dielectric material and a set of evenly distributed copper strips-indeed resulted in a local increase in RF transmission. Here, we demonstrate that non-uniform designs of this metamaterial-like structure can be used to boost the ultimate RF field distribution. A non-uniform dielectric distribution can yield longer electric dipoles, thus extending the RF transmit field coverage. A non-uniform distribution of conducting strips enables the tailoring of the local electric field hot spots, where a concave distribution resulted in lower power deposition. Simulations of the brain and calf regions using our new metamaterial-like design, which combines non-uniform distributions of both the dielectric and conducting strips, revealed a 1.4-fold increase in the RF field coverage compared to the uniform distribution, and a 1.5-2-fold increase in the transmit efficiency compared to the standard surface-coil.

A Metamaterial Surface Avoiding Loss from the Radome for a Millimeter-Wave Signal-Sensing Array Antenna.

Radar systems are a type of sensor that detects radio signals reflected from objects located a long distance from transmitters. For covering a longer range and a higher resolution in the operation of a radar, a high-frequency band and an array antenna are measures to take. Given a limited size to the antenna aperture in the front end of the radar, the choice of a millimeter-wave band leads to a denser layout for the array antenna and a higher antenna gain. Millimeter-wave signals tend to become attenuated faster by a larger loss of the covering material like the radome, implying this disadvantage offsets the advantage of high antenna directivity, compared to the C-band and X-band ones. As the radome is essential to the radar system to protect the array antenna from rain and dust, a metamaterial surface in the layer is suggested to meet multiple objectives. Firstly, the proposed electromagnetic structure is the protection layer for the source of radiation. Secondly, the metasurface does not disturb the millimeter-wave signal and makes its way through the cover layer to the air. This electromagnetically transparent surface transforms the phase distribution of the incident wave into the equal phase in the transmitted wave, resulting in an increased antenna gain. This is fabricated and assembled with the array antenna held in a 3D-printed jig with harnessing accessories. It is examined in view of S21 as the transfer coefficient between two ports of the VNA, having the antenna alone and with the metasurface. Additionally, the far-field test comes next to check the validity of the suggested structure and design. The bench test shows around a 7 dB increase in the transfer coefficient, and the anechoic chamber field test gives about a 5 dB improvement in antenna gain for a 24-band GHz array antenna.