Programming nonreciprocity and reversibility in multistable mechanical metamaterials

AcousTac: Tactile Sensing with Acoustic Resonance for Electronics-Free Soft Skin

Sound is a rich information medium that transmits through air; people communicate through speech and can even discern material through tapping and listening. To capture frequencies in the human hearing range, commercial microphones typically have a sampling rate of over 40 kHz. These accessible acoustic technologies are not yet widely adopted for the explicit purpose of giving robots a sense of touch. Some researchers have used sound to sense tactile information, both monitoring ambient soundscape and with embedded speakers and microphones to measure sounds within structures. However, these options commonly do not provide a direct measure of steady state force or require electronics integrated somewhere near the contact location. In this work, we present AcousTac, an acoustic tactile sensor for electronics-free, force-sensitive soft skin. Compliant silicone caps and plastic tubes compose the resonant chambers that emit pneumatic-driven sound measurable with a conventional off-board microphone. The resulting frequency changes depend on the external loads on the compliant endcaps. The compliant cap vibrates with the resonant pressure waves and is a nonidealized boundary condition, initially producing a nonmonotonic force response. We characterize two solutions-adding a distal hole and mass to the cap-resulting in monotonic and nonhysteretic force readings with this technology. We can tune each AcousTac taxel to specific force and frequency ranges, based on geometric parameters including tube length, and thus uniquely sense each taxel simultaneously in an array. We demonstrate AcousTac's functionality on two robotic systems: a 4-taxel array and a 3-taxel astrictive gripper. Simple to implement with off-the-shelf parts, AcousTac is a promising concept for force sensing on soft robotic surfaces, especially in situations where electronics near the contact are not suitable. Equipping robots with tactile sensing and soft skin provides them with a sense of touch and the ability to safely interact with their surroundings.

Temperature-responsive metamaterials made of highly sensitive thermostat metal strips

Temperature-responsive metamaterials have remarkable shape-morphing ability during thermal energy conversion. However, integrating the thermal shape programmability, wide-working temperature range, fast temperature response, and actuation into metamaterials remains challenging. Here, we introduce using thermostat metal strips to assemble metamaterials with desirable and balanced temperature-responsive properties, and we systematically investigate the thermal deformation performance. Achieving 70 to 80% of the designed strain requires only 5 seconds of heating. A thermal strain of around 30% is achieved for the assembled metamaterials, surpassing other bimetallic metamaterials by a magnitude of 100 to 200. The actuation capacity of thermostat metal strips exceeds 26 times their weight. Further, by leveraging the highly programmable thermal deformation, the tuneable bandgap range is 3847 to 40,000 hertz. These fully integrated mechanical performances in the multiphysics have great application potential, for example, as soft actuators and soft robots in intelligent structure systems, vibration isolation and noise reduction in hypersonic vehicles, and unique thermal deformation in precision instruments.

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.

Engineered moiré photonic and phononic superlattices

Recent discoveries of Mott insulating and unconventional superconducting states in twisted bilayer graphene with moiré superlattices have not only reshaped the landscape of 'twistronics' but also sparked the rapidly growing fields of moiré photonic and phononic structures. These innovative moiré structures have opened new routes of exploration for classical wave physics, leading to intriguing phenomena and robust control of electromagnetic and mechanical waves. Drawing inspiration from the success of twisted bilayer graphene, this Perspective describes an overarching framework of the emerging moiré photonic and phononic structures that promise novel classical wave devices. We begin with the fundamentals of moiré superlattices, before highlighting recent studies that exploit twist angle and interlayer coupling as new ingredients with which to engineer and tailor the band structures and effective material properties of photonic and phononic structures. Finally, we discuss the future directions and prospects of this emerging area in materials science and wave physics.

Programmable nonreciprocal Poynting effect enabled by lattice metamaterials

Shear nonreciprocity, implying unequal shear forces in opposite shear directions, can be achieved by arranging structures asymmetrically. However, the nonreciprocal Poynting effect, i.e., unequal normal stresses induced by the same shear displacements to the left and right, has not been fully explored. We discover the nonreciprocal Poynting effect using a generalized directional truss model. Inspired by this discovery, the cylindrical lattice metamaterials constructed from antisymmetric curled microstructures are used as a case study to generate the nonreciprocal Poynting effect. We develop a design framework that integrates digital generation, finite deformation theory, finite element modeling, and three-dimensional printing to program the nonreciprocal Poynting effect. Applications such as bionic Poynting effect matching, wave energy converter, and unidirectional motion limitation are demonstrated. This framework allows the one-to-one mapping between the torque and normal forces, paving the way for designing soft devices with precise force transmission capabilities.

Droplet-based mechanical transducers modulated by the symmetry of wettability patterns

Asymmetric mechanical transducers have important applications in energy harvesting, signal transmission, and micro-mechanics. To achieve asymmetric transformation of mechanical motion or energy, active robotic metamaterials, as well as materials with asymmetric microstructures or internal orientation, are usually employed. However, these strategies usually require continuous energy supplement and laborious fabrication, and limited transformation modes are achieved. Herein, utilizing wettability patterned surfaces for precise control of the droplet contact line and inner flow, we demonstrate a droplet-based mechanical transducer system, and achieve multimodal responses to specific vibrations. By virtue of the synergistic effect of surface tension and solid-liquid adhesion on the liquid dynamics, the droplet on the patterned substrate can exhibit symmetric/asymmetric vibration transformation when the substrate vibrates horizontally. Based on this, we construct arrayed patterns with distinct arrangements on the substrate, and employ the swarm effect of the arrayed droplets to achieve three-dimensional and multimodal actuation of the target plate under a fixed input vibration. Further, we demonstrate the utilization of the mechanical transducers for vibration management, object transport, and laser modulation. These findings provide a simple yet efficient strategy to realize a multimodal mechanical transducer, which shows significant potential for aseismic design, optical molding, as well as micro-electromechanical systems (MEMS).

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.

Non-reciprocal topological solitons in active metamaterials

From protein motifs1 to black holes2, topological solitons are pervasive nonlinear excitations that are robust and can be driven by external fields3. So far, existing driving mechanisms all accelerate solitons and antisolitons in opposite directions3,4. Here we introduce a local driving mechanism for solitons that accelerates both solitons and antisolitons in the same direction instead: non-reciprocal driving. To realize this mechanism, we construct an active mechanical metamaterial consisting of non-reciprocally coupled oscillators5-8 subject to a bistable potential9-14. We find that such nonlinearity coaxes non-reciprocal excitations-so-called non-Hermitian skin waves5-8,15-22, which are typically unstable-into robust one-way (anti)solitons. We harness such non-reciprocal topological solitons by constructing an active waveguide capable of transmitting and filtering unidirectional information. Finally, we illustrate this mechanism in another class of metamaterials that shows the breaking of 'supersymmetry'23,24 causing only antisolitons to be driven. Our observations and models demonstrate a subtle interplay between non-reciprocity and topological solitons, whereby solitons create their own driving force by locally straining the material. Beyond the scope of our study, non-reciprocal solitons might provide an efficient driving mechanism for robotic locomotion25 and could emerge in other settings, for example, quantum mechanics26,27, optics28-30 and soft matter31.

Drive-specific selection in multistable mechanical networks

Systems with many stable configurations abound in nature, both in living and inanimate matter, encoding a rich variety of behaviors. In equilibrium, a multistable system is more likely to be found in configurations with lower energy, but the presence of an external drive can alter the relative stability of different configurations in unexpected ways. Living systems are examples par excellence of metastable nonequilibrium attractors whose structure and stability are highly dependent on the specific form and pattern of the energy flow sustaining them. Taking this distinctively lifelike behavior as inspiration, we sought to investigate the more general physical phenomenon of drive-specific selection in nonequilibrium dynamics. To do so, we numerically studied driven disordered mechanical networks of bistable springs possessing a vast number of stable configurations arising from the two stable rest lengths of each spring, thereby capturing the essential physical properties of a broad class of multistable systems. We found that there exists a range of forcing amplitudes for which the attractor states of driven disordered multistable mechanical networks are fine-tuned with respect to the pattern of external forcing to have low energy absorption from it. Additionally, we found that these drive-specific attractor states are further stabilized by precise matching between the multidimensional shape of their orbit and that of the potential energy well they inhabit. Lastly, we showed evidence of drive-specific selection in an experimental system and proposed a general method to estimate the range of drive amplitudes for drive-specific selection.

Multi-Stability of the Extensible Origami Structures

Multi-stable structures and metamaterials with more than two stable states are widely applied in diversified engineering applications. Non-rigid foldable origami patterns have provided an effective way of designing multi-stable structures. But most of them have only two stable states and therefore require a combination of many units to achieve multi-stability. Here, a series of extensible origami structures are proposed with generic multi-stability based on non-rigid wrapping origami. Through a kinematic analysis and experiments, it is demonstrate that a sequential folding among different layers of the structures is created to generate a continuous rigid origami range and several discrete rigid origami states, which consequently leads to the multi-stability of the extensible origami structures. Moreover, the effects of design parameters on the mechanical properties of the structures are investigated by numerical simulation, enabling properties programmability upon specific needs. This study thus paves a new pathway for the development of novel multi-stable origami structures.

In Situ Activation of Snap-Through Instability in Multi-Response Metamaterials through Multistable Topological Transformation

Snap-through instability has been widely leveraged in metamaterials to attain non-monotonic responses for a specific subset of applications where conventional monotonic materials fail to perform. In the remaining more plentiful set of ordinary applications, snap-through instability is harmful, and current snapping metamaterials become inadequate because their capacity to snap cannot be suppressed post-fabrication. Here, a class of topology-transformable metamaterials is introduced to enable in situ activation and deactivation of the snapping capacity, providing a remarkable level of versatility in switching between responses from monotonic to monostable and bistable snap-through. Theoretical analysis, numerical simulations, and experiments are combined to unveil the role played by contact in the topological transformation capable of increasing the geometry incompatibility and confinement stiffness of selected architectural members. The strategy here presented for post-fabrication reprogrammability of matter and on-the-fly response switching paves the way to multifunctionality for application in multiple sectors from mechanical logic gates, and adjustable energy dissipators, to in situ adaptable sport equipment.

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.

Mere tension output from spring-linkage-based mechanical metamaterials

Metamaterials whose properties are inaccessible with conventional materials offer powerful tools for unprecedentedly manipulating physical signals. However, an effective design strategy of metamaterials still remains a challenge for changing the compression or tension characters of stress waves during forward propagation. Here, we introduce a class of spring-linkage-based metamaterials exhibiting mere tension output at the distal end, no matter that the input is an axial impact, a sudden tension, or even alternating tension-compression. The metamaterials can turn compressive waves into pure tension and filter them out from the tension-compression mixed ones while allowing tensile signal stably propagating in soliton form. This is achieved by combining nonuniform and nonlinear properties of the proposed cells. In particular, these extraordinary functions of the metamaterial can be turned on or off and adjusted by tuning a key switch cell; thus, it is anticipated to serve as a start for more complex manipulation and utilization of mechanical signals.

Mechanical nonreciprocity in a uniform composite material

Mechanical nonreciprocity, or the asymmetric transmission of mechanical quantities between two points in space, is crucial for developing systems that can guide, damp, and control mechanical energy. We report a uniform composite hydrogel that displays substantial mechanical nonreciprocity, owing to direction-dependent buckling of embedded nanofillers. This material exhibits an elastic modulus more than 60 times higher when sheared in one direction compared with the opposite direction. Consequently, it can transform symmetric vibrations into asymmetric ones that are applicable for mass transport and energy harvest. Furthermore, it exhibits an asymmetric deformation when subjected to local interactions, which can induce directional motion of various objects, including macroscopic objects and even small living creatures. This material could promote the development of nonreciprocal systems for practical applications such as energy conversion and biological manipulation.

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.

Effect of interaction of adjacent unit-cells on wave propagation in coupled mass-in-mass metamaterials

This paper aims to study the effect of the interaction of adjacent unit-cells in coupled mass-in-mass metamaterial on wave behaviors, which enables us to achieve a wavy dispersion relationship. Elastic wave propagation in a coupled mass-in-mass metamaterial is investigated to clarify the effect of the interaction of adjacent unit-cells on the dispersion relation and wave velocity. Elastic wave behavior based on an infinite system is studied in terms of the band structure and group velocity. The dynamic responses in frequency domain and time domain of the finite mass-in-mass lattice are calculated by using Laplace transform and numerical methods. The band structures and transmittances show that the coupled mass-in-mass metamaterial has a bandgap, which can be used to suppress and isolate vibration. The parameter study shows that changing the stiffness and location of the coupled springs can adjust the distribution of the bandgap. Importantly, we also calculate the ratio of group velocity to phase velocity that indicates the negative group velocity appearing in the wavy dispersion relation of coupled mass-in-mass metamaterials. These results show that the interaction of adjacent unit-cells plays a crucial role in the wave behavior of the coupled mass-in-mass metamaterial.

Kirigami-based metastructures with programmable multistability

Different from most existing multistable structures whose multiple stable states are achieved through the combinational effect of bistable units, we invent a generic tristable kirigami cuboid. The three stable states have fundamentally distinct geometric configurations and chirality, and the transformation among them can be realized by tension/compression or clockwise/counterclockwise twist. Tessellating the units in series, a family of multistable metamaterials can be constructed, the mechanical behaviors of which are programmable by the unit geometry, the material of the elastic joints, the number of units, and the loading conditions. As a demonstration of the potential applications, a frequency reconfigurable antenna for 5G triple-band communication is developed based on a tristable unit, and the frequency tunability is verified by experiments.

Multistability plays an important role in advanced engineering applications such as metastructures, deployable structures, and reconfigurable robotics. However, most existing multistability design is based on the two-dimensional (2D)/3D series or parallel combinations of bistable unit cells, which are derived from snap-through instability, nonrigid foldable origami structures, and compliant mechanism, due to the lack of a generic multistable unit cell. Here, we develop a tristable kirigami cuboid by creating a set of elastic joints only effective in a specific motion range which integrates the elastic sheets and switchable hinge axes inspired by the kinematic behaviors of a kirigami cuboid with thick facets. The energy barriers between the stable states can be programmed by the geometric design parameters and material properties of the elastic joints. Taking the tristable cuboid as a unit cell, we construct a family of metastructures with multiple stable states. The number of stable states, the combination of unit stable states, and their transform sequences can be programmed by the number of unit cells, unit design parameters, and loading modes and loading sequences. We also apply this tristable cuboid to the design of frequency reconfigurable antenna with three programmable working frequencies, which demonstrates that such versatile multistability and structural diversity facilitate the development of multifunctional materials and devices.

Recent Progress in Active Mechanical Metamaterials and Construction Principles

Active mechanical metamaterials (AMMs) (or smart mechanical metamaterials) that combine the configurations of mechanical metamaterials and the active control of stimuli-responsive materials have been widely investigated in recent decades. The elaborate artificial microstructures of mechanical metamaterials and the stimulus response characteristics of smart materials both contribute to AMMs, making them achieve excellent properties beyond the conventional metamaterials. The micro and macro structures of the AMMs are designed based on structural construction principles such as, phase transition, strain mismatch, and mechanical instability. Considering the controllability and efficiency of the stimuli-responsive materials, physical fields such as, the temperature, chemicals, light, electric current, magnetic field, and pressure have been adopted as the external stimuli in practice. In this paper, the frontier works and the latest progress in AMMs from the aspects of the mechanics and materials are reviewed. The functions and engineering applications of the AMMs are also discussed. Finally, existing issues and future perspectives in this field are briefly described. This review is expected to provide the basis and inspiration for the follow-up research on AMMs.