Mechanical computing

Chemical reservoir computation in a self-organizing reaction network

Chemical reaction networks, such as those found in metabolism and signalling pathways, enable cells to process information from their environment1,2. Current approaches to molecular information processing and computation typically pursue digital computation models and require extensive molecular-level engineering3. Despite considerable advances, these approaches have not reached the level of information processing capabilities seen in living systems. Here we report on the discovery and implementation of a chemical reservoir computer based on the formose reaction4. We demonstrate how this complex, self-organizing chemical reaction network can perform several nonlinear classification tasks in parallel, predict the dynamics of other complex systems and achieve time-series forecasting. This in chemico information processing system provides proof of principle for the emergent computational capabilities of complex chemical reaction networks, paving the way for a new class of biomimetic information processing systems.

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.

Mechanical Neural Networks with Explicit and Robust Neurons

Mechanical computing provides an information processing method to realize sensing-analyzing-actuation integrated mechanical intelligence and, when combined with neural networks, can be more efficient for data-rich cognitive tasks. The requirement of solving implicit and usually nonlinear equilibrium equations of motion in training mechanical neural networks makes computation challenging and costly. Here, an explicit mechanical neuron is developed of which the response can be directly determined without the need of solving equilibrium equations. A training method is proposed to ensure the robustness of the neuron, i.e., insensitivity to defects and perturbations. The explicitness and robustness of the neurons facilitate the assembly of various network structures. Two exemplified networks, a robust mechanical convolutional neural network and a mechanical recurrent neural network with long short-term memory capabilities for associative learning, are experimentally demonstrated. The introduction of the explicit and robust mechanical neuron streamlines the design of mechanical neural networks fulfilling robotic matter with a level of intelligence.

Controlled pathways and sequential information processing in serially coupled mechanical hysterons

The complex sequential response of frustrated materials results from the interactions between material bits called hysterons. Hence, a central challenge is to understand and control these interactions, so that materials with targeted pathways and functionalities can be realized. Here, we show that hysterons in serial configurations experience geometrically controllable antiferromagnetic-like interactions. We create hysteron-based metamaterials that leverage these interactions to realize targeted pathways, including those that break the return point memory property, characteristic of independent or weakly interacting hysterons. We uncover that the complex response to sequential driving of such strongly interacting hysteron-based materials can be described by finite state machines. We realize information processing operations such as string parsing in materia, and outline a general framework to uncover and characterize the FSMs for a given physical system. Our work provides a general strategy to understand and control hysteron interactions, and opens a broad avenue toward material-based information processing.

Design rules for controlling active topological defects

Topological defects play a central role in the physics of many materials, including magnets, superconductors, and liquid crystals. In active fluids, defects become autonomous particles that spontaneously propel from internal active stresses and drive chaotic flows stirring the fluid. The intimate connection between defect textures and active flow suggests that properties of active materials can be engineered by controlling defects, but design principles for their spatiotemporal control remain elusive. Here, we propose a symmetry-based additive strategy for using elementary activity patterns, as active topological tweezers, to create, move, and braid such defects. By combining theory and simulations, we demonstrate how, at the collective level, spatial activity gradients act like electric fields which, when strong enough, induce an inverted topological polarization of defects, akin to a negative susceptibility dielectric. We harness this feature in a dynamic setting to collectively pattern and transport interacting active defects. Our work establishes an additive framework to sculpt flows and manipulate active defects in both space and time, paving the way to design programmable active and living materials for transport, memory, and logic.

Emergent disorder and mechanical memory in periodic metamaterials

Ordered mechanical systems typically have one or only a few stable rest configurations, and hence are not considered useful for encoding memory. Multistable and history-dependent responses usually emerge from quenched disorder, for example in amorphous solids or crumpled sheets. In contrast, due to geometric frustration, periodic magnetic systems can create their own disorder and espouse an extensive manifold of quasi-degenerate configurations. Inspired by the topological structure of frustrated artificial spin ices, we introduce an approach to design ordered, periodic mechanical metamaterials that exhibit an extensive set of spatially disordered states. While our design exploits the correspondence between frustration in magnetism and incompatibility in meta-mechanics, our mechanical systems encompass continuous degrees of freedom, and thus generalize their magnetic counterparts. We show how such systems exhibit non-Abelian and history-dependent responses, as their state can depend on the order in which external manipulations were applied. We demonstrate how this richness of the dynamics enables to recognize, from a static measurement of the final state, the sequence of operations that an extended system underwent. Thus, multistability and potential to perform computation emerge from geometric frustration in ordered mechanical lattices that create their own disorder.

Valley Pseudospin Polarized Evanescent Coupling between Microwave Ring Resonator and Waveguide in Phononic Topological Insulators

A coupled ring-waveguide structure is at the core of bosonic wave-based information processing systems, enabling advanced wave manipulations such as filtering, routing, and multiplexing. However, its miniaturization is challenging due to momentum conservation issues in rings with larger curvature that induce significant backscattering and radiation leakage and hampering stable operation. Here, we address it by taking an alternative approach of using topological technology in wavelength-scale and microwave ring-waveguide coupled systems built in nanoengineered phononic crystals. Our approach, which leverages pseudospin conservation in valley topological systems, eliminates phonon backscattering and achieves directional evanescent coupling. The resultant hypersonic waves in the tiny ring exhibit robust transport and resonant circulation. Furthermore, the ring-waveguide hybridization enables critical coupling, where valley-dependent ring-waveguide interference blocks the transmission. Our findings reveal the capability of topological phenomena for managing ultrahigh-frequency phonons in nano/microscale structures and pave the way for advanced phononic circuits in classical and quantum signal processing applications.

Complexity biomechanics: a case study of dragonfly wing design from constituting composite material to higher structural levels

Presenting a novel framework for sustainable and regenerative design and development is a fundamental future need. Here we argue that a new framework, referred to as complexity biomechanics, which can be used for holistic analysis and understanding of natural mechanical systems, is key to fulfilling this need. We also present a roadmap for the design and development of intelligent and complex engineering materials, mechanisms, structures, systems, and processes capable of automatic adaptation and self-organization in response to ever-changing environments. We apply complexity biomechanics to elucidate how the different structural components of a complex biological system as dragonfly wings, from ultrastructure of the cuticle, the constituting bio-composite material of the wing, to higher structural levels, collaboratively contribute to the functionality of the entire wing system. This framework not only proposes a paradigm shift in understanding and drawing inspiration from natural systems but also holds potential applications in various domains, including materials science and engineering, biomechanics, biomimetics, bionics, and engineering biology.

Integrated mechanical computing for autonomous soft machines

Mechanical computing offers a new modality to formulate computational autonomy in intelligent matter or machines without any external powering or active elements. Transition (or solitary) waves, induced by nonreciprocity in mechanical metamaterials comprising a chain of bistable elements, have proven to be a key ingredient for dissipation-free transmission and computation of mechanical information. However, advanced processing of mechanical information in existing designs is hindered by its dissipation when interacting with networked logic gates. Here, we present a metamaterial design strategy that allows non-dispersive mechanical solitary waves to compute multi-level cascaded logic functions, termed 'integrated mechanical computing', by propagating through a network of structurally heterogeneous computing units. From a perspective of characteristic potential energy, we establish an analytical framework that helps in understanding the solitary wave-based mechanical computation, and governs the mechanical design of key determinants for realizing cascaded logic computation, such as soliton profile and logic elements. The developed integrated mechanical computing systems are shown to receive, transmit and compute mechanical information to actuate intelligent soft machine prototypes in a seamless and integrated manner. These findings would pave the way for future intelligent robots and machines that perform computational operations between various non-electrical environmental inputs.

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.

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

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

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.

Engineering Kirigami Frameworks Toward Real-World Applications

The surge in advanced manufacturing techniques has led to a paradigm shift in the realm of material design from developing completely new chemistry to tailoring geometry within existing materials. Kirigami, evolved from a traditional cultural and artistic craft of cutting and folding, has emerged as a powerful framework that endows simple 2D sheets with unique mechanical, thermal, optical, and acoustic properties, as well as shape-shifting capabilities. Given its flexibility, versatility, and ease of fabrication, there are significant efforts in developing kirigami algorithms to create various architectured materials for a wide range of applications. This review summarizes the fundamental mechanisms that govern the transformation of kirigami structures and elucidates how these mechanisms contribute to their distinctive properties, including high stretchability and adaptability, tunable surface topography, programmable shape morphing, and characteristics of bistability and multistability. It then highlights several promising applications enabled by the unique kirigami designs and concludes with an outlook on the future challenges and perspectives of kirigami-inspired metamaterials toward real-world applications.

Architected Poly(ionic liquid) Composites with Spatially Programmable Mechanical Properties and Mixed Conductivity

Structural electrolytes present advantages over liquid varieties, which are critical to myriad applications. In particular, structural electrolytes based on polymerized ionic liquids or poly(ionic liquids) (pILs) provide wide electrochemical windows, high thermal stability, nonvolatility, and modular chemistry. However, current methods of fabricating structural electrolytes from pILs and their composites present limitations. Recent advances have been made in 3D printing pIL electrolytes, but current printing techniques limit the complexity of forms that can be achieved, as well as the ability to control mechanical properties or conductivity. We introduce a method for fabricating architected pIL composites as structural electrolytes via embedded 3D (EMB3D) printing. We present a modular design for formulating ionic liquid (IL) monomer composite inks that can be printed into sparse, lightweight, free-standing lattices with different functionalities. In addition to characterizing the rheological and mechanical behaviors of IL monomer inks and pIL lattices, we demonstrate the self-sensing capabilities of our printed structural electrolytes during cyclic compression. Finally, we use our inks and printing method to spatially program self-sensing capabilities in pIL lattices through heterogeneous architectures as well as ink compositions that provide mixed ionic-electronic conductivity. Our free-form approach to fabricating structural electrolytes in complex, 3D forms with programmable, anisotropic properties has broad potential use in next-generation sensors, soft robotics, bioelectronics, energy storage devices, and more.

Duality and Sheared Analytic Response in Mechanism-Based Metamaterials

Mechanical metamaterials designed around a zero-energy pathway of deformation known as a mechanism, challenge the conventional picture of elasticity and generate complex spatial response that remains largely uncharted. Here, we present a unified theoretical framework to showing that the presence of a unimode in a 2D structure generates a space of anomalous zero-energy sheared analytic modes. The spatial profiles of these stress-free strain patterns is dual to equilibrium stress configurations. We show a transition at an exceptional point between bulk modes in structures with conventional Poisson ratios (anauxetic) and evanescent surface modes for negative Poisson ratios (auxetic). We suggest a first application of these unusual response properties as a switchable signal amplifier and filter for use in mechanical circuitry and computation.

Interlinking spatial dimensions and kinetic processes in dissipative materials to create synthetic systems with lifelike functionality

Biological systems spontaneously convert energy input into the actions necessary to survive. Motivated by the efficacy of these processes, researchers aim to forge materials systems that exhibit the self-sustained and autonomous functionality found in nature. Success in this effort will require synthetic analogues of the following: a metabolism to generate energy, a vasculature to transport energy and materials, a nervous system to transmit 'commands', a musculoskeletal system to translate commands into physical action, regulatory networks to monitor the entire enterprise, and a mechanism to convert 'nutrients' into growing materials. Design rules must interconnect the material's structural and kinetic properties over ranges of length (that can vary from the nano- to mesoscale) and timescales to enable local energy dissipations to power global functionality. Moreover, by harnessing dynamic interactions intrinsic to the material, the system itself can perform the work needed for its own functionality. Here, we assess the advances and challenges in dissipative materials design and at the same time aim to spur developments in next-generation functional, 'living' materials.

The bumpy road to friction control

The frictional properties of material interfaces can be rationally designed.

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.

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.

Higher-order singularities in phase-tracked electromechanical oscillators

Singularities ubiquitously exist in different fields and play a pivotal role in probing the fundamental laws of physics and developing highly sensitive sensors. Nevertheless, achieving higher-order (≥3) singularities, which exhibit superior performance, typically necessitates meticulous tuning of multiple (≥3) coupled degrees of freedom or additional introduction of nonlinear potential energies. Here we propose theoretically and confirm using mechanics experiments, the existence of an unexplored cusp singularity in the phase-tracked (PhT) steady states of a pair of coherently coupled mechanical modes without the need for multiple (≥3) coupled modes or nonlinear potential energies. By manipulating the PhT singularities in an electrostatically tunable micromechanical system, we demonstrate an enhanced cubic-root response to frequency perturbations. This study introduces a new phase-tracking method for studying interacting systems and sheds new light on building and engineering advanced singular devices with simple and well-controllable elements, with potential applications in precision metrology, portable nonreciprocal devices, and on-chip mechanical computing.

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.

Strain topological metamaterials and revealing hidden topology in higher-order coordinates

Topological physics has revolutionized materials science, introducing topological phases of matter in diverse settings ranging from quantum to photonic and phononic systems. Herein, we present a family of topological systems, which we term "strain topological metamaterials", whose topological properties are hidden and unveiled only under higher-order (strain) coordinate transformations. We firstly show that the canonical mass dimer, a model that can describe various settings such as electrical circuits and optics, among others, belongs to this family where strain coordinates reveal a topological nontriviality for the edge states at free boundaries. Subsequently, we introduce a mechanical analog of the Majorana-supporting Kitaev chain, which supports topological edge states for both fixed and free boundaries within the proposed framework. Thus, our findings not only extend the way topological edge states are identified, but also promote the fabrication of novel topological metamaterials in various fields, with more complex, tailored boundaries.

Uncovering and Experimental Realization of Multimodal 3D Topological Metamaterials for Low-Frequency and Multiband Elastic Wave Control

Topological mechanical metamaterials unlock confined and robust elastic wave control. Recent breakthroughs have precipitated the development of 3D topological metamaterials, which facilitate extraordinary wave manipulation along 2D planar and layer-dependent waveguides. The 3D topological metamaterials studied thus far are constrained to function in single-frequency bandwidths that are typically in a high-frequency regime, and a comprehensive experimental investigation remains elusive. In this paper, these research gaps are addressed and the state of the art is advanced through the synthesis and experimental realization of a 3D topological metamaterial that exploits multimodal local resonance to enable low-frequency elastic wave control over multiple distinct frequency bands. The proposed metamaterial is geometrically configured to create multimodal local resonators whose frequency characteristics govern the emergence of four unique low-frequency topological states. Numerical simulations uncover how these topological states can be employed to achieve polarization-, frequency-, and layer-dependent wave manipulation in 3D structures. An experimental study results in the attainment of complete wave fields that illustrate 2D topological waveguides and multi-polarized wave control in a physical testbed. The outcomes from this work provide insight that will aid future research on 3D topological mechanical metamaterials and reveal the applicability of the proposed metamaterial for wave control applications.

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.

Statics and diffusive dynamics of surfaces driven by p-atic topological defects

Inspired by epithelial morphogenesis, we consider a minimal model for the shaping of a surface driven by p-atic topological defects. We show that a positive (negative) defect can dynamically generate a (hyperbolic) cone whose shape evolves diffusively, and predict that a defect of charge + 1/p leads to a final semi-cone angle β which satisfies the inequality . By exploiting the fact that for axisymmetric surfaces, the extrinsic geometry is tightly coupled to the intrinsic geometry, we further show that the resulting stationary shape of a membrane with negligible bending modulus and embedded polar order is a deformed lemon with two defects at antipodal points. Finally, we close by pointing out that our results may be relevant beyond epithelial morphogenesis in such contexts as shape transitions in macroscopic closed spheroidal surfaces such as pollen grains.

Phase-transforming mechanical metamaterials with dynamically controllable shape-locking performance

Active mechanical metamaterials with customizable structures and deformations, active reversible deformation, dynamically controllable shape-locking performance and stretchability are highly suitable for applications in soft robotics and flexible electronics, yet it is challenging to integrate them due to their mutual conflicts. Here, we introduce a class of phase-transforming mechanical metamaterials (PMMs) that integrate the above properties. Periodically arranging basic actuating units according to the designed pattern configuration and positional relationship, PMMs can customize complex and diverse structures and deformations. Liquid-vapor phase transformation provides active reversible large deformation while a silicone matrix offers stretchability. The contained carbonyl iron powder endows PMMs with dynamically controllable shape-locking performance, thereby achieving magnetically assisted shape locking and energy storing in different working modes. We build a theoretical model and finite element simulation to guide the design process of PMMs, so as to develop a variety of PMMs with different functions suitable for different applications, such as a programmed PMM, reconfigurable antenna, soft lens, soft mechanical memory, biomimetic hand, biomimetic flytrap and self-contained soft gripper. PMMs are applicable to achieve various 2D deformations and 2D-to-3D deformations, and integrate multiple properties, including customizable structures and deformations, active reversible deformation, rapid reversible shape locking, adjustable energy storing and stretchability, which could open a new application avenue in soft robotics and flexible electronics.

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.

A modular strategy for distributed, embodied control of electronics-free soft robots

Robots typically interact with their environments via feedback loops consisting of electronic sensors, microcontrollers, and actuators, which can be bulky and complex. Researchers have sought new strategies for achieving autonomous sensing and control in next-generation soft robots. We describe here an electronics-free approach for autonomous control of soft robots, whose compositional and structural features embody the sensing, control, and actuation feedback loop of their soft bodies. Specifically, we design multiple modular control units that are regulated by responsive materials such as liquid crystal elastomers. These modules enable the robot to sense and respond to different external stimuli (light, heat, and solvents), causing autonomous changes to the robot's trajectory. By combining multiple types of control modules, complex responses can be achieved, such as logical evaluations that require multiple events to occur in the environment before an action is performed. This framework for embodied control offers a new strategy toward autonomous soft robots that operate in uncertain or dynamic environments.

Hydration solids

Hygroscopic biological matter in plants, fungi and bacteria make up a large fraction of Earth's biomass1. Although metabolically inert, these water-responsive materials exchange water with the environment and actuate movement2-5 and have inspired technological uses6,7. Despite the variety in chemical composition, hygroscopic biological materials across multiple kingdoms of life exhibit similar mechanical behaviours including changes in size and stiffness with relative humidity8-13. Here we report atomic force microscopy measurements on the hygroscopic spores14,15 of a common soil bacterium and develop a theory that captures the observed equilibrium, non-equilibrium and water-responsive mechanical behaviours, finding that these are controlled by the hydration force16-18. Our theory based on the hydration force explains an extreme slowdown of water transport and successfully predicts a strong nonlinear elasticity and a transition in mechanical properties that differs from glassy and poroelastic behaviours. These results indicate that water not only endows biological matter with fluidity but also can-through the hydration force-control macroscopic properties and give rise to a 'hydration solid' with unusual properties. A large fraction of biological matter could belong to this distinct class of solid matter.

Counting and Sequential Information Processing in Mechanical Metamaterials

Materials with an irreversible response to cyclic driving exhibit an evolving internal state which, in principle, encodes information on the driving history. Here we realize irreversible metamaterials that count mechanical driving cycles and store the result into easily interpretable internal states. We extend these designs to aperiodic metamaterials that are sensitive to the order of different driving magnitudes, and realize "lock and key" metamaterials that only reach a specific state for a given target driving sequence. Our metamaterials are robust, scalable, and extendable, give insight into the transient memories of complex media, and open new routes towards smart sensing, soft robotics, and mechanical information processing.

Non-orientable order and non-commutative response in frustrated metamaterials

From atomic crystals to animal flocks, the emergence of order in nature is captured by the concept of spontaneous symmetry breaking^1-4. However, this cornerstone of physics is challenged when broken symmetry phases are frustrated by geometrical constraints. Such frustration dictates the behaviour of systems as diverse as spin ices^5-8, confined colloidal suspensions⁹ and crumpled paper sheets¹⁰. These systems typically exhibit strongly degenerated and heterogeneous ground states and hence escape the Ginzburg-Landau paradigm of phase ordering. Here, combining experiments, simulations and theory we uncover an unanticipated form of topological order in globally frustrated matter: non-orientable order. We demonstrate this concept by designing globally frustrated metamaterials that spontaneously break a discrete [Formula: see text] symmetry. We observe that their equilibria are necessarily heteregeneous and extensively degenerated. We explain our observations by generalizing the theory of elasticity to non-orientable order-parameter bundles. We show that non-orientable equilibria are extensively degenerated due to the arbitrary location of topologically protected nodes and lines where the order parameter must vanish. We further show that non-orientable order applies more broadly to objects that are non-orientable themselves, such as buckled Möbius strips and Klein bottles. Finally, by applying time-dependent local perturbations to metamaterials with non-orientable order, we engineer topologically protected mechanical memories^11-19, achieve non-commutative responses and show that they carry an imprint of the braiding of the loads' trajectories. Beyond mechanics, we envision non-orientability as a robust design principle for metamaterials that can effectively store information across scales, in fields as diverse as colloidal science⁸, photonics²⁰, magnetism⁷ and atomic physics²¹.

Robotic Materials Transformable Between Elasticity and Plasticity

Robotic materials, with coupled sensing, actuation, computation, and communication, have attracted increasing attention because they are able to not only tune their conventional passive mechanical property via geometrical transformation or material phase change but also become adaptive and even intelligent to suit varying environments. However, the mechanical behavior of most robotic materials is either reversible (elastic) or irreversible (plastic), but not transformable between them. Here, a robotic material whose behavior is transformable between elastic and plastic is developed, based upon an extended neutrally stable tensegrity structure. The transformation does not depend on conventional phase transition and is fast. By integrating with sensors, the elasticity-plasticity transformable (EPT) material is able to self-sense deformation and decides whether to undergo transformation or not. This work expands the capability of the mechanical property modulation of robotic materials.

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.

An interconnect-free micro-electromechanical 7-bit arithmetic device for multi-operand programmable computing

Computational power density and interconnection between transistors have grown to be the dominant challenges for the continued scaling of complementary metal-oxide-semiconductor (CMOS) technology due to limited integration density and computing power. Herein, we designed a novel, hardware-efficient, interconnect-free microelectromechanical 7:3 compressor using three microbeam resonators. Each resonator is configured with seven equal-weighted inputs and multiple driven frequencies, thus defining the transformation rules for transmitting resonance frequency to binary outputs, performing summation operations, and displaying outputs in compact binary format. The device achieves low power consumption and excellent switching reliability even after 3 × 10³ repeated cycles. These performance improvements, including enhanced computational power capacity and hardware efficiency, are paramount for moderately downscaling devices. Finally, our proposed paradigm shift for circuit design provides an attractive alternative to traditional electronic digital computing and paves the way for multioperand programmable computing based on electromechanical systems.

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.

Technology Roadmap for Flexible Sensors

Humans rely increasingly on sensors to address grand challenges and to improve quality of life in the era of digitalization and big data. For ubiquitous sensing, flexible sensors are developed to overcome the limitations of conventional rigid counterparts. Despite rapid advancement in bench-side research over the last decade, the market adoption of flexible sensors remains limited. To ease and to expedite their deployment, here, we identify bottlenecks hindering the maturation of flexible sensors and propose promising solutions. We first analyze challenges in achieving satisfactory sensing performance for real-world applications and then summarize issues in compatible sensor-biology interfaces, followed by brief discussions on powering and connecting sensor networks. Issues en route to commercialization and for sustainable growth of the sector are also analyzed, highlighting environmental concerns and emphasizing nontechnical issues such as business, regulatory, and ethical considerations. Additionally, we look at future intelligent flexible sensors. In proposing a comprehensive roadmap, we hope to steer research efforts towards common goals and to guide coordinated development strategies from disparate communities. Through such collaborative efforts, scientific breakthroughs can be made sooner and capitalized for the betterment of humanity.

Bounded Wang tilings with integer programming and graph-based heuristics

Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging applications in materials engineering, we consider the bounded version of the tiling problem and offer four integer programming formulations to construct valid or nearly-valid Wang tilings: a decision, maximum-rectangular tiling, maximum cover, and maximum adjacency constraint satisfaction formulations. To facilitate a finer control over the resulting tilings, we extend these programs with tile-based, color-based, packing, and variable-sized periodic constraints. Furthermore, we introduce an efficient heuristic algorithm for the maximum-cover variant based on the shortest path search in directed acyclic graphs and derive simple modifications to provide a 1/2 approximation guarantee for arbitrary tile sets, and a 2/3 guarantee for tile sets with cyclic transducers. Finally, we benchmark the performance of the integer programming formulations and of the heuristic algorithms showing that the heuristics provide very competitive outputs in a fraction of time. As a by-product, we reveal errors in two well-known aperiodic tile sets: the Knuth tile set contains a tile unusable in two-way infinite tilings, and the Lagae corner tile set is not aperiodic.

There’s Plenty of Room Right Here: Biological Systems as Evolved, Overloaded, Multi-Scale Machines

The applicability of computational models to the biological world is an active topic of debate. We argue that a useful path forward results from abandoning hard boundaries between categories and adopting an observer-dependent, pragmatic view. Such a view dissolves the contingent dichotomies driven by human cognitive biases (e.g., a tendency to oversimplify) and prior technological limitations in favor of a more continuous view, necessitated by the study of evolution, developmental biology, and intelligent machines. Form and function are tightly entwined in nature, and in some cases, in robotics as well. Thus, efforts to re-shape living systems for biomedical or bioengineering purposes require prediction and control of their function at multiple scales. This is challenging for many reasons, one of which is that living systems perform multiple functions in the same place at the same time. We refer to this as “polycomputing”—the ability of the same substrate to simultaneously compute different things, and make those computational results available to different observers. This ability is an important way in which living things are a kind of computer, but not the familiar, linear, deterministic kind; rather, living things are computers in the broad sense of their computational materials, as reported in the rapidly growing physical computing literature. We argue that an observer-centered framework for the computations performed by evolved and designed systems will improve the understanding of mesoscale events, as it has already done at quantum and relativistic scales. To develop our understanding of how life performs polycomputing, and how it can be convinced to alter one or more of those functions, we can first create technologies that polycompute and learn how to alter their functions. Here, we review examples of biological and technological polycomputing, and develop the idea that the overloading of different functions on the same hardware is an important design principle that helps to understand and build both evolved and designed systems. Learning to hack existing polycomputing substrates, as well as to evolve and design new ones, will have massive impacts on regenerative medicine, robotics, and computer engineering.

Reprogrammable allosteric metamaterials from disordered networks

Prior works on disordered mechanical metamaterial networks-consisting of fixed nodes connected by discrete bonds-have shown that auxetic and allosteric responses can be achieved by pruning a specific set of the bonds from an originally random network. However, bond pruning is irreversible and yields a single bulk response. Using material stiffness as a tunable design parameter, we create metamaterial networks where allosteric responses are achieved without bond removal. Such systems are experimentally realized through variable stiffness bonds that can strengthen and weaken on-demand. In a disordered mechanical network with variable stiffness bonds, different subsets of bonds can be strategically softened to achieve different bulk responses, enabling a multiplicity of reprogrammable input/output allosteric responses.

Self-Sustained Snapping Drives Autonomous Dancing and Motion in Free-Standing Wavy Rings

Harnessing snapping, an instability phenomenon observed in nature (e.g., Venus flytraps), for autonomy has attracted growing interest in autonomous soft robots. However, achieving self-sustained snapping and snapping-driven autonomous motions in soft robots remains largely unexplored. Here, harnessing bistable, ribbon ring-like structures for realizing self-sustained snapping in a library of soft liquid-crystal elastomer wavy rings under constant thermal and photothermal actuation are reported. The self-sustained snapping induces continuous ring flipping that drives autonomous dancing or crawling motions on the ground and underwater. The 3D, free-standing wavy rings employ either a highly symmetric or symmetry-broken twisted shape with tunable geometric asymmetries. It is found that the former favors periodic self-dancing motion in place due to isotropic friction, while the latter shows a directional crawling motion along the predefined axis of symmetry during fabrication due to asymmetric friction. It shows that the crawling speed can be tuned by the geometric asymmetries with a peak speed achieved at the highest geometric asymmetry. Lastly, it is shown that the autonomous crawling ring can also adapt its body shape to pass through a confined space that is over 30% narrower than its body size.

Simulation of reversible molecular mechanical logic gates and circuits

Landauer's principle places a fundamental lower limit on the work required to perform a logically irreversible operation. Logically reversible gates provide a way to avoid these work costs and also simplify the task of making the computation as a whole thermodynamically reversible. The inherent reversibility of mechanical logic gates would make them good candidates for the design of practical logically reversible computing systems if not for the relatively large size and mass of such systems. In this paper we outline the design and simulation of reversible molecular mechanical logic gates that come close to the limits of thermodynamic reversibility even under the effects of thermal noise, and outline associated circuit components from which arbitrary combinatorial reversible circuits can be constructed and simulated. We demonstrate that isolated components can be operated in a thermodynamically reversible manner, and explore the complexities of combining components to implement more complex computations. Finally, we demonstrate a method to construct arbitrarily large reversible combinatorial circuits using multiple external controls and signal boosters with a working half-adder circuit.

Variable-position centrifugal platform achieves droplet manipulation and logic circuitries on-chip

Taking information as material to realize non-electronic physical computing is a promising idea, which facilitates the integration of technologies in different fields such as chemistry, biology, and mechanical control into a new computing platform. Here, we propose a novel, efficient and robust manipulation platform that drives droplet computing by way of inertial force. Combining this with droplet flow path design, we demonstrated multiple basic functions of droplet manipulation, including storage, dosing, interrupts, controllable release and addressing. These basic functions without external control lay the foundation for the realization of droplet calculation. We developed AND, OR, and XOR logic gates of the "liquid circuit" and combined them into a binary adder, which successfully completed the addition of four-digit binary numbers through droplet movement. Moreover, we attempted to perform algorithmic design for biological information under the control of droplets based on synchronous logical operations, developing the possibility of biological applications. This programmable physical computing system exists independently of electronic computing, aiming to supplement and expand the computing methods outside the field of electronic technology and to open a new method for the algorithmic operation of materials after combining new physical computing technologies such as biological or chemical computing.

Early career scientists converse on the future of soft robotics

During the recent decade, we have witnessed an extraordinary flourishing of soft robotics. Rekindled interest in soft robots is partially associated with the advances in manufacturing techniques that enable the fabrication of sophisticated multi-material robotic bodies with dimensions ranging across multiple length scales. In recent manuscripts, a reader might find peculiar-looking soft robots capable of grasping, walking, or swimming. However, the growth in publication numbers does not always reflect the real progress in the field since many manuscripts employ very similar ideas and just tweak soft body geometries. Therefore, we unreservedly agree with the sentiment that future research must move beyond "soft for soft's sake." Soft robotics is an undoubtedly fascinating field, but it requires a critical assessment of the limitations and challenges, enabling us to spotlight the areas and directions where soft robots will have the best leverage over their traditional counterparts. In this perspective paper, we discuss the current state of robotic research related to such important aspects as energy autonomy, electronic-free logic, and sustainability. The goal is to critically look at perspectives of soft robotics from two opposite points of view provided by early career researchers and highlight the most promising future direction, that is, in our opinion, the employment of soft robotic technologies for soft bio-inspired artificial organs.

Programming Multistable Metamaterials to Discover Latent Functionalities

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

Triclinic Metamaterials by Tristable Origami with Reprogrammable Frustration

Geometrical-frustration-induced anisotropy and inhomogeneity are explored to achieve unique properties of metamaterials that set them apart from conventional materials. According to Neumann's principle, to achieve anisotropic responses, the material unit cell should possess less symmetry. Based on such guidelines, a triclinic metamaterial system of minimal symmetry is presented, which originates from a Trimorph origami pattern with a simple and insightful geometry: a basic unit cell with four tilted panels and four corresponding creases. The intrinsic geometry of the Trimorph origami, with its changing tilting angles, dictates a folding motion that varies the primitive vectors of the unit cell, couples the shear and normal strains of its extrinsic bulk, and leads to an unusual Poisson effect. Such an effect, associated with reversible auxeticity in the changing triclinic frame, is observed experimentally, and predicted theoretically by elegant mathematical formulae. The nonlinearities of the folding motions allow the unit cell to display three robust stable states, connected through snapping instabilities. When the tristable unit cells are tessellated, phenomena that resemble linear and point defects emerge as a result of geometric frustration. The frustration is reprogrammable into distinct stable and inhomogeneous states by arbitrarily selecting the location of a single or multiple point defects. The Trimorph origami demonstrates the possibility of creating origami metamaterials with symmetries that are hitherto nonexistent, leading to triclinic metamaterials with tunable anisotropy for potential applications such as wave propagation control and compliant microrobots.

Mechanical signaling cascades

Mechanical computing has seen resurgent interest recently owing to the potential to embed sensing and computation into new classes of programmable metamaterials. To realize this, however, one must push signals from one part of a device to another and do so in a way that can be reset robustly. We investigate the propagation of signals in a bistable mechanical cascade uphill in energy. By identifying a penetration length for perturbations, we show that signals can propagate uphill for finite distances and map out parameters for this to occur. Experiments on soft elastomers corroborate our results.

Logic-enabled textiles

Textiles hold great promise as a soft yet durable material for building comfortable robotic wearables and assistive devices at low cost. Nevertheless, the development of smart wearables composed entirely of textiles has been hindered by the lack of a viable sheet-based logic architecture that can be implemented using conventional fabric materials and textile manufacturing processes. Here, we develop a fully textile platform for embedding pneumatic digital logic in wearable devices. Our logic-enabled textiles support combinational and sequential logic functions, onboard memory storage, user interaction, and direct interfacing with pneumatic actuators. In addition, they are designed to be lightweight, easily integrable into regular clothing, made using scalable fabrication techniques, and durable enough to withstand everyday use. We demonstrate a textile computer capable of input-driven digital logic for controlling untethered wearable robots that assist users with functional limitations. Our logic platform will facilitate the emergence of future wearables powered by embedded fluidic logic that fully leverage the innate advantages of their textile construction.

Nematic bits and universal logic gates

Liquid crystals (LCs) can host robust topological defect structures that essentially determine their optical and elastic properties. Although recent experimental progress enables precise control over nematic LC defects, their practical potential for information storage and processing has yet to be explored. Here, we introduce the concept of nematic bits (nbits) by exploiting a quaternionic mapping from LC defects to the Poincaré-Bloch sphere. Through theory and simulations, we demonstrate how single-nbit operations can be implemented using electric fields, to construct LC analogs of Pauli, Hadamard, and other elementary logic gates. Using nematoelastic interactions, we show how four-nbit configurations can realize universal classical NOR and NAND gates. Last, we demonstrate the implementation of generalized logical functions that take values on the Poincaré-Bloch sphere. These results open a route toward the implementation of classical digital and nonclassical continuous computation strategies in topological soft matter systems.