Programmable Metamaterials Research Articles

Far field ring beam generation based on 3-bit encoded metasurface

Abstract The encoding metasurface establishes a bridge between the physical and digital worlds, ushering in a new era of manipulating electromagnetic waves and realizing programmable metamaterials through digital coding sequences. This "digital metasurface," relying on binary logic, significantly simplifies the design process, thereby enhancing the flexibility and efficiency of controlling electromagnetic waves. While most encoding metasurfaces control beamforming for pencil-shaped beams, we propose a 3-bit encoding metasurface with a "well structure" in the microwave band.The 3-bit encoding metasurface features a more extensive encoding sequence, offering increased degrees of freedom and flexibility in manipulating the direction of electromagnetic wave propagation. Its symmetric design features polarization-insensitive characteristics, suitable for generating annular beams by varying gradient-encoded numbers radially. This approach enables the production of linearly polarized omnidirectional radiation within the desired elevation angle range. Additionally, adjustments in quantity and orientation of the produced annular beams are achieved through Fourier convolution theorem. This type of annular beams holds promise for applications in various fields, including wireless radio broadcasting and wireless local area networks.

Programmable Quasi-Zero-Stiffness Metamaterials

Quasi-zero-stiffness (QZS) metamaterials have attracted significant interest for application in low-frequency vibration isolation. However, previous work has been limited by the design mechanism of QZS metamaterials, as it is still difficult to achieve a simplified structure suitable for practical engineering applications. Here, we introduce a class of programmable QZS metamaterials and a novel design mechanism that address this long-standing difficulty. The proposed QZS metamaterials are formed by an array of representative unit cells (RUCs) with the expected QZS features, where the QZS features of the RUC are tailored by means of a structural bionic mechanism. In our experiments, we validate the QZS features exhibited by the RUCs, the programmable QZS behavior, and the potential promising applications of these programmable QZS metamaterials in low-frequency vibration isolation. The obtained results could inspire a new class of programmable QZS metamaterials for low-frequency vibration isolation in current and future mechanical and other engineering applications.

Automated model discovery for textile structures: The unique mechanical signature of warp knitted fabrics

Textile fabrics have unique mechanical properties, which make them ideal candidates for many engineering and medical applications: They are initially flexible, nonlinearly stiffening, and ultra-anisotropic. Various studies have characterized the response of textile structures to mechanical loading; yet, our understanding of their exceptional properties and functions remains incomplete. Here we integrate biaxial testing and constitutive neural networks to automatically discover the best model and parameters to characterize warp knitted polypropylene fabrics. We use experiments from different mounting orientations, and discover interpretable anisotropic models that perform well during both training and testing. Our study shows that constitutive models for warp knitted fabrics are highly sensitive to an accurate representation of the textile microstructure, and that models with three microstructural directions outperform classical orthotropic models with only two in-plane directions. Strikingly, out of 214=16,384 possible combinations of terms, we consistently discover models with two exponential linear fourth invariant terms that inherently capture the initial flexibility of the virgin mesh and the pronounced nonlinear stiffening as the loops of the mesh tighten. We anticipate that the tools we have developed and prototyped here will generalize naturally to other textile fabrics–woven or knitted, weft knit or warp knit, polymeric or metallic–and, ultimately, will enable the robust discovery of anisotropic constitutive models for a wide variety of textile structures. Beyond discovering constitutive models, we envision to exploit automated model discovery for the generative material design of wearable devices, stretchable electronics, and smart fabrics, as programmable textile metamaterials with tunable properties and functions. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN. Statement of significanceTextile structures are rapidly gaining popularity in many biomedical applications including tissue engineering, wound healing, and surgical repair. A precise understanding of their unique mechanical properties is critical to tailor them to their specific functions. Here we integrate mechanical testing and machine learning to automatically discover the best models for knitted polypropylene fabrics. We show that warp knitted fabrics possess a complex symmetry with three distinct microstructural directions. Along these, the behavior is dominated by an exponential linear term that characterize the initial flexibility of the virgin mesh and the nonlinear stiffening as the loops of the fabric tighten. We expect that our technology will generalize naturally to other fabrics and enable the robust discovery of complex anisotropic models for a wide variety of textile structures.

Intelligent Reversible Reconfigurable Metamaterials Based on a Two-Way Shape Memory Polymer.

The development of intelligent reversible reconfigurable metamaterials has great significance in constructing three-dimensional metamaterials and introducing reversible tunability into metamaterials. Here, we introduce an intelligent metamaterial consisting of a two-way shape memory polymer (2W-SMP) ethylene vinyl acetate copolymer (EVA) actuator substrate and a patterned flexible-rigid film. Mechanical buckling of the 2W-SMP substrate was controlled by thermal stimulation. This makes it possible to afford an ability to initiate 3D structure formation or shape reconfiguration remotely in an on-demand fashion. In addition, the shape of the 2W-SMP substrate is temperature-dependent, allowing repeatable reversible deformation through temperature control after a single programming. Therefore, the electromagnetic properties of metamaterials can also be repeatedly and reversibly tuned between 9.15 and 10.82 GHz. Experimental demonstrations include the deformation and tunable electromagnetic properties of intelligent reversible reconfigurable metamaterial cells. The results create many opportunities for advanced programmable three-dimensional metamaterials.

Novel 4D-printed multi-stable metamaterials: programmability of force-displacement behaviour and deformation sequence.

The unique properties of metamaterials are determined by the configuration and spatial arrangement of artificially designed unit structures. However, the configuration and mechanical properties of conventional metamaterials are challenging to reverse and adjust. Based on curved beams, two types of novel three-dimensional (3D) multi-stable metamaterials with reconfigurable deformation and tunable mechanical properties are designed and fabricated using a four-dimensional (4D) printing method. The effects of temperature and curved-beam thickness on the force-displacement curves and multi-stable snapping sequence of the 3D multi-stable metamaterials are investigated by finite-element analysis (FEA) and experiments. In addition, based on the designed four-branch multi-stable metamaterials, three- and six-branched multi-stable structures are designed by changing the number of curved-beam branches. It is shown that, owing to shape memory effects, the 3D multi-stable metamaterials can realize mechanical programmability, and the multi-stable deformation sequence can be precisely regulated by varying the temperature and curved-beam thickness. These 4D-printed multi-stable metamaterials provide valuable contributions to the design of programmable multi-stable metamaterials and their applications in soft robots and intelligent structures. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Programmable responsive metamaterials for mechanical computing and robotics.

Unconventional computing based on mechanical metamaterials has been of growing interest, including how such metamaterials might process information via autonomous interactions with their environment. Here we describe recent efforts to combine responsive materials with nonlinear mechanical metamaterials to achieve stimuli-responsive mechanical logic and computation. We also describe some key challenges and opportunities in the design and construction of these devices, including the lack of comprehensive computational tools, and the challenges associated with patterning multi-material mechanisms.

Machine learning-accelerated inverse design of programmable bi-functional metamaterials

Bi-functional metamaterials with programmable coefficients of thermal expansion (CTEs) and Poisson’s ratios (PRs) have garnered significant attention among researchers due to the ability to manifest desired deformations under thermal and mechanical loads. Nevertheless, a current challenge lies in efficiently achieving the inverse design of these metamaterials to meet diverse application requirements. This paper presents a machine learning (ML) model that can establish a logical mapping relationship between geometric/material parameters and mechanical properties, and it is applied to the inverse design of bi-functional metamaterials with desired CTEs and PRs. Furthermore, the inverse design capability of the ML model was validated by the finite element analysis and experimental test. The results demonstrate that the geometric models obtained from the inverse prediction can effectively exhibit the desired deformation behavior under thermal and mechanical loads. And the ML model proves to be a valuable tool, offering effective guidance for the design of bi-functional metamaterials with specific CTEs and PRs.

Active mechanical cloaking for unsupervised damage resilience in programmable elastic metamaterials.

Owing to the architected void-filled low-density configurations, metamaterials are prone to defects during the complex manufacturing process, or damages under operational conditions. Recently mechanical cloaking has been proposed to shield the effect of such disorders in terms of homogenized mechanical responses. The major drawback in these studies are that the damage location should be known a priori, and the cloak is designed around that damaged zone before manufacturing. Such postulation does not allow unsupervised damage resilience during the manufacturing and service life of metamaterials by active reconfiguration of the stress field depending on the random and unpredictable evolution of damage. Here, we propose a radically different approach by introducing piezoelectric lattices where the effect of random appearance of any single or multiple disorders and damages with complex shapes, sizes and distributions can be shielded through active multi-physically controlled cloaks by voltage-dependent modulation of the stress fields within the cloaking region. Notably, this can be achieved without breaking periodicity and any additional material in the cloaking region unlike earlier studies concerning mechanical cloaks. The proposed active class of elastic metamaterials will bring a step-change in the on-demand mechanical performance of critically important structural components and unsupervised damage resilience for enhanced durability and sustainability.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Tuning negative stiffness mechanical metamaterial's snap-through behavior with a series-connected spring

Negative stiffness mechanical metamaterials have shown great promise for various applications and are progressing toward programmability. The key challenge in designing programmable metamaterials lies in achieving efficient tunability. However, due to the limitations of current tuning strategies, many existing programmable metamaterials fall short of expectations. Here, we introduce a strategy that facilitates efficient response transformation and performance tuning across scales for negative stiffness mechanical metamaterials. The implementation of this novel tuning approach requires only the adjustment of a serial spring's stiffness which is much easier and more practical than controlling the non-linear contributions of the buckling parts. A systematic theoretical model has been developed to illustrate this innovative approach, and the results have been validated through simulations and experiments. This research can serve as a reference for designing programmable negative stiffness mechanical metamaterials (NSMMs).

3D‐Printed Mechano‐Optic Force Sensor for Soft Robotic Gripper Enabled by Programmable Structural Metamaterials

Rapid deployment of automation in today's world has opened up exciting possibilities in the realm of design and fabrication of soft robotic grippers endowed with sensing capabilities. Herein, a novel design and rapid fabrication by 3D printing of a mechano‐optic force sensor with a large dynamic range, sensitivity, and linear response, enabled by metamaterials‐based structures, is presented. A simple approach for programming the metamaterial's behavior based on mathematical modeling of the sensor under dynamic loading is proposed. Machine learning models are utilized to predict the complete force–deformation profile, encompassing the linear range, the onset of nonlinear behavior, and the slope of profiles in both bending and compression‐dominated regions. The design supports seamless integration of the sensor into soft grippers, enabling 3D printing of the soft gripper with an embedded sensor in a single step, thus overcoming the tedious and complex and multiple fabrication steps commonly applied in conventional processes. The sensor boasts a fine resolution of 0.015 N, a measurement range up to 16 N, linearity (adj. R2–0.991), and delivers consistent performance beyond 100 000 cycles. The sensitivity and range of the embedded mechano‐optic force sensor can be easily programmed by both the metamaterial structure and the material's properties.

Kinematotropic linkage-based cellular metamaterials with bifurcation motion: Construction and analysis

This paper proposes the design and networking method of a metamorphic Ori-block unit and develops a novel family of cellular mechanical metamaterials. First, a novel 6R (Revolute pair) diamond kinematotropic linkage (DKL) with two bifurcation motions is presented and its kinematic model is analyzed using the improved Denavit–Hartenberg parameter method. Additionally, the screw theory is used to analyze its mobility and verify it has not instantaneity in every configuration. This linkage exhibits two bifurcation motions with one rotational degree-of-freedom (DOF). Moreover, a metamorphic Ori-block unit is designed based on the 6R DKL and optimized to assemble a novel metamaterial cell. According to performance analysis, the first motion mode of this metamaterial cell exhibits a negative Poisson's ratio performance, while the second motion mode involves a large deployed/folded ratio. Based on this metamaterial cell, two methods are proposed for networking cellular metamaterials. On the basis of preserving the kinematic characteristics and performance of the metamaterial cell, an optimized design is conducted, and subsequently the optimized metamaterial cells are assembled into novel cellular metamaterials. This study provides a novel concept for the design and movable network of deployable and programmable cellular metamaterials.

Bio-Inspired Pressure-Dependent Programmable Mechanical Metamaterial with Self-Sealing Ability.

Self-sealing is one of the fascinating functions in nature that enables living material systems to respond immediately to damage. A prime plant model is Delosperma cooperi, which can rapidly self-seal damaged succulent leaves by systematically deforming until the wound closes. Inspired by this self-sealing principle, a novel programmable mechanical metamaterial has been developed to mimic the underlying damage management concept. This material is able to react autonomously to changes in its physical condition caused by an induced damage. To design this ability into the programmable metamaterial, a permeable unit cell design has been developed that can change size depending on the internal pressure. The parameter space and associated mechanical functionality of the unit cell design is simulated and analyzed under periodic boundary conditions and various pressures. The principles of self-sealing behavior in designed metamaterials are investigated, crack closure efficiency is identified for different crack lengths, the limitations of the proposed approach are discussed, and successful crack closure is experimentally demonstrated in the fabricated metamaterial. Although this study facilitates the first step on the way of integrating new bio-inspired principles in the metamaterials, the results show how programmable mechanical metamaterials might extend materials design space from pure properties to life-likeabilities.

Photonic Spin‐Hall Logic Devices Based on Programmable Spoof Plasmonic Metamaterial

AbstractThe entanglement of the momentum of light with its spin at interfaces or inside structured media, known as the photonic spin‐Hall effect, holds great promise for various applications, such as beam splitting, focusing, and polarization detection. However, the photonic spin‐Hall effect remains unexplored in the field of logic operation. In this work, the photonic spin‐Hall effect of spoof surface plasmon polaritons (SSPPs) in programmable metamaterial is demonstrated. Moreover, photonic spin‐Hall logic devices based on programmable spoof plasmonic metamaterial are designed, enabling the control of energy flow through the utilization of both spin and digital coding, with examples including SSPPs logic gates such as the “AND” gate, the “NIMPLY” gate (A AND NOT B), the “OR” gate, and the “NOT” gate. The findings introduce the combination of digital coding metamaterial with the photonic spin Hall effect, which offers a powerful and flexible platform for controlling electromagnetic waves in information processing.

Programmable mechanical metamaterials: basic concepts, types, construction strategies—a review

Metamaterials have been a hot topic over the past 2 decades, involving scientific research directions in materials, engineering, and physics. Among them, programmable mechanical metamaterials are an emerging class of metamaterials that offer intelligent programming and control of diverse mechanical properties, such as stiffness, damping, thermal expansion, and shape memory behavior. Meanwhile, it can be rationally designed to have specific geometric architectures and programming strategies in response to different types of external stimuli, such as temperature, electric and magnetic fields, and mechanical loads. These intelligent mechanical properties have a wide range of potential applications due to their uniqueness and controllability, including soft robotics, adaptive structures, and wearable devices. Thus, the programming strategies to achieve them are particularly critical. Combined with related programmable thinking concepts, this paper briefly reviews programming strategies for programmable mechanical metamaterials, including geometric, structural, and external driving force programming. Meanwhile, this paper presents the principles of programming strategies classified according to different programmable mechanical properties (e.g., programmable stiffness, deformation, multistability) and looks ahead to the challenges and opportunities for future research.

Lattice concrete: 3D printed periodic cellular structures through selective cement hydration

3D printing of concrete allows fabrication of complex shapes and structures. Among various 3D printing approaches, the particle bed 3D printing technique has gained attention in recent years, especially for its ability to generate complex topologies that are otherwise impossible to make using cement-paste extrusion-based techniques. In this work, we present our trials on 3D printing cellular lattice concrete structures using a powder bed technique by employing selective cement hydration. Specifically, we print two-types of cellular concrete blocks (i) with interconnected spherical voids and (ii) with gyroid structures, each block with uniform edge lengths of 15 cm. We use Ordinary Portland Cement, fine-grained sand, and normal water, without the use of any admixtures or additives. The printing technology used was custom-made and is quite simple and inexpensive involving a syringe based water jetting on to a powder bed of cement and sand mixture. We discuss the quality of the printed specimens obtained as well as their strength characteristics. An inadvertent observation was made, where a compressive strength gain by a factor of more than 2 was obtained in specimens that were exposed to open atmosphere for a long duration after a 28 day curing period compared to those that were tested immediately after curing. The current study demonstrates the feasibility of fabricating cellular lattice concrete structures that can potentially be useful as programmable metamaterials for civil engineering applications.

Response Speed Characterization of a Thermally Actuated Programmable Metamaterial

Response Speed Characterization of a Thermally Actuated Programmable Metamaterial

Programmable and resilient metamaterials with anisotropic and non-linear mechanical responses composed exclusively of stiff constituents.

Recently, significant progress has been made in the field of flexible bulk metamaterials composed of soft and elastic materials, unlocking the potential for achieving programmable non-linear mechanical responses, such as shape morphing, energy absorption, and information processing. However, the majority of these metamaterials utilize expensive hyperelastic materials and require complex fabrication processes. Additionally, constructing eco-friendly stiff constituents for these metamaterials remains challenging due to their limited elastic limit strains (<0.1). Here, we propose a systematic design strategy by combining curved beams with chiral metastructures to generate a family of three-dimensional programmable resilient mechanical metamaterials without relying on flexible or hyperelastic constituents. These tiled metamaterials demonstrate robust, anisotropic and non-linear resilience under large elastic compression strains (>0.75), while exhibiting a programmable effective modulus reduction of nearly 6 orders of magnitude compared to the native stiff components. Furthermore, leveraging their stable resilience under high-frequency stimuli, we successfully developed a meter-scale soft robot capable of traversing complex narrow scenarios on demand without the need for flexible materials or sophisticated pipelines. We anticipate that these mechanical metamaterials could serve as a universal platform for programmable active dampers, modular flexible robots, and medical rehabilitation equipment at various scales.

Inverse design of Bézier curve-based mechanical metamaterials with programmable negative thermal expansion and negative Poisson's ratio via a data augmented deep autoencoder.

Controlling stress and deformation induced by thermo-mechanical stimulation in high-precision mechanical systems can be achieved by mechanical metamaterials (MM) exhibiting negative thermal expansion (NTE) and negative Poisson's ratio (NPR). However, the inverse design of MM exhibiting a wide range of arbitrary target NTEs and NPRs is a challenging task due to the low design flexibility of analytical methods and parametric studies based on numerical simulation. In this study, we propose Bézier curve-based programmable chiral mechanical metamaterials (BPCMs) and a deep autoencoder-based inverse design model (DAIM) for the inverse design of BPCMs. Through iterative transfer learning with data augmentation, DAIM can generate BPCMs with a curved rib shape inaccessible with the Bézier curve, which improves the inverse design performance of the DAIM in the data sparse domain. This approach decreases the mean absolute error of NTE and NPR between the inverse design target and the numerical simulation results of inverse designed BPCMs on the data-sparse domain by 79.25% and 83.33% on average, respectively. A 3D-printed BPCM is validated experimentally and exhibits good coincidence with the target NTE and NPR. Our proposed BPCM and the corresponding inverse design framework enable the inverse design of BPCMs with NTE in the range of -1100 to 0 ppm K-1 and NPR in the range of -0.6 to -0.1. Furthermore, programmable thermal deformation modes with a fixed Poisson's ratio are realized by combining various inverse designed BPCM unit cells. BPCMs and the DAIM for their inverse design are expected to improve the mechanical robustness of high-precision mechanical systems through tunable modulation of thermo-mechanical stimulation.

Thermally active programmable metamaterials with holey tilted struts

Bistable transition is often applied in the design of microstructures in metamaterials. In this study, we introduce a series of strategically placed holes in the tilted struts, and observe, through numerical and experimental analysis, an effect of the perforation on the snap-through buckling behavior of the structure. By infilling the holes with thermal-sensitive polymer bars, we realize actively tuning the local stiffness of the holey struts, thereby enabling a means to switch the metamaterial between bistable and monostable states. Furthermore, we propose a multi-stable metamaterial by stacking bistable units with different arrange of infilled and empty holes. The designed metamaterial demonstrates a progressive restoration from the deformed shape to its original shape as the environment temperature reaches up to certain values. These findings highlight the potential of holey-type bistable metamaterials in the design of actuators, deployable structures, and reusable energy absorbers.

Emergence and inversion of chirality in hierarchical assemblies of CdS nanocrystal fibers.

Arranging semiconducting nanocrystals into ordered superstructures is a promising platform to study fundamental light-matter interactions and develop programmable optical metamaterials. We investigated how the geometrical arrangement of CdS nanocrystals in hierarchical assemblies affects chiroptical properties. To create these structures, we controlled the evaporation of a colloidal CdS nanocrystal solution between two parallel plates. We combined in situ microscopy and computational modeling to establish a formation mechanism involving the shear-induced alignment of nanocrystal fibers and the subsequent mechanical relaxation of the stretched fibers to form Raman noodle-type band textures. The high linear anisotropy in these films shares many similarities with cholesteric liquid crystals. The films deposited on top and bottom surfaces exhibit opposite chirality. The mechanistic insights from this study are consequential to enable future advances in the design and fabrication of programmable optical metamaterials for further development of polarization-based optics toward applications in sensing, hyperspectral imaging, and quantum information technology.