Stable propagation of mechanical signals in soft media using stored elastic energy

Tailoring Stress-Strain Curves of Flexible Snapping Mechanical Metamaterial for On-Demand Mechanical Responses via Data-Driven Inverse Design

By incorporating soft materials into the architecture, flexible mechanical metamaterials enable promising applications, e.g., energy modulation, and shape morphing, with a well-controllable mechanical response, but suffer from spatial and temporal programmability towards higher-level mechanical intelligence. One feasible solution is to introduce snapping structures and then tune their responses by accurately tailoring the stress-strain curves. However, owing to the strongly coupled nonlinearity of structural deformation and material constitutive model, it is difficult to deduce their stress-strain curves using conventional ways. Here, a machine learning pipeline is trained with the finite element analysis data that considers those strongly coupled nonlinearities to accurately tailor the stress-strain curves of snapping metamaterialfor on-demand mechanical response with an accuracy of 97.41%, conforming well to experiment. Utilizing the established approach, the energy absorption efficiency of the snapping-metamaterial-based device can be tuned within the accessible range to realize different rebound heights of a falling ball, and soft actuators can be spatially and temporally programmed to achieve synchronous and sequential actuation with a single energy input. Purely relying on structure designs, the accurately tailored metamaterials increase the devices' tunability/programmability. Such an approach can potentially extend to similar nonlinear scenarios towards predictable or intelligent mechanical responses.

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.

Natural tristability of a confined helical filament with anisotropic bending rigidities

We find that whenc 0 R ∼ 0.5 andτ 0 R < 0.11 < c 0 R , confining a helical filament with anisotropic bending rigidities within a cylindrical tube of radius R can create a natural tristable status which is consisted of two low-pitch helices and one high-pitch helix, where a helical filament is referred to as a filament that has both an intrinsic curvature ( c 0 ) and an intrinsic twist rate ( τ 0 ). The formation of the tristable status also requires that the filament has a significant difference between two bending rigidities and a large twisting rigidity. The relative heights of two low-pitch helices in a tristable status are close to zero, and the smaller the intrinsic twisting angle, the smaller the difference between these two heights. Moreover, at a large intrinsic twisting angle, two low-pitch helices display a large energy difference, and the energy difference increases with decreasing τ 0 . Meanwhile, the relative height of the high-pitch helix is always close to that of a straight line. Finally, at some specific intrinsic parameters, the tristable status can include an isoenergic status with two helices of the same energy but distinct pitches.

Tuning the Properties of Multi-Stable Structures Post-Fabrication Via the Two-Way Shape Memory Polymer Effect

Multi-stable elements are commonly employed to design reconfigurable and adaptive structures, because they enable large and reversible shape changes in response to changing loads, while simultaneously allowing self-locking capabilities. However, existing multi-stable structures have properties that depend on their initial design and cannot be tailored post-fabrication. Here, a novel design approach is presented that combines multi-stable structures with two-way shape memory polymers. By leveraging both the one-way and two-way shape memory effect under bi-axial strain conditions, the structures can re-program their 3D shape, bear loads, and self-actuate. Results demonstrate that the structures' shape and stiffness can be tuned post-fabrication at the user's need and the multi-stability can be suppressed or activated on command. The control of multi-stability prevents undesired snapping of the structures and enables higher load-bearing capability, compared to conventional multi-stable systems. The proposed approach offers the possibility to augment the functionality of existing multi-stable concepts, showing potential for the realization of highly adaptable mechanical structures that can reversibly switch between being mono and multi-stable and that can undergo shape changes in response to a change in temperature.

Diffusive coupling facilitates and impedes noise-induced escape in interacting bistable elements

Diverse complex systems often undergo sudden changes in their states, such as epileptic seizures, climate changes, and social uprisings. Such behavior has been modeled by noise-induced escape of bistable elements, which is the escape from an attracting state driven by a fluctuation in the system's state. We consider a system of interacting bistable elements and investigate the effect of diffusive coupling among elements on the process of noise-induced escape. We focus on the influence of the coupling strength over the escape time, which is the time it takes for noise-induced escape to occur. We performed numerical simulations and observed that weak coupling reduced the mean escape time, whereas strong coupling impeded escape. We argue that, although diffusive coupling both facilitates and impedes escape, the facilitating effect is dominant when coupling is weak. For weak coupling cases, we develop an approximate theory that can predict the mean and variance of escape times. In contrast, strong coupling reduces the effective noise intensity to impede escape. Our results suggest that diffusive coupling among multistable elements contributes to regulating the rate of transitions among attracting states.

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.

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.

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.

Diffusive kinks turn kirigami into machines

Kinks define boundaries between distinct configurations of a material. In the context of mechanical metamaterials, kinks have recently been shown to underpin logic, shape-changing and locomotion functionalities. So far such kinks propagate by virtue of inertia or of an external load. Here, we discover the emergence of propagating kinks in purely dissipative kirigami. To this end, we create kirigami that shape-change into different textures depending on how fast they are stretched. We find that if we stretch fast and wait, the viscoelastic kirigami can eventually snap from one texture to another. Crucially, such a snapping instability occurs in a sequence and a propagating diffusive kink emerges. As such, it mimics the slow sequential folding observed in biological systems, e.g., Mimosa Pudica. We finally demonstrate that diffusive kinks can be harnessed for basic machine-like functionalities, such as sensing, dynamic shape morphing, transport and manipulation of objects.

Phase transitions in 2D multistable mechanical metamaterials via collisions of soliton-like pulses

In recent years, mechanical metamaterials have been developed that support the propagation of an intriguing variety of nonlinear waves, including transition waves and vector solitons (solitons with coupling between multiple degrees of freedom). Here we report observations of phase transitions in 2D multistable mechanical metamaterials that are initiated by collisions of soliton-like pulses in the metamaterial. Analogous to first-order phase transitions in crystalline solids, we observe that the multistable metamaterials support phase transitions if the new phase meets or exceeds a critical nucleus size. If this criterion is met, the new phase subsequently propagates in the form of transition waves, converting the rest of the metamaterial to the new phase. More interestingly, we numerically show, using an experimentally validated model, that the critical nucleus can be formed via collisions of soliton-like pulses. Moreover, the rich direction-dependent behavior of the nonlinear pulses enables control of the location of nucleation and the spatio-temporal shape of the growing phase.

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.

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 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.

A double-well potential model for glass transition in a glassy hydrogel undergoing bi-stable interactions with water

The key mechanisms for achieving ultra-high mechanical properties of glassy hydrogels have not been fully understood, and it is commonly believed that their glass transitions are the crucial reasons due to the existence of significant bi-stable interactions between polymer macromolecules and water molecules. In this study, a double-well potential model is formulated to describe the mechanical properties of glassy hydrogels undergoing glass transition, by combining phase evolution theory and a rubber elasticity model. Bi-stable interactions between polymer macromolecules and water molecules (for both the trapped and free water) have been characterized using this double-well potential model, and various parameters are studied, including depth of well (for elasticity), distance between two wells (for yielding), and energy difference between two wells (for transition probability). Furthermore, constitutive stress-strain relationships are developed to explore the working principles for achieving ultra-high mechanical properties of these glassy hydrogels. Finally, the effectiveness of the proposed models is verified using finite element analysis (FEA) and also the experimental results reported in the literature, thus providing physical and mechanical insights into the ultra-high mechanical properties of glassy hydrogels.

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.

Breathers in lattices with alternating strain-hardening and strain-softening interactions

This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain hardening and strain softening. The existence, stability, and bifurcation structure of such solutions, as well as the system dynamics in the presence of damping and driving, are studied systematically. It is found that the linear resonant peaks in the system bend toward the frequency gap in the presence of nonlinearity. The time-periodic solutions that lie within the frequency gap compare well to Hamiltonian breathers if the damping and driving are small. In the Hamiltonian limit of the problem, we use a multiple scale analysis to derive a nonlinear Schrödinger equation to construct both acoustic and optical breathers. The latter compare very well with the numerically obtained breathers in the Hamiltonian limit.

Modulation instability in nonlinear flexible mechanical metamaterials

In this paper, we study modulation instabilities (MI) in a one-dimensional chain configuration of a flexible mechanical metamaterial (flexMM). Using the lumped element approach, flexMMs can be modeled by a coupled system of discrete equations for the longitudinal displacements and rotations of the rigid mass units. In the long wavelength regime, and applying the multiple-scales method we derive an effective nonlinear Schrödinger equation for slowly varying envelope rotational waves. We are then able to establish a map of the occurrence of MI to the parameters of the metamaterials and the wave numbers. We also highlight the key role of the rotation-displacement coupling between the two degrees of freedom in the manifestation of MI. All analytical findings are confirmed by numerical simulations of the full discrete and nonlinear lump problem. These results provide interesting design guidelines for nonlinear metamaterials offering either stability to high amplitude waves, or conversely being good candidates to observe instabilities.

Embedded 3D Printing of Multimaterial Polymer Lattices via Graph-Based Print Path Planning

Recent advances in computational design and 3D printing enable the fabrication of polymer lattices with high strength-to-weight ratio and tailored mechanics. To date, 3D lattices composed of monolithic materials have primarily been constructed due to limitations associated with most commercial 3D printing platforms. Here, freeform fabrication of multi-material polymer lattices via embedded three-dimensional (EMB3D) printing is demonstrated. An algorithm is developed first that generates print paths for each target lattice based on graph theory. The effects of ink rheology on filamentary printing and the effects of the print path on resultant mechanical properties are then investigated. By co-printing multiple materials with different mechanical properties, a broad range of periodic and stochastic lattices with tailored mechanical responses can be realized opening new avenues for constructing architected matter.

Discrete breathers in a mechanical metamaterial

We consider a previously experimentally realized discrete model that describes a mechanical metamaterial consisting of a chain of pairs of rigid units connected by flexible hinges. Upon analyzing the linear band structure of the model, we identify parameter regimes in which this system may possess discrete breather solutions with frequencies inside the gap between optical and acoustic dispersion bands. We compute numerically exact solutions of this type for several different parameter regimes and investigate their properties and stability. Our findings demonstrate that upon appropriate parameter tuning within experimentally tractable ranges, the system exhibits a plethora of discrete breathers, with multiple branches of solutions that feature period-doubling and symmetry-breaking bifurcations, in addition to other mechanisms of stability change such as saddle-center and Hamiltonian Hopf bifurcations. The relevant stability analysis is corroborated by direct numerical computations examining the dynamical properties of the system and paving the way for potential further experimental exploration of this rich nonlinear dynamical lattice setting.

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.

A bioinspired snap-through metastructure for manipulating micro-objects

Micro-objects stick tenaciously to each other-a well-known show-stopper in microtechnology and in handling micro-objects. Inspired by the trigger plant, we explore a mechanical metastructure for overcoming adhesion involving a snap-action mechanism. We analyze the nonlinear mechanical response of curved beam architectures clamped by a tunable spring, incorporating mono- and bistable states. As a result, reversible miniaturized snap-through devices are successfully realized by micron-scale direct printing, and successful pick-and-place handling of a micro-object is demonstrated. The technique is applicable to universal scenarios, including dry and wet environment, or smooth and rough counter surfaces. With an unprecedented switching ratio (between high and low adhesion) exceeding 10⁴, this concept proposes an efficient paradigm for handling and placing superlight objects.

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.

Bi-stable lateral buckled beam: quasi-static snap-through behaviour analysis

A cantilever beam with lateral buckled deformation performs bi-stable characteristic. The snapping mechanism between its two stable configurations can be triggered when applying displacement or angle on the free end. In this paper, an analytical model based on the modal superposition method is established to investigate the snap-through behaviour. A spring with stiffness k introduced in the analytical model ensures the quasi-static loading, bringing about the accurate snapping response. In addition, the initial lateral buckling of the cantilever beams and the snap-through behaviour of the lateral buckled beams are simulated using the FE method. The theoretical and numerical results are then validated on specially designed and built apparatus. Geometric parameters analysis indicates that the theoretical model is more accurate in predicating the snapping responses of bi-stable lateral buckled beams with slender features. Understanding the mechanics of snap-through behaviour is important for designing novel lateral buckled beams with target shapes and functions.

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.

Transition fronts and their universality classes

Steadily moving transition (switching) fronts, associated with local transformation, symmetry breaking, or collapse, are among the most important dynamic coherent structures. The nonlinear mechanical waves of this type play a major role in many modern applications involving the transmission of mechanical information in systems ranging from crystal lattices and metamaterials to macroscopic civil engineering structures. While many different classes of such dynamic fronts are known, the interrelation between them remains obscure. Here we consider a minimal prototypical mechanical system, the Fermi-Pasta-Ulam (FPU) chain with piecewise linear nonlinearity, and show that there are exactly three distinct classes of switching fronts, which differ fundamentally in how (and whether) they produce and transport oscillations. The fact that all three types of fronts could be obtained as explicit Wiener-Hopf solutions of the same discrete FPU problem allows one to identify the exact mathematical origin of the particular features of each class. To make the underlying Hamiltonian dynamics analytically transparent, we construct a minimal quasicontinuum approximation of the FPU model that captures all three classes of the fronts and reveals interrelation between them. This approximation is of higher order than conventional ones (KdV, Boussinesq) and involves mixed space-time derivatives. The proposed framework unifies previous attempts to classify the mechanical transition fronts as radiative, dispersive, topological, or compressive and categorizes them instead as irreducible types of dynamic lattice defects.

Novel Motion Sequences in Plant-Inspired Robotics: Combining Inspirations from Snap-Trapping in Two Plant Species into an Artificial Venus Flytrap Demonstrator

The field of plant-inspired robotics is based on principles underlying the movements and attachment and adaptability strategies of plants, which together with their materials systems serve as concept generators. The transference of the functions and underlying structural principles of plants thus enables the development of novel life-like technical materials systems. For example, principles involved in the hinge-less movements of carnivorous snap-trap plants and climbing plants can be used in technical applications. A combination of the snap-trap motion of two plant species (Aldrovanda vesiculosa and Dionaea muscipula) has led to the creation of a novel motion sequence for plant-inspired robotics in an artificial Venus flytrap system, the Venus Flyflap. The novel motion pattern of Venus Flyflap lobes has been characterized by using four state-of-the-art actuation systems. A kinematic analysis of the individual phases of the new motion cycle has been performed by utilizing precise pneumatic actuation. Contactless magnetic actuation augments lobe motion into energy-efficient resonance-like oscillatory motion. The use of environmentally driven actuator materials has allowed autonomous motion generation via changes in environmental conditions. Measurement of the energy required for the differently actuated movements has shown that the Venus Flyflap is not only faster than the biological models in its closing movement, but also requires less energy in certain cases for the execution of this movement.

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.

A Heating-Assisted Direct Ink Writing Method for Preparation of PDMS Cellular Structure with High Manufacturing Fidelity

In response to the fact that most of the current research on silicone 3D printing suffers from structure collapse and dimensional mismatch, this paper proposes a heating-assisted direct writing printing method for commercial silicone rubber materials for preparing silicone foam with enhanced fidelity. In the experimental processes, the effects of substrate temperature, printing pressure, and printing speed on the filament width were investigated using a controlled variable method. The results showed the following: (1) the diameter of silicone rubber filaments was positively correlated with the printing pressure and substrate temperature, but negatively correlated with the printing speed; (2) the filament collapse of the large filament spaced foams was significantly improved by the addition of the thermal field, which, in turn, improved the mechanical properties and manufacturing stability of the silicon foams. The heating-assisted direct writing process in this paper can facilitate the development of the field of microelectronics and the direct printing of biomaterials.

Active elastocapillarity in soft solids with negative surface tension

Active solids consume energy to allow for actuation, shape change, and wave propagation not possible in equilibrium. Whereas active interfaces have been realized across many experimental systems, control of three-dimensional (3D) bulk materials remains a challenge. Here, we develop continuum theory and microscopic simulations that describe a 3D soft solid whose boundary experiences active surface stresses. The competition between active boundary and elastic bulk yields a broad range of previously unexplored phenomena, which are demonstrations of so-called active elastocapillarity. In contrast to thin shells and vesicles, we discover that bulk 3D elasticity controls snap-through transitions between different anisotropic shapes. These transitions meet at a critical point, allowing a universal classification via Landau theory. In addition, the active surface modifies elastic wave propagation to allow zero, or even negative, group velocities. These phenomena offer robust principles for programming shape change and functionality into active solids, from robotic metamaterials down to shape-shifting nanoparticles.

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.

Wave manipulation using a bistable chain with reversible impurities

We systematically study linear and nonlinear wave propagation in a chain composed of piecewise-linear bistable springs. Such bistable systems are ideal test beds for supporting nonlinear wave dynamical features including transition and (supersonic) solitary waves. We show that bistable chains can support the propagation of subsonic wave packets which in turn can be trapped by a low-energy phase to induce energy localization. The spatial distribution of these energy foci strongly affects the propagation of linear waves, typically causing scattering, but, in special cases, leading to a reflectionless mode analogous to the Ramsauer-Townsend effect. Furthermore, we show that the propagation of nonlinear waves can spontaneously generate or remove additional foci, which act as effective "impurities." This behavior serves as a new mechanism for reversibly programming the dynamic response of bistable chains.

A mechanical metamaterial with reprogrammable logical functions

Embedding mechanical logic into soft robotics, microelectromechanical systems (MEMS), and robotic materials can greatly improve their functional capacity. However, such logical functions are usually pre-programmed and can hardly be altered during in-life service, limiting their applications under varying working conditions. Here, we propose a reprogrammable mechanological metamaterial (ReMM). Logical computing is achieved by imposing sequential excitations. The system can be initialized and reprogrammed via selectively imposing and releasing the excitations. Realization of universal combinatorial logic and sequential logic (memory) is demonstrated experimentally and numerically. The fabrication scalability of the system is also discussed. We expect the ReMM can serve as a platform for constructing reusable and multifunctional mechanical systems with strong computation and information processing capability.

Mechanical computing

Mechanical mechanisms have been used to process information for millennia, with famous examples ranging from the Antikythera mechanism of the Ancient Greeks to the analytical machines of Charles Babbage. More recently, electronic forms of computation and information processing have overtaken these mechanical forms, owing to better potential for miniaturization and integration. However, several unconventional computing approaches have recently been introduced, which blend ideas of information processing, materials science and robotics. This has raised the possibility of new mechanical computing systems that augment traditional electronic computing by interacting with and adapting to their environment. Here we discuss the use of mechanical mechanisms, and associated nonlinearities, as a means of processing information, with a view towards a framework in which adaptable materials and structures act as a distributed information processing network, even enabling information processing to be viewed as a material property, alongside traditional material properties such as strength and stiffness. We focus on approaches to abstract digital logic in mechanical systems, discuss how these systems differ from traditional electronic computing, and highlight the challenges and opportunities that they present.

Programmable Multistable Perforated Shellular

Developing bistable metamaterials has recently offered a new design paradigm for deployable structures and reusable dampers. While most bistable mechanisms possess inclined/curved struts, a new 3D multistable shellular metamaterial is developed by introducing delicate perforations on the surface of Schwarz's Primitive shellular, integrating the unique properties of shellular materials such as high surface area, stiffness, and energy absorption with the multistability concept. Denoting the fundamental snapping part by motif, certain shellular motifs with elliptical perforations exhibit mechanical bistability. To bring the concept of multistability to a single motif, multistable shellular motifs are developed by introducing multilayer staggered perforations that form hinges and facilitate local instability. Adopting an n-layer staggered perforation (n hinges) design leads to a maximum 2^n-1 stable states within one shellular motif during loading and unloading. Three-directional multistable shellulars are attained by extending the perforation design in three orthogonal directions. Harnessing snap-through and snap-back behaviors and self-contact, the introduced multistable perforated shellulars exhibit strong rigidity both in loading and unloading, and enhanced energy dissipation. The introduced design strategy opens up new horizons for creating multidirectional multistable metamaterials with load bearing capabilities for applications in soft robotics, shape-morphing architectures, and reusable and deployable energy absorbers/dampers.

Buckling-Mediated Phase Transitions in Nano-Electromechanical Phononic Waveguides

Waveguides for mechanical signal transmission in the megahertz to gigahertz regimes enable on-chip phononic circuitry, which brings new capabilities complementing photonics and electronics. Lattices of coupled nano-electromechanical drumhead resonators are suitable for these waveguides due to their high Q-factor and precisely engineered band structure. Here, we show that thermally induced elastic buckling of such resonators causes a phase transition in the waveguide leading to reversible control of signal transmission. Specifically, when cooled, the lowest-frequency transmission band associated with the primary acoustic mode vanishes. Experiments show the merging of the lower and upper band gaps, such that signals remain localized at the excitation boundary. Numerical simulations show that the temperature-induced destruction of the pass band is a result of inhomogeneous elastic buckling, which disturbs the waveguide's periodicity and suppresses the wave propagation. Mechanical phase transitions in waveguides open opportunities for drastic phononic band reconfiguration in on-chip circuitry and computing.

Temperature-Responsive Multistable Metamaterials

The ability for materials to adapt their shape and mechanical properties to the local environment is useful in a variety of applications, from soft robots to deployable structures. In this work, we integrate liquid crystal elastomers (LCEs) with multistable structures to allow autonomous reconfiguration in response to local changes in temperature. LCEs are incorporated in a kirigami-inspired system in which squares are connected at their vertices by small hinges composed of LCE-silicone bilayers. These bend and soften as the temperature increases above room temperature. By choosing geometric parameters for the hinges such that bifurcation points in the stability exist, a transition from mono- or tristability to bistability can be triggered by a sufficient increase in temperature, forcing rearrangements of the structure as minima in the energy landscape are removed. We demonstrate temperature-induced propagation of transition waves, enabling local structural changes to autonomously propagate and affect other parts of the structure. These effects could be harnessed in applications in interface control, reconfigurable structures, and soft robotics.

Wavenumber-space band clipping in nonlinear periodic structures

In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent correction of the dispersion relation. This phenomenon can manifest either as a frequency shift or as a wavenumber shift depending on whether the excitation is prescribed as an initial condition or as a boundary condition, respectively. Several models have been proposed to capture the frequency shifts observed when the system is subjected to harmonic initial excitations. However, these models are not compatible with harmonic boundary excitations, which represent the conditions encountered in most practical applications. To overcome this limitation, we present a multiple scales framework to analytically capture the wavenumber shift experienced by dispersion relation of nonlinear monatomic chains under harmonic boundary excitations. We demonstrate that the wavenumber shifts result in an unusual dispersion correction effect, which we term wavenumber-space band clipping. We then extend the framework to locally resonant periodic structures to explore the implications of this phenomenon on bandgap tunability. We show that the tuning capability is available if the cubic nonlinearity is deployed in the internal springs supporting the resonators.

Programming nonreciprocity and reversibility in multistable mechanical metamaterials

Nonreciprocity can be passively achieved by harnessing material nonlinearities. In particular, networks of nonlinear bistable elements with asymmetric energy landscapes have recently been shown to support unidirectional transition waves. However, in these systems energy can be transferred only when the elements switch from the higher to the lower energy well, allowing for a one-time signal transmission. Here, we show that in a mechanical metamaterial comprising a 1D array of bistable arches nonreciprocity and reversibility can be independently programmed and are not mutually exclusive. By connecting shallow arches with symmetric energy wells and decreasing energy barriers, we design a reversible mechanical diode that can sustain multiple signal transmissions. Further, by alternating arches with symmetric and asymmetric energy landscapes we realize a nonreciprocal chain that enables propagation of different transition waves in opposite directions.

This work presents a mechanical metamaterial with 1D array of bistable arches where nonreciprocity and reversibility can be independently programmed. The effects of asymmetry both at the structural and element level on propagation of transition waves are examined.

Soft Adaptive Mechanical Metamaterials

Soft materials are inherently flexible and make suitable candidates for soft robots intended for specific tasks that would otherwise not be achievable (e.g., smart grips capable of picking up objects without prior knowledge of their stiffness). Moreover, soft robots exploit the mechanics of their fundamental building blocks and aim to provide targeted functionality without the use of electronics or wiring. Despite recent progress, locomotion in soft robotics applications has remained a relatively young field with open challenges yet to overcome. Justly, harnessing structural instabilities and utilizing bistable actuators have gained importance as a solution. This report focuses on substrate-free reconfigurable structures composed of multistable unit cells with a nonconvex strain energy potential, which can exhibit structural transitions and produce strongly nonlinear transition waves. The energy released during the transition, if sufficient, balances the dissipation and kinetic energy of the system and forms a wave front that travels through the structure to effect its permanent or reversible reconfiguration. We exploit a triangular unit cell’s design space and provide general guidelines for unit cell selection. Using a continuum description, we predict and map the resulting structure’s behavior for various geometric and material properties. The structural motion created by these strongly nonlinear metamaterials has potential applications in propulsion in soft robotics, morphing surfaces, reconfigurable devices, mechanical logic, and controlled energy absorption.

Exploiting Mechanical Instabilities in Soft Robotics: Control, Sensing, and Actuation

The rapidly expanding field of soft robotics has provided multiple examples of how entirely soft machines and actuators can outperform conventional rigid robots in terms of adaptability, maneuverability, and safety. Unfortunately, the soft and flexible materials used in their construction impose intrinsic limitations on soft robots, such as low actuation speeds and low output forces. Nature offers multiple examples where highly flexible organisms exploit mechanical instabilities to store and rapidly release energy. Guided by these examples, researchers have recently developed a variety of strategies to overcome speed and power limitations in soft robotics using mechanical instabilities. These mechanical instabilities provide, through rapid transitions from structurally stable states, a new route to achieve high output power amplification and attain impressive actuation speeds. Here, an overview of the literature related to the development of soft robots and actuators that exploit mechanical instabilities to expand their actuation speed, output power, and functionality is presented. Additionally, strategies using structural phase transitions to address current challenges in the area of soft robotic control, sensing, and actuation are discussed. Approaches using instabilities to create entirely soft logic modules to imbue soft robots with material intelligence and distributed computational capabilities are also reviewed.

Peristalsis by pulses of activity

Peristalsis by actively generated waves of muscle contraction is one of the most fundamental ways of producing motion in living systems. We show that peristalsis can be modeled by a train of rectangular-shaped solitary waves of localized activity propagating through otherwise passive matter. Our analysis is based on the Fermi-Pasta-Ulam (FPU) type discrete model accounting for active stresses and we reveal the existence in this problem of a critical regime which we argue to be physiologically advantageous.

Extreme Frequency Conversion from Soliton Resonant Interactions

We present a metastructure architecture with a bistable microstructure that enables extreme broadband frequency conversion. We use numerical and experimental tools to unveil the relationship between input excitations at the unit cell level and output responses at the macrostructural level. We identify soliton-lattice mode resonances resulting in input-independent energy transfer into desired metabeam vibration modes as long as transition waves are triggered within the metastructure. We observe both low-to-high and high-to-low incommensurate frequency interactions in the metabeams, thus enabling energy exchange between bands 2 orders of magnitude apart. This behavior generalizes fluxon-cavity mode resonance in superconducting electronics, providing a general method to extreme frequency conversion in mechanics. Importantly, the introduced architecture allows for expanding the metamaterials design paradigm by fundamentally breaking the dependence of macroscopic dynamics on the unit cell properties. The resulting input-independent nature implies potential applications in broadband frequency regulation and energy transduction.

Hierarchical mechanical metamaterials built with scalable tristable elements for ternary logic operation and amplitude modulation

Multistable mechanical metamaterials are artificial materials whose microarchitectures offer more than two different stable configurations. Existing multistable mechanical metamaterials mainly rely on origami/kirigami-inspired designs, snap-through instability, and microstructured soft mechanisms, with mostly bistable fundamental unit cells. Scalable, tristable structural elements that can be built up to form mechanical metamaterials with an extremely large number of programmable stable configurations remains illusive. Here, we harness the elastic tensile/compressive asymmetry of kirigami microstructures to design a class of scalable X-shaped tristable structures. Using these structure as building block elements, hierarchical mechanical metamaterials with one-dimensional (1D) cylindrical geometries, 2D square lattices, and 3D cubic/octahedral lattices are designed and demonstrated, with capabilities of torsional multistability or independent controlled multidirectional multistability. The number of stable states increases exponentially with the cell number of mechanical metamaterials. The versatile multistability and structural diversity allow demonstrative applications in mechanical ternary logic operators and amplitude modulators with unusual functionalities.

Universally bistable shells with nonzero Gaussian curvature for two-way transition waves

Multi-welled energy landscapes arising in shells with nonzero Gaussian curvature typically fade away as their thickness becomes larger because of the increased bending energy required for inversion. Motivated by this limitation, we propose a strategy to realize doubly curved shells that are bistable for any thickness. We then study the nonlinear dynamic response of one-dimensional (1D) arrays of our universally bistable shells when coupled by compressible fluid cavities. We find that the system supports the propagation of bidirectional transition waves whose characteristics can be tuned by varying both geometric parameters as well as the amount of energy supplied to initiate the waves. However, since our bistable shells have equal energy minima, the distance traveled by such waves is limited by dissipation. To overcome this limitation, we identify a strategy to realize thick bistable shells with tunable energy landscape and show that their strategic placement within the 1D array can extend the propagation distance of the supported bidirectional transition waves.

Curved elastic shells have unique mechanical behavior and multiple stable configurations, but these properties fade when the shell thickness increases. Here the authors report a strategy to realize bistable doubly curved shells with arbitrary thickness, and how to optimize the dynamic response of one-dimensional connected arrays of such doubly-curved bistable shells.

Artificial Venus Flytraps: A Research Review and Outlook on Their Importance for Novel Bioinspired Materials Systems

Bioinspired and biomimetic soft machines rely on functions and working principles that have been abstracted from biology but that have evolved over 3.5 billion years. So far, few examples from the huge pool of natural models have been examined and transferred to technical applications. Like living organisms, subsequent generations of soft machines will autonomously respond, sense, and adapt to the environment. Plants as concept generators remain relatively unexplored in biomimetic approaches to robotics and related technologies, despite being able to grow, and continuously adapt in response to environmental stimuli. In this research review, we highlight recent developments in plant-inspired soft machine systems based on movement principles. We focus on inspirations taken from fast active movements in the carnivorous Venus flytrap (Dionaea muscipula) and compare current developments in artificial Venus flytraps with their biological role model. The advantages and disadvantages of current systems are also analyzed and discussed, and a new state-of-the-art autonomous system is derived. Incorporation of the basic structural and functional principles of the Venus flytrap into novel autonomous applications in the field of robotics not only will inspire further plant-inspired biomimetic developments but might also advance contemporary plant-inspired robots, leading to fully autonomous systems utilizing bioinspired working concepts.

Non-Reciprocal Supratransmission in Mechanical Lattices with Non-Local Feedback Control Interactions

We numerically investigate the supratransmission phenomenon in an active nonlinear system modeled by the 1D/2D discrete sine-Gordon equation with non-local feedback. While, at a given frequency, the typical passive system exhibits a single amplitude threshold marking the onset of the phenomenon, we show that the inclusion of non-local feedback manifests additional thresholds that depend upon the specific boundary from which supratransmission is stimulated, realizing asymmetric (i.e., non-reciprocal) dynamics. The results illustrate a new means of controlling nonlinear wave propagation and energy transport for, e.g., signal amplification and mechanical logic.