Digital logic gates in soft, conductive mechanical metamaterials

Bioinspired, Rapidly Responsive Magnetically Tunable Stiffness Metamaterials

Programmable mechanical materials often require dynamic stiffness adaptability, but existing solutions face challenges with slow response times and limited precision. This study introduces magnetically tunable stiffness metamaterials (MTSM) that utilize a bioinspired ternary programming framework to achieve rapid and precise stiffness modulation. Drawing inspiration from biological sarcomeres, which naturally adjust stiffness through structural changes, the MTSM design employs direct ink writing, a 4D printing method, to incorporate neodymium microparticles and a styrene-isoprene-styrene polymer matrix. This approach enables the metamaterial to transition between three distinct stiffness states-soft, moderate, and stiff-through structural deformation controlled by magnetic torque. Integration of MTSM into a 3D array further enhances its versatility, allowing multi-layer stiffness adjustments under magnetic fields. The MTSM array achieves an impressive 390 percent stiffness modulation range and rapid changes in response to an external magnetic field, surpassing the limitations of prior designs. These findings emphasize the potential of ternary programming in MTSM as a foundation for creating next-generation programmable mechanical systems capable of rapid and efficient adaptability.

Inverse Design of Kirigami through Shape Programming of Rotating Units

Kirigami metamaterials have enabled a plethora of morphing patterns across art and engineering. However, the inverse design of kirigami for complex shapes remains a puzzle that so far cannot be solved without relying on complex numerical methods. Here, we present a purely geometric design method to overcome the reliance on sophisticated numerical algorithms and showcase how to leverage it for three distinct types of morphing targets, i.e., the contracted shape, the deployed shape, and the internal trajectories of the rotating units in kirigami specimens. Our results unveil the fundamental relations between the kirigami deformation and the shape of its rotating units and enable us to establish the underpinning physics through theoretical investigations validated via numerical simulations. This work brings ground-rule insights into morphing matter with rotating units and offers an intuitive, firsthand geometric route for the swift design of complex kirigami.

Programmable Metamaterials with Perforated Shell Group Supporting Versatile Information Processing

Mechanical metamaterials have emerged as promising tools for enabling mechanical intelligence in soft machines through interaction with the external environment. Note that most representative results in the literature focused on certain features of information processing with the designs of novel metamaterials. It remains challenging to design metamaterials with more integrated information processing capabilities toward comprehensive intelligence. In this work, a novel approach employing programmable multi-stability of perforated shells (PS) with staggered trapezoidal voids is proposed to develop transformable, information-processing metamaterials with high-density information. Multi-layer information storage, encoding, decoding, and reading are achieved by designing and arranging different types of PSs under mechanical compression or magnetic actuation. In addition, various application-oriented functionalities, such as information encryption, mechanical computing, wave amplification, and pressure transmission, are also demonstrated by taking advantage of the stable memory and tunable stiffness distributions of metamaterials. The proposed design strategy paves the way for multifunctional, miniaturized, and scalable information mechanical metamaterials, with significant potential for soft-material-based intelligent devices.

Harnessing Liquid Crystal Elastomers for Locomotion and Mechanical Intelligence in a Soft Robot

Recently, there has been an increased interest in endowing intelligent behaviors and features in soft robotic systems. As a prerequisite for intelligence, a system must integrate sensing, information processing, and the ability to act in response to external stimuli. This work presents a soft robotic crawler that demonstrates locomotion using electroactive liquid crystal elastomers (LCEs). By integrating independent components such as a photo-responsive LCE switch into a conductive electromechanical processing network based on sequential logic, the robot can sense optical indicators and process this information to change direction autonomously. This study expands the design of the individual mechanical material subsystems and experimentally showcases the autonomous operation of the soft robot. The embedded bistable mechanism stores the present operational state of the robot and enforces directional locomotion by controlling the position of a mechanical hard stop that interfaces with the legs. The robot exemplifies the advanced potential of soft intelligent material systems for complex autonomous behavior, leveraging the unique properties of LCEs and a mechanical-electrical network for information processing without the need for traditional electronic controllers.

Light-Controlled Soft Switches for Optical Logic Gate Operations

While liquid crystal elastomers (LCEs) show promise for diverse soft actuators due to their strong stimulus responsiveness, limited investigation into their light perception and processing restricts their wider use in intelligent systems. This study employs a hollow double-layer structure to design light-controlled logic soft switches based on LCEs. The design realizes digital logic circuits including AND gates, OR gates, and NOT gates, as well as an optical switch array capable of converting light signals into visualized digital signals. These light-controlled soft switches exhibit strong photothermal responsiveness (~12 s), high programmability, and excellent cyclic stability (>500 times). This research provides a new perspective on light-controlled logic soft switches and their applications in logic circuits.

Bistable Soft Shells for Programmable Mechanical Logic

Mechanical computing promises to integrate semiconductor-based digital logic in several applications, but it needs straightforward programmable devices for changing computing rules in situ. A methodology based on strain-governed, bistable soft shells that process digital information by interchanging their internal/external surfaces is proposed. This bistable behavior, explained via model-based design, safeguards robustness by working only once for each input pulse. Thus, these shells are leveraged to create a buffer and a NOT gate that lead to six fundamental gates (AND, OR, NAND, NOR, XOR, and XNOR). All these functions are integrated into a unique programmable device, making mechanically integrated circuits more adaptable with rule-changeable logic operations. This design ensures continuous processes and general applicability to multiple types of signals (a pressurized fluid can replace mechanical driving signals is shown). It also empowers more complex logic functions suitable for expanded applications, such as the half and full adders is addressed.

Bioinspired Microhinged Actuators for Active Mechanism-Based Metamaterials

Mechanism-based metamaterials, comprising rigid elements interconnected by flexible hinges, possess the potential to develop intelligent micromachines with programmable motility and morphology. However, the absence of efficient microactuators has constrained the ability to achieve multimodal locomotion and active shape-morphing behaviors at the micro and nanoscale. In this study, inspiration from the flight mechanisms of tiny insects is drawn to develop a biomimetic microhinged actuator by integrating compliant mechanisms with soft hydrogel muscle. A Pseudo-Rigid-Body mechanical model is introduced to analyze structural deformation, demonstrating that this hydrogel-based microactuator can undergo significant folding while maintaining high structural stiffness. Furthermore, multiple microhinged actuators are combined to facilitate folding in multiple degrees of freedom and arbitrary directions. Fabricated by a multi-step four-dimensional (4D) direct laser writing technique, the microhinged actuators are integrated into 2D and 3D metamaterials enabling programable shape morphing. Additionally, micro-kirigami with photonic structures is demonstrated to show the pattern transforming actuated by the microhinges. This bioinspired design approach opens new avenues for the development of active mechanism-based metamaterials capable of intricate shape-morphing behaviors.

Parallel mechanical computing: Metamaterials that can multitask

Decades after being replaced with digital platforms, analogue computing has experienced a surging interest following developments in metamaterials and intricate fabrication techniques. Specifically, wave-based analogue computers which impart spatial transformations on an incident wavefront, commensurate with a desired mathematical operation, have gained traction owing to their ability to directly encode the input in its unprocessed form, bypassing analogue-to-digital conversion. While promising, these systems are inherently limited to single-task configurations. Their inability to concurrently perform multiple tasks, or compute in parallel, represents a major hindrance to advancing conceptual mechanical devices with broader computational capabilities. In here, we present a pathway to simultaneously process independent computational tasks within the same architected structure. By breaking time invariance in a set of metasurface building blocks, multiple frequency-shifted beams are self-generated which absorb notable energy amounts from the fundamental signal. The onset of these tunable harmonics enables distinct computational tasks to be assigned to different independent "channels," effectively allowing an analogue mechanical computer to multitask.

Digital Mechanical Metamaterial with Programmable Functionality

Digitization has brought a new era to the world, liberating information from physical media. The material structure-property relation is high-dimensional and nonlinear, and the digitization of structure-property relations may bring unprecedented functional programmability and diversity. Here, a new concept of digital mechanical metamaterial (DMM) is presented, where property design is realized by programming the digital states of the DMM to decouple the design of the structure and property. Transforming the binary stable states of a curved beam to the digital bit, one unit cell of DMM manifests three distinct deformation responses under compression, i.e., compression-twist coupling (CTC), compression-shear coupling (CSC), and pure compression (PC). These deformation modes show notable differences in motion and stiffness, which, by digitally programming a series of DMM, can yield a spectrum of functionalities, including information encryption, stress-strain relation customization, energy absorption in cushioning, effective vibration isolation, and tunable force transmission. This study pioneers a versatile material design paradigm that provides much greater freedom for the property design of intelligent mechanical metamaterials.

Janus Swarm Metamaterials for Information Display, Memory, and Encryption

Metamaterials are emerging as an unconventional platform to perform computing abstractions in physical systems by processing environmental stimuli into information. While computation functions have been demonstrated in mechanical systems, they rely on compliant mechanisms to achieve predefined states, which impose inherent design restrictions that limit their miniaturization, deployment, reconfigurability, and functionality. Here, a metamaterial system is described based on responsive magnetoactive Janus particle (MAJP) swarms with multiple programmable functions. MAJPs are designed with tunable structure and properties in mind, that is, encoded swarming behavior and fully reversible switching mechanisms, to enable programmable dynamic display, non-volatile and semi-volatile memory, Boolean logic, and information encryption functions in soft, wearable devices. MAJPs and their unique swarming behavior open new functions for the design of multifunctional and reconfigurable display devices, and constitute a promising building block to develop the next generation of soft physical computing devices, with growing applications in security, defense, anti-counterfeiting, camouflage, soft robotics, and human-robot interaction.

Anisotropic nonlinear optical responses of Ta2NiS5 flake towards ultrafast logic gates and secure all-optical information transmission

Optical logic gates based on nonlinear optical property of material with ultrafast response speed and excellent computational processing power can break the performance bottleneck of electronic transistors. As one of the layered 2D materials, Ta2NiS5 exhibits high anisotropic mobility, exotic electrical response, and intriguing optical properties. Due to the low-symmetrical crystal structures, it possesses in-plane anisotropic physical properties. The optical absorption information of Ta2NiS5 is investigated by anisotropic linear absorption spectra, femtosecond laser intensity scanning (I-scan), and non-degenerate pump-probe technology. The I-scan results show a distinct maximum of ∼4.9 % saturable absorption (SA) and ∼4 % reverse saturable absorption (RSA) at different polarization directions of the incident laser. And, these unique nonlinear optical (NLO) properties originate from the anisotropic optical transition probability. Furthermore, the novel Ta2NiS5-based all-optical logic gates are proposed by manipulating the NLO absorption processes. And, the all-optical OR and NOR logic gates possess an ultrafast response speed approaching 1.7 THz. Meanwhile, an all-optical information transmission method with higher security and accuracy is achieved, which has promising potential to avoid the disclosure of information. This work provides a new path for designing versatile and novel optical applications based on Ta2NiS5 materials.

Geometric mechanics of kiri-origami-based bifurcated mechanical metamaterials

We explore a new design strategy of leveraging kinematic bifurcation in creating origami/kirigami-based three-dimensional (3D) hierarchical, reconfigurable, mechanical metamaterials with tunable mechanical responses. We start from constructing three basic, thick, panel-based structural units composed of 4, 6 and 8 rigidly rotatable cubes in close-looped connections. They are modelled, respectively, as 4R, 6R and 8R (R stands for revolute joint) spatial looped kinematic mechanisms, and are used to create a library of reconfigurable hierarchical building blocks that exhibit kinematic bifurcations. We analytically investigate their reconfiguration kinematics and predict the occurrence and locations of kinematic bifurcations through a trial-correction modelling method. These building blocks are tessellated in 3D to create various 3D bifurcated hierarchical mechanical metamaterials that preserve the kinematic bifurcations in their building blocks to reconfigure into different 3D architectures. By combining the kinematics and considering the elastic torsional energy stored in the folds, we develop the geometric mechanics to predict their tunable anisotropic Poisson's ratios and stiffnesses. We find that kinematic bifurcation can significantly effect mechanical responses, including changing the sign of Poisson's ratios from negative to positive beyond bifurcation, tuning the anisotropy, and overcoming the polarity of structural stiffness and enhancing the number of deformation paths with more reconfigured shapes.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Innovative Bistable Composites for Aerospace and High-Stress Applications: Integrating Soft and Hard Materials in Experimental, Modeling, and Simulation Studies

This study explores the development and performance of bistable materials, emphasizing their potential applications in aero-vehicles and high-stress environments. By integrating soft and hard materials within a composite structure, the research demonstrates the creation of bistable composites that exhibit remarkable flexibility and rigidity. Advanced simulations using COMSOL Multiphysics and 3D-printed prototypes reveal that these materials effectively absorb and dissipate stress, maintaining structural integrity under high-pressure conditions. Compression tests highlight the ability of bistable structures to bear significant loads, distributing stress efficiently across multiple layers. The innovative proposal of combining stiff and flexible materials within a single unit cell enhances bistable behavior, offering superior energy absorption and resilience. This work underscores the promise of bistable materials in advancing materials science, providing robust solutions for aerospace, automotive, and protective gear applications and paving the way for future research in optimizing bistable structures for diverse engineering challenges.

Computation Implemented by the Interaction of Chemical Reaction, Clustering, and De-Clustering of Molecules

A chemical reaction and its reaction environment are intrinsically linked, especially within the confines of narrow cellular spaces. Traditional models of chemical reactions often use differential equations with concentration as the primary variable, neglecting the density heterogeneity in the solution and the interaction between the reaction and its environment. We model the interaction between a chemical reaction and its environment within a geometrically confined space, such as inside a cell, by representing the environment through the size of molecular clusters. In the absence of fluctuations, the interplay between cluster size changes and the activation and inactivation of molecules induces oscillations. However, in unstable environments, the system reaches a fluctuating steady state. When an enzyme is introduced to this steady state, oscillations akin to action potential spike trains emerge. We examine the behavior of these spike trains and demonstrate that they can be used to implement logic gates. We discuss the oscillations and computations that arise from the interaction between a chemical reaction and its environment, exploring their potential for contributing to chemical intelligence.

Zeolitic Imidazolate Frameworks as Solid-State Nanomachines

Machines have continually developed with the needs of daily life and industrial applications. While the careful design of molecular-scale devices often displays enhanced properties along with mechanical movements, controlling mechanics within solid-state molecular structures remains a significant challenge. Here, we explore the distinct mechanical properties of zeolitic imidazolate frameworks (ZIFs)-frameworks that contain hidden mechanical components. Using a combination of experimental and theoretical approaches, we uncover the machine-like capabilities of ZIFs, wherein connected composite building units operate similarly to a mechanical linkage system. Importantly, this research suggests that certain ZIF subunits act as core mechanical components, paving an innovative view for the future design of solid-state molecular machines.

Reprogrammable and reconfigurable mechanical computing metastructures with stable and high-density memory

Mechanical computing encodes information in deformed states of mechanical systems, such as multistable structures. However, achieving stable mechanical memory in most multistable systems remains challenging and often limited to binary information. Here, we report leveraging coupling kinematic bifurcation in rigid cube-based mechanisms with elasticity to create transformable, multistable mechanical computing metastructures with stable, high-density mechanical memory. Simply stretching the planar metastructure forms a multistable corrugated platform. It allows for independent mechanical or magnetic actuation of individual bistable element, serving as pop-up voxels for display or binary units for various tasks such as information writing, erasing, reading, encryption, and mechanologic computing. Releasing the pre-stretched strain stabilizes the prescribed information, resistant to external mechanical or magnetic perturbations, whereas re-stretching enables editable mechanical memory, akin to selective zones or disk formatting for information erasure and rewriting. Moreover, the platform can be reprogrammed and transformed into a multilayer configuration to achieve high-density memory.

Unconventional acoustic wave propagation transitions induced by resonant scatterers in the high-density limit

Experiments on ultrasound propagation through a gel doped with resonant encapsulated microbubbles provided evidence for a discontinuous transition between wave propagation regimes at a critical excitation frequency. Such behavior is unlike that observed for soft materials doped with non-resonant air or through liquid foams, and disagrees with a simple mixture model for the effective sound speed. Here, we study the discontinuous transition by measuring the transition as a function of encapsulated microbubble volume fraction. The results show the transition always occurs in the strong-scattering limit (l/λ < 1, l and λ are the mean free path and wavelength, respectively), that at the critical frequency the effective phase velocity changes discontinuously to a constant value with increasing microbubble volume fraction, and the measured critical frequency shows a power law dependence on microbubble volume fraction. The results cannot be explained by multiple scattering theory, viscous effects, mode decoupling, or a critical density of states. It is hypothesized the transition depends upon the microbubble on-resonance effective properties, and we discuss the results within the context of percolation theory. The results shed light on the discontinuous transition's physics, and suggest soft materials can be engineered in this manner to achieve a broad range of physical properties with potential application in ultrasonic actuators and switches.

Intelligent electroactive material systems with self-adaptive mechanical memory and sequential logic

By synthesizing the requisite functionalities of intelligence in an integrated material system, it may become possible to animate otherwise inanimate matter. A significant challenge in this vision is to continually sense, process, and memorize information in a decentralized way. Here, we introduce an approach that enables all such functionalities in a soft mechanical material system. By integrating nonvolatile memory with continuous processing, we develop a sequential logic-based material design framework. Soft, conductive networks interconnect with embedded electroactive actuators to enable self-adaptive behavior that facilitates autonomous toggling and counting. The design principles are scaled in processing complexity and memory capacity to develop a model 8-bit mechanical material that can solve linear algebraic equations based on analog mechanical inputs. The resulting material system operates continually to monitor the current mechanical configuration and to autonomously search for solutions within a desired error. The methods created in this work are a foundation for future synthetic general intelligence that can empower materials to autonomously react to diverse stimuli in their environment.

Mechanical Metamaterials for Handwritten Digits Recognition

The increasing needs for new types of computing lie in the requirements in harsh environments. In this study, the successful development of a non-electrical neural network is presented that functions based on mechanical computing. By overcoming the challenges of low mechanical signal transmission efficiency and intricate layout design methodologies, a mechanical neural network based on bistable kirigami-based mechanical metamaterials have designed. In preliminary tests, the system exhibits high reliability in recognizing handwritten digits and proves operable in low-temperature environments. This work paves the way for a new, alternative computing system with broad applications in areas where electricity is not accessible. By integrating with the traditional electronic computers, the present system lays the foundation for a more diversified form of computing.

Reprogrammable Metamaterial Processors for Soft Machines

Soft metamaterials have attracted extensive attention due to their remarkable properties. These materials hold the potential to program and control the morphing behavior of soft machines, however, their combination is limited by the poor reprogrammability of metamaterials and incompatible communication between them. Here, printable and recyclable soft metamaterials possessing reprogrammable embedded intelligence to regulate the morphing of soft machines are introduced. These metamaterials are constructed from interconnected and periodically arranged logic unit cells that are able to perform compound logic operations coupling multiplication and negation. The scalable computation capacity of the unit cell empowers it to simultaneously process multiple fluidic signals with different types and magnitudes, thereby allowing the execution of sophisticated and high-level control operations. By establishing the laws of physical Boolean algebra and formulating a universal design route, soft metamaterials capable of diverse logic operations can be readily created and reprogrammed. Besides, the metamaterials' potential of directly serving as fluidic processors for soft machines is validated by constructing a soft latched demultiplexer, soft controllers capable of universal and customizable morphing programming, and a reprogrammable processor without reconnection. This work provides a facile way to create reprogrammable soft fluidic control systems to meet on-demand requirements in dynamic situations.

Anisotropic Morphing in Bistable Kirigami through Symmetry Breaking and Geometric Frustration

Shape morphing in bistable kirigami enables remarkable functionalities appealing to a diverse range of applications across the spectrum of length scale. At the core of their shape shifting lies the architecture of their repeating unit, where highly deformable slits and quasi-rigid rotating units often exhibit multiple symmetries that confer isotropic deployment obeying uniform scaling transformation. In this work, symmetry breaking in bistable kirigami is investigated to access geometric frustration and anisotropic morphing, enabling arbitrarily scaled deployment in planar and spatial bistable domains. With an analysis on their symmetry properties complemented by a systematic investigation integrating semi-analytical derivations, numerical simulations, and experiments on elastic kirigami sheets, this work unveils the fundamental relations between slit symmetry, geometric frustration, and anisotropic bistable deployment. Furthermore, asymmetric kirigami units are leveraged in planar and flat-to-3D demonstrations to showcase the pivotal role of shear deformation in achieving target shapes and functions so far unattainable with uniformly stretchable kirigami. The insights provided in this work unveil the role of slit symmetry breaking in controlling the anisotropic bistable deployment of soft kirigami metamaterials, enriching the range of achievable functionalities for applications spanning deployable space structures, wearable technologies, and soft machines.

Modulating photothermocapillary interactions for logic operations at the air-water interface

We demonstrate a system for performing logical operations (OR, AND, and NOT gates) at the air-water interface based on Marangoni optical trapping and repulsion between photothermal particles. We identify a critical separation distance at which the trapped particle assemblies become unstable, providing insight into the potential for scaling to larger arrays of logic elements.

Optical computing metasurfaces: applications and advances

Integrated photonic devices and artificial intelligence have presented a significant opportunity for the advancement of optical computing in practical applications. Optical computing technology is a unique computing system based on optical devices and computing functions, which significantly differs from the traditional electronic computing technology. On the other hand, optical computing technology offers the advantages such as fast speed, low energy consumption, and high parallelism. Yet there are still challenges such as device integration and portability. In the burgeoning development of micro-nano optics technology, especially the deeply ingrained concept of metasurface technique, it provides an advanced platform for optical computing applications, including edge detection, image or motion recognition, logic computation, and on-chip optical computing. With the aim of providing a comprehensive introduction and perspective for optical computing metasurface applications, we review the recent research advances of optical computing, from nanostructure and computing methods to practical applications. In this work, we review the challenges and analysis of optical computing metasurfaces in engineering field and look forward to the future development trends of optical computing.

Flexible nanomechanical bit based on few-layer graphene

Mechanical computers have gained intense research interest at size scales ranging from nano to macro as they may complement electronic computers operating in extreme environments. While nanoscale mechanical computers may be easier to integrate with traditional electronic components, most current nanomechanical computers are based on volatile resonator systems that require continuous energy input. In this study, we propose a non-volatile nanomechanical bit based on the quasi-stable configurations of few-layer graphene with void defects, and demonstrate its multiple quasi-stable states by deriving an analytic relationship for the void configuration based on a competition between the bending energy and the cohesive energy. Using this nanomechanical bit, typical logic gates are constructed to perform Boolean calculations, including NOT, AND, OR, NAND and NOR gates, and demonstrate reprogrammability between these logic gates. We also study the accuracy and the stability of the nanomechanical bits based on the few-layer graphene. These findings provide a novel approach to realize the nanomechanical computing process.

Digital Mechanical Metamaterial: Encoding Mechanical Information with Graphical Stiffness Pattern for Adaptive Soft Machines

Inspired by the adaptive features exhibited by biological organisms like the octopus, soft machines that can tune their shape and mechanical properties have shown great potential in applications involving unstructured and continuously changing environments. However, current soft machines are far from achieving the same level of adaptability as their biological counterparts, hampered by limited real-time tunability and severely deficient reprogrammable space of properties and functionalities. As a steppingstone toward fully adaptive soft robots and smart interactive machines, an encodable multifunctional material that uses graphical stiffness patterns is introduced here to in situ program versatile mechanical capabilities without requiring additional infrastructure. Through independently switching the digital binary stiffness states (soft or rigid) of individual constituent units of a simple auxetic structure with elliptical voids, in situ and gradational tunability is demonstrated here in various mechanical qualities such as shape-shifting and -memory, stress-strain response, and Poisson's ratio under compressive load as well as application-oriented functionalities such as tunable and reusable energy absorption and pressure delivery. This digitally programmable material is expected to pave the way toward multienvironment soft robots and interactive machines.

Liquid Metal Actuators: A Comparative Analysis of Surface Tension Controlled Actuation

Liquid metals, with their unique combination of electrical and mechanical properties, offer great opportunities for actuation based on surface tension modulation. Thanks to the scaling laws of surface tension, which can be electrochemically controlled at low voltages, liquid metal actuators stand out from other soft actuators for their remarkable characteristics such as high contractile strain rates and higher work densities at smaller length scales. This review summarizes the principles of liquid metal actuators and discusses their performance as well as theoretical pathways toward higher performances. The objective is to provide a comparative analysis of the ongoing development of liquid metal actuators. The design principles of the liquid metal actuators are analyzed, including low-level elemental principles (kinematics and electrochemistry), mid-level structural principles (reversibility, integrity, and scalability), and high-level functionalities. A wide range of practical use cases of liquid metal actuators from robotic locomotion and object manipulation to logic and computation is reviewed. From an energy perspective, strategies are compared for coupling the liquid metal actuators with an energy source toward fully untethered robots. The review concludes by offering a roadmap of future research directions of liquid metal actuators.

Embodying Multifunctional Mechano-Intelligence in and Through Phononic Metastructures Harnessing Physical Reservoir Computing

Recent advances in autonomous systems have prompted a strong demand for the next generation of adaptive structures and materials to possess built-in intelligence in their mechanical domain, the so-called mechano-intelligence (MI). Previous MI attempts mainly focused on specific case studies and lacked a systematic foundation in effectively and efficiently constructing and integrating different intelligent functions. Here, a new approach is uncovered to create multifunctional MI in adaptive structures using physical reservoir computing (PRC). That is, to concurrently embody computing power and the key elements of intelligence, namely perception, decision-making, and commanding, directly in the mechanical domain, advancing from conventional reliance on add-on computers and massive electronics. As an exemplar platform, a mechanically intelligent phononic metastructure is developed by harnessing its high-degree-of-freedom nonlinear dynamics as PRC power. Through analyses and experiments, multiple intelligent structural functions are demonstrated ranging from self-tuning wave controls to wave-based logic gates. This research provides the much-needed basis for creating future smart structures and materials that greatly surpass the state of the art-such as lower power consumption, more direct interactions, and better survivability in harsh environments or under cyberattacks. Moreover, it enables the addition of new functions and autonomy to systems without overburdening the onboard computers.

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.

Multifunctional Intelligent Wearable Devices Using Logical Circuits of Monolithic Gold Nanowires

Although multifunctional wearable devices have been widely investigated for healthcare systems, augmented/virtual realities, and telemedicines, there are few reports on multiple signal monitoring and logical signal processing by using one single nanomaterial without additional algorithms or rigid application-specific integrated circuit chips. Here, multifunctional intelligent wearable devices are developed using monolithically patterned gold nanowires for both signal monitoring and processing. Gold bulk and hollow nanowires show distinctive electrical properties with high chemical stability and high stretchability. In accordance, the monolithically patterned gold nanowires can be used to fabricate the robust interfaces, programmable sensors, on-demand heating systems, and strain-gated logical circuits. The stretchable sensors show high sensitivity for strain and temperature changes on the skin. Furthermore, the micro-wrinkle structures of gold nanowires exhibit the negative gauge factor, which can be used for strain-gated logical circuits. Taken together, this multifunctional intelligent wearable device would be harnessed as a promising platform for futuristic electronic and biomedical applications.

A reprogrammable mechanical metamaterial with origami functional-group transformation and ring reconfiguration

Recent advancements in reprogrammable metamaterials have enabled the development of intelligent matters with variable special properties in situ. These metamaterials employ intra-element physical reconfiguration and inter-element structural transformation. However, existing mono-characteristic homo-element mechanical metamaterials have limited reprogramming functions. Here, we introduce a reprogrammable mechanical metamaterial composed of origami elements with heterogeneous mechanical properties, which achieves various mechanical behavior patterns by functional group transformations and ring reconfigurations. Through the anisotropic assembly of two heterogeneous elements into a functional group, we enable mechanical behavior switching between positive and negative stiffness. The resulting polygonal ring exhibits rotational deformation, zero Poisson's ratio stretching/compression deformation, and negative Poisson's ratio auxetic deformation. Arranging these rings periodically yields homogeneous metamaterials. The reconfiguration of quadrilateral rings allows for continuous fine-tunability of the mechanical response and negative Poisson's ratio. This mechanical metamaterial could provide a versatile material platform for reprogrammable mechanical computing, multi-purpose robots, transformable vehicles and architectures at different scales.

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.

Optomechanical computing in liquid crystal elastomers

Embodied decision-making in soft, engineered matter has sparked recent interest towards the development of intelligent materials. Such decision-making capabilities can be realized in soft materials via digital information processing with combinational logic operations. Although previous research has explored soft material actuators and embedded logic in soft materials, achieving a high degree of autonomy in these material systems remains a challenge. Light is an ideal stimulus to trigger information processing in soft materials due to its low thermal effect and remote use. Thus, one approach for developing soft, autonomous materials is to integrate optomechanical computing capabilities in photoresponsive materials. Here, we establish a methodology to embed combinational logic circuitry in a photoresponsive liquid crystal elastomer (LCE) film. These LCEs are designed with embedded switches and integrated circuitry using liquid metal-based conductive traces. The resulting optomechanical computing LCEs can effectively process optical information via light, thermal, and mechanical energy conversion. The methods introduced in this work to fabricate a material capable of optical information processing can facilitate the implementation of a sense of sight in soft robotic systems and other compliant devices.

In-memory mechanical computing

Mechanical computing requires matter to adapt behavior according to retained knowledge, often through integrated sensing, actuation, and control of deformation. However, inefficient access to mechanical memory and signal propagation limit mechanical computing modules. To overcome this, we developed an in-memory mechanical computing architecture where computing occurs within the interaction network of mechanical memory units. Interactions embedded within data read-write interfaces provided function-complete and neuromorphic computing while reducing data traffic and simplifying data exchange. A reprogrammable mechanical binary neural network and a mechanical self-learning perceptron were demonstrated experimentally in 3D printed mechanical computers, as were all 16 logic gates and truth-table entries that are possible with two inputs and one output. The in-memory mechanical computing architecture enables the design and fabrication of intelligent mechanical systems.

Encoding and Storage of Information in Mechanical Metamaterials

Information processing using material's own properties has gained increasing interest. Mechanical metamaterials, due to their diversity of deformation modes and wide design space, can be used to realize information processing, such as computing and storage. Here a mechanical metamaterial system is demonstrated for material-based encoding and storage of data through programmed reconfigurations of the metamaterial's structured building blocks. Sequential encoding and decoding are achieved in the three-dimensional (3D) printed pixelated mechanical metamaterial via kirigami-based "pixels" with programmable, temperature-dependent bistability. The mechanical metamaterial is demonstrated via a multistep deformation of encoding messages of texts and surfaces with arrays of binary data, and then decoding them by applying a predetermined stretching and heating regimen to sequentially retrieve layers of stored information and display them on its surface. This approach serves as a general framework to enable the encoding and storage of data with mechanical metamaterials.

Origami-based integration of robots that sense, decide, and respond

Origami-inspired engineering has enabled intelligent materials and structures to process and react to environmental stimuli. However, it is challenging to achieve complete sense-decide-act loops in origami materials for autonomous interaction with environments, mainly due to the lack of information processing units that can interface with sensing and actuation. Here, we introduce an integrated origami-based process to create autonomous robots by embedding sensing, computing, and actuating in compliant, conductive materials. By combining flexible bistable mechanisms and conductive thermal artificial muscles, we realize origami multiplexed switches and configure them to generate digital logic gates, memory bits, and thus integrated autonomous origami robots. We demonstrate with a flytrap-inspired robot that captures 'living prey', an untethered crawler that avoids obstacles, and a wheeled vehicle that locomotes with reprogrammable trajectories. Our method provides routes to achieve autonomy for origami robots through tight functional integration in compliant, conductive materials.

Topological transformability and reprogrammability of multistable mechanical metamaterials

Concepts from quantum topological states of matter have been extensively utilized in the past decade to create mechanical metamaterials with topologically protected features, such as one-way edge states and topologically polarized elasticity. Maxwell lattices represent a class of topological mechanical metamaterials that exhibit distinct robust mechanical properties at edges/interfaces when they are topologically polarized. Realizing topological phase transitions in these materials would enable on-and-off switching of these edge states, opening opportunities to program mechanical response and wave propagation. However, such transitions are extremely challenging to experimentally control in Maxwell topological metamaterials due to mechanical and geometric constraints. Here we create a Maxwell lattice with bistable units to implement synchronized transitions between topological states and demonstrate dramatically different stiffnesses as the lattice transforms between topological phases both theoretically and experimentally. By combining multistability with topological phase transitions, this metamaterial not only exhibits topologically protected mechanical properties that swiftly and reversibly change, but also offers a rich design space for innovating mechanical computing architectures and reprogrammable neuromorphic metamaterials. Moreover, we design and fabricate a topological Maxwell lattice using multimaterial 3D printing and demonstrate the potential for miniaturization via additive manufacturing. These design principles are applicable to transformable topological metamaterials for a variety of tasks such as switchable energy absorption, impact mitigation, wave tailoring, neuromorphic metamaterials, and controlled morphing systems.

3D morphable systems via deterministic microfolding for vibrational sensing, robotic implants, and reconfigurable telecommunication

DNA and proteins fold in three dimensions (3D) to enable functions that sustain life. Emulation of such folding schemes for functional materials can unleash enormous potential in advancing a wide range of technologies, especially in robotics, medicine, and telecommunication. Here, we report a microfolding strategy that enables formation of 3D morphable microelectronic systems integrated with various functional materials, including monocrystalline silicon, metallic nanomembranes, and polymers. By predesigning folding hosts and configuring folding pathways, 3D microelectronic systems in freestanding forms can transform across various complex configurations with modulated functionalities. Nearly all transitional states of 3D microelectronic systems achieved via the microfolding assembly can be easily accessed and modulated in situ, offering functional versatility and adaptability. Advanced morphable microelectronic systems including a reconfigurable microantenna for customizable telecommunication, a 3D vibration sensor for hand-tremor monitoring, and a bloomable robot for cardiac mapping demonstrate broad utility of these assembly schemes to realize advanced functionalities.

Fabrication and Functionality Integration Technologies for Small-Scale Soft Robots

Small-scale soft robots are attracting increasing interest for visible and potential applications owing to their safety and tolerance resulting from their intrinsic soft bodies or compliant structures. However, it is not sufficient that the soft bodies merely provide support or system protection. More importantly, to meet the increasing demands of controllable operation and real-time feedback in unstructured/complicated scenarios, these robots are required to perform simplex and multimodal functionalities for sensing, communicating, and interacting with external environments during large or dynamic deformation with the risk of mismatch or delamination. Challenges are encountered during fabrication and integration, including the selection and fabrication of composite/materials and structures, integration of active/passive functional modules with robust interfaces, particularly with highly deformable soft/stretchable bodies. Here, methods and strategies of fabricating structural soft bodies and integrating them with functional modules for developing small-scale soft robots are investigated. Utilizing templating, 3D printing, transfer printing, and swelling, small-scale soft robots can be endowed with several perceptual capabilities corresponding to diverse stimulus, such as light, heat, magnetism, and force. The integration of sensing and functionalities effectively enhances the agility, adaptability, and universality of soft robots when applied in various fields, including smart manufacturing, medical surgery, biomimetics, and other interdisciplinary sciences.

Flexible Metamaterial Electronics

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

Fluidic innervation sensorizes structures from a single build material

Multifunctional materials with distributed sensing and programmed mechanical properties are required for myriad emerging technologies. However, current fabrication techniques constrain these materials' design and sensing capabilities. We address these needs with a method for sensorizing architected materials through fluidic innervation, where distributed networks of empty, air-filled channels are directly embedded within an architected material's sparse geometry. By measuring pressure changes within these channels, we receive feedback regarding material deformation. Thus, this technique allows for three-dimensional printing of sensorized structures from a single material. With this strategy, we fabricate sensorized soft robotic actuators on the basis of handed shearing auxetics and accurately predict their kinematics from the sensors' proprioceptive feedback using supervised learning. Our strategy for facilitating structural, sensing, and actuation capabilities through control of form alone simplifies sensorized material design for applications spanning wearables, smart structures, and robotics.

Mechanical integrated circuit materials

Recent developments in autonomous engineered matter have introduced the ability for intelligent materials to process environmental stimuli and functionally adapt^1-4. To formulate a foundation for such an engineered living material paradigm, researchers have introduced sensing^5-11 and actuating^12-16 functionalities in soft matter. Yet, information processing is the key functional element of autonomous engineered matter that has been recently explored through unconventional techniques with limited computing scalability^17-20. Here we uncover a relation between Boolean mathematics and kinematically reconfigurable electrical circuits to realize all combinational logic operations in soft, conductive mechanical materials. We establish an analytical framework that minimizes the canonical functions of combinational logic by the Quine-McCluskey method, and governs the mechanical design of reconfigurable integrated circuit switching networks in soft matter. The resulting mechanical integrated circuit materials perform higher-level arithmetic, number comparison, and decode binary data to visual representations. We exemplify two methods to automate the design on the basis of canonical Boolean functions and individual gate-switching assemblies. We also increase the computational density of the materials by a monolithic layer-by-layer design approach. As the framework established here leverages mathematics and kinematics for system design, the proposed approach of mechanical integrated circuit materials can be realized on any length scale and in a wide variety of physics.

3D Printed Acoustically Programmable Soft Microactuators

The concept of creating all-mechanical soft microrobotic systems has great potential to address outstanding challenges in biomedical applications, and introduce more sustainable and multifunctional products. To this end, magnetic fields and light have been extensively studied as potential energy sources. On the other hand, coupling the response of materials to pressure waves has been overlooked despite the abundant use of acoustics in nature and engineering solutions. In this study, we show that programmed commands can be contained on 3D nanoprinted polymer systems with the introduction of selectively excited air bubbles and rationally designed compliant mechanisms. A repertoire of micromechanical systems is engineered using experimentally validated computational models that consider the effects of primary and secondary pressure fields on entrapped air bubbles and the surrounding fluid. Coupling the dynamics of bubble oscillators reveals rich acoustofluidic interactions that can be programmed in space and time. We prescribe kinematics by harnessing the forces generated through these interactions to deform structural elements, which can be remotely reconfigured on demand with the incorporation of mechanical switches. These basic actuation and analog control modules will serve as the building blocks for the development of a novel class of micromechanical systems powered and programmed by acoustic signals.

Construction of liquid metal-based soft microfluidic sensors via soft lithography

Background

Liquid metal (LM) can be integrated into microfluidic channel, bringing new functionalities of microfluidics and opening a new window for soft microfluidic electronics, due to the superior advantages of the conductivity and deformability of LMs. However, patterning the LMs into microfluidic channels requires either selective surface wetting or complex fabrication process.

Results

In this work, we develop a method to pattern the LMs onto the soft elastomer via soft lithographic process for fabrication of soft microfluidic sensors without the surface modification, bulky facilities, and complicated processes. The combination of the interfacial hydrogen bond and surface tension enables the LM patterns transfer to the soft elastomer. The transferred LM patterns with an ellipse-like cross-section further improve the stability under the mechanical deformation. Three proof-of-concept experiments were conducted to demonstrate the utilization of this method for development of thermochromic sensors, self-powered capacity sensors and flexible biosensor for glucose detection.

Conclusions

In summary, the proposed method offers a new patterning method to obtain soft microfluidic sensors and brings new possibilities for microfluidics-related wearable devices.

Graphical Abstract

Supplementary Information

The online version contains supplementary material available at 10.1186/s12951-022-01471-0.

Noise logic with an InGaN/SiNx/Si uniband diode photodetector

Noise logic is introduced by the wavelength dependent photocurrent noise of an InGaN/SiNx/Si uniband diode photodetector. A wavelength versus photocurrent noise discrimination map is constructed from the larger photocurrent noise for red light than that for green light. A minimum measurement time of four seconds is deduced from the standard deviation of the photocurrent noise for a safe wavelength distinction. A logic NOT gate is realized as representative with on or off red or green light as binary 1 or 0 inputs and the photocurrent noise above or below a defined threshold as binary 1 or 0 outputs.

Bio-Inspired Bianisotropic Magneto-Sensitive Elastomers with Excellent Multimodal Transformation

Magneto-sensitive soft materials that can accomplish fast, remote, and reversible shape morphing are highly desirable for practical applications including biomedical devices, soft robotics, and flexible electronics. In conventional magneto-sensitive elastomers (MSEs), there is a tradeoff between employing hard magnetic particles with costly magnetic programming and utilizing soft magnetic particle chains causing tedious and small deformation. Here, inspired by the shape and movement of mimosa, a novel soft magnetic particle doped shape material bianisotropic magneto-sensitive elastomer (SM bianisotropic MSE) with multimodal transformation and superior deformability is developed. The high-aspect-ratio shape anisotropy and the material anisotropy in which the magnetic particles are arranged in a chainlike structure together impart magnetic anisotropy to the SM bianisotropic MSE. A magneto-elastic analysis model is proposed, and it is elucidated that magnetic anisotropy leads to peculiar field-direction-dependent multimodal transformation. More importantly, a quadrilateral assembly and a regular hexagon assembly based on this SM bianisotropic MSE are designed, and they exhibit 2.4 and 1.7 times the deformation capacity of shape anisotropic samples, respectively. By exploiting the multidegree of freedom and excellent deformability of the SM bianisotropic MSE, flexible logic switches and ultrasoft magnetic manipulators are further demonstrated, which prove its potential applications in future intelligent flexible electronics and autonomous soft robotics.

Review of Electronics-Free Robotics: Toward a Highly Decentralized Control Architecture

In recent years, conventional model-based motion control has become more challenging owing to the continuously increasing complexity of areas in which robots must operate and navigate. A promising approach for solving this issue is by employing interaction-based robotics, which includes behavior-based robotics, morphological computations, and soft robotics that generate control and computation functions based on interactions between the robot body and environment. These control strategies, which incorporate the diverse dynamics of the environment to generate control and computation functions, may alleviate the limitations imposed by the finite physical and computational resources of conventional robots. However, current interaction-based robots can only perform a limited number of actions compared with conventional robots. To increase the diversity of behaviors generated from body–environment interactions, a robotic body design methodology that can generate appropriate behaviors depending on the various situations and environmental stimuli that arise from them is necessitated. Electronics-free robotics is reviewed herein as a paradigm for designing robots with control and computing functions in each part of the body. In electronics-free robotics, instead of using electrical sensors or computers, a control system is constructed based on only mechanical or chemical reactions. Robotic bodies fabricated using this approach do not require bulky electrical wiring or peripheral circuits and can perform control and computational functions by obtaining energy from a central source. Therefore, by distributing these electronics-free controllers throughout the body, we hope to design autonomous and highly decentralized robotic bodies than can generate various behaviors in response to environmental stimuli. This new paradigm of designing and controlling robot bodies can enable realization of completely electronics-free robots as well as expand the range of conventional electronics-based robot designs.

Biomimetic and Biologically Compliant Soft Architectures via 3D and 4D Assembly Methods: A Perspective

Recent progress in soft material chemistry and enabling methods of 3D and 4D fabrication-emerging programmable material designs and associated assembly methods for the construction of complex functional structures-is highlighted. The underlying advances in this science allow the creation of soft material architectures with properties and shapes that programmably vary with time. The ability to control composition from the molecular to the macroscale is highlighted-most notably through examples that focus on biomimetic and biologically compliant soft materials. Such advances, when coupled with the ability to program material structure and properties across multiple scales via microfabrication, 3D printing, or other assembly techniques, give rise to responsive (4D) architectures. The challenges and prospects for progress in this emerging field in terms of its capacities for integrating chemistry, form, and function are described in the context of exemplary soft material systems demonstrating important but heretofore difficult-to-realize biomimetic and biologically compliant behaviors.