Buckling-induced sound production in the aeroelastic tymbals of Yponomeuta.

The loss of elastic stability (buckling) can lead to catastrophic failure in the context of traditional engineering structures. Conversely, in nature, buckling often serves a desirable function, such as in the prey-trapping mechanism of the Venus fly trap (Dionaea muscipula). This paper investigates the buckling-enabled sound production in the wingbeat-powered (aeroelastic) tymbals of Yponomeuta moths. The hindwings of Yponomeuta possess a striated band of ridges that snap through sequentially during the up- and downstroke of the wingbeat cycle-a process reminiscent of cellular buckling in compressed slender shells. As a result, bursts of ultrasonic clicks are produced that deter predators (i.e. bats). Using various biological and mechanical characterization techniques, we show that wing camber changes during the wingbeat cycle act as the single actuation mechanism that causes buckling to propagate sequentially through each stria on the tymbal. The snap-through of each stria excites a bald patch of the wing's membrane, thereby amplifying sound pressure levels and radiating sound at the resonant frequencies of the patch. In addition, the interaction of phased tymbal clicks from the two wings enhances the directivity of the acoustic signal strength, suggesting an improvement in acoustic protection. These findings unveil the acousto-mechanics of Yponomeuta tymbals and uncover their buckling-driven evolutionary origin. We anticipate that through bioinspiration, aeroelastic tymbals will encourage novel developments in the context of multi-stable morphing structures, acoustic structural monitoring, and soft robotics.

Insect-scale jumping robots enabled by a dynamic buckling cascade.

Millions of years of evolution have allowed animals to develop unusual locomotion capabilities. A striking example is the legless-jumping of click beetles and trap-jaw ants, which jump more than 10 times their body length. Their delicate musculoskeletal system amplifies their muscles' power. It is challenging to engineer insect-scale jumpers that use onboard actuators for both elastic energy storage and power amplification. Typical jumpers require a combination of at least two actuator mechanisms for elastic energy storage and jump triggering, leading to complex designs having many parts. Here, we report the new concept of dynamic buckling cascading, in which a single unidirectional actuation stroke drives an elastic beam through a sequence of energy-storing buckling modes automatically followed by spontaneous impulsive snapping at a critical triggering threshold. Integrating this cascade in a robot enables jumping with unidirectional muscles and power amplification (JUMPA). These JUMPA systems use a single lightweight mechanism for energy storage and release with a mass of 1.6 g and 2 cm length and jump up to 0.9 m, 40 times their body length. They jump repeatedly by reengaging the latch and using coiled artificial muscles to restore elastic energy. The robots reach their performance limits guided by theoretical analysis of snap-through and momentum exchange during ground collision. These jumpers reach the energy densities typical of the best macroscale jumping robots, while also matching the rapid escape times of jumping insects, thus demonstrating the path toward future applications including proximity sensing, inspection, and search and rescue.

Snap buckling of bistable beams under combined mechanical and magnetic loading.

We investigate the mechanics of bistable, hard-magnetic, elastic beams, combining experiments, finite-element modelling (FEM) and a reduced-order theory. The beam is made of a hard magneto-rheological elastomer, comprising two segments with antiparallel magnetization along the centreline, and is set into a bistable curved configuration by imposing an end-to-end shortening. Reversible snapping is possible between these two stable states. First, we experimentally characterize the critical field strength for the onset of snapping, at different levels of end-to-end shortening. Second, we perform three-dimensional FEM simulations using the Riks method to analyse high-order deformation modes during snapping. Third, we develop a reduced-order centreline-based beam theory to rationalize the observed magneto-elastic response. The theory and simulations are validated against experiments, with an excellent quantitative agreement. Finally, we consider the case of combined magnetic loading and poking force, examining how the applied field affects the bistability and quantifying the maximum load-bearing capacity. Our work provides a set of predictive tools for the rational design of one-dimensional, bistable, magneto-elastic structural elements. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Pseudo-bistability of viscoelastic shells.

Viscoelastic shells subjected to a pressure loading exhibit rich and complex time-dependent responses. Here we focus on the phenomenon of pseudo-bistability, i.e. a viscoelastic shell can stay inverted when pressure is removed, and snap to its natural shape after a delay time. We model and explain the mechanism of pseudo-bistability with a viscoelastic shell model. It combines the small strain, moderate rotation shell theory with the standard linear solid as the viscoelastic constitutive law, and is applicable to shells with arbitrary axisymmetric shapes. As a case study, we investigate the pseudo-bistable behaviour of viscoelastic ellipsoidal shells. Using the proposed model, we successfully predict buckling of a viscoelastic ellipsoidal shell into its inverted configuration when subjected to an instantaneous pressure, creeping when the pressure is held, staying inverted after the pressure is removed, and eventually snapping back after a delay time. The stability transition of the shell from a monostable, temporarily bistable and eventually back to the monostable state is captured by examining the evolution of the instantaneous pressure-volume change relation at different time of the holding and releasing process. A systematic parametric study is conducted to investigate the effect of geometry, viscoelastic properties and loading history on the pseudo-bistable behaviour. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

DC Signature of Snap-through Bistability in Carbon Nanotube Mechanical Resonators.

Bistable arched beams exhibiting Euler-Bernoulli snap-through buckling are widely investigated as promising candidates for various potential applications, such as memory devices, energy harvesters, sensors, and actuators. Recently, we reported the realization of a buckled suspended carbon nanotube (CNT) based bistable resonator, which exhibits a unique three-dimensional snap-through transition and an extremely large change in frequency as a result. In this article, we address a unique characteristic of these devices in which a significant change in the DC conductance is also observed at the mechanical snap-through transition. Through the analysis of this phenomenon, we arrive at several important conclusions: we find that the common approach to determining CNT vibrational resonance amplitude is inaccurate; we find evidence that latching phenomena should be easily realizable, relevant for RF switches and nonvolatile memory devices. Finally, we present evidence for possible inner shell sliding, which is relevant for understanding interlayer coupling and moiré pattern research.

Snap-through of graphene nanowrinkles under out-of-plane compression.

Nanowrinkles (i.e. the buckled nanoribbons) are widely observed in nano-devices assembled by two-dimensional (2D) materials. The existence of nanowrinkles significantly affects the physical (such as mechanical, electrical and thermal) properties of 2D materials, and thus further, impedes the applications of those devices. In this paper, we take the nanowrinkle formed in a monolayer graphene as a model system to study its deformation behaviours, especially the configuration evolution and the snap-through buckling instabilities, when subjected to the out-of-plane compression. By performing molecular dynamics simulation, the graphene nanowrinkles with or without self-adhesion (which are notated as 'clipped' state or 'bump' state, respectively) are obtained depending on the geometric size and the applied axial compressive pre-strain. The elastica theory is employed to quantify the shape of 'bump' nanowrinkles, as well as the critical condition of the transition between 'clipped' and 'bump' states. By applying out-of-plane compression to the generated graphene nanowrinkle, it flips to an opposite configuration via snap-through buckling. We identify four different buckling modes according to the configuration evolution. An unified phase diagram is constructed to describe those buckling modes. For the cases with negligible van der Waals interaction getting involved in the snap-buckling process, i.e. without self-adhesion, the force-displacement curves for nanowrinkles with same axial pre-strain but different sizes can be scaled to collapse. Moreover, the critical buckling loads can also be scaled and predicted by the extended elastica theory. Otherwise, for the cases with self-adhesion, which corresponds to the greater axial pre-strain, the van der Waals interaction makes the scaling collapse break down. It is expected that the analysis about the snap-through buckling of graphene nanowrinkles reported in this work will advance the understanding of the mechanical behaviours of wrinkled 2D materials and promote the design of functional nanodevices, such as nanomechanical resonators and capacitors.

Flow sensor based on the snap-through detection of a curved micromechanical beam.

We report on a flow velocity measurement technique based on snap-through detection of an electrostatically actuated, bistable micromechanical beam. We show that induced elecro-thermal Joule heating and the convective air cooling change the beam curvature and consequently the critical snap-through voltage (VST ). Using single crystal silicon beams, we demonstrate the snap-through voltage to flow velocity sensitivity of dV ST/du ≈ 0.13 V s m -1 with a power consumption of ≈ 360 µ W. Our experimental results were in accord with the reduced order, coupled, thermo-electro-mechanical model prediction. We anticipate that electrostatically induced snap-through in curved, micromechanical beams will open new directions for the design and implementation of downscaled flow sensors for autonomous applications and environmental sensors.

Geometrically controlled snapping transitions in shells with curved creases.

Curvature and mechanics are intimately connected for thin materials, and this coupling between geometry and physical properties is readily seen in folded structures from intestinal villi and pollen grains to wrinkled membranes and programmable metamaterials. While the well-known rules and mechanisms behind folding a flat surface have been used to create deployable structures and shape transformable materials, folding of curved shells is still not fundamentally understood. Shells naturally deform by simultaneously bending and stretching, and while this coupling gives them great stability for engineering applications, it makes folding a surface of arbitrary curvature a nontrivial task. Here we discuss the geometry of folding a creased shell, and demonstrate theoretically the conditions under which it may fold smoothly. When these conditions are violated we show, using experiments and simulations, that shells undergo rapid snapping motion to fold from one stable configuration to another. Although material asymmetry is a proven mechanism for creating this bifurcation of stability, for the case of a creased shell, the inherent geometry itself serves as a barrier to folding. We discuss here how two fundamental geometric concepts, creases and curvature, combine to allow rapid transitions from one stable state to another. Independent of material system and length scale, the design rule that we introduce here explains how to generate snapping transitions in arbitrary surfaces, thus facilitating the creation of programmable multistable materials with fast actuation capabilities.

Amplifying the response of soft actuators by harnessing snap-through instabilities.

Soft, inflatable segments are the active elements responsible for the actuation of soft machines and robots. Although current designs of fluidic actuators achieve motion with large amplitudes, they require large amounts of supplied volume, limiting their speed and compactness. To circumvent these limitations, here we embrace instabilities and show that they can be exploited to amplify the response of the system. By combining experimental and numerical tools we design and construct fluidic actuators in which snap-through instabilities are harnessed to generate large motion, high forces, and fast actuation at constant volume. Our study opens avenues for the design of the next generation of soft actuators and robots in which small amounts of volume are sufficient to achieve significant ranges of motion.

Intrinsically Multistable Soft Actuator Driven by Mixed-Mode Snap-Through Instabilities.

Actuators utilizing snap-through instabilities are widely investigated for high-performance fast actuators and shape reconfigurable structures owing to their rapid response and limited reliance on continuous energy input. However, prevailing approaches typically involve a combination of multiple bistable actuator units and achieving multistability within a single actuator unit still remains an open challenge. Here, a soft actuator is presented that uses shape memory alloy (SMA) and mixed-mode elastic instabilities to achieve intrinsically multistable shape reconfiguration. The multistable actuator unit consists of six stable states, including two pure bending states and four bend-twist states. The actuator is composed of a pre-stretched elastic membrane placed between two elastomeric frames embedded with SMA coils. By controlling the sequence and duration of SMA activation, the actuator is capable of rapid transition between all six stable states within hundreds of milliseconds. Principles of energy minimization are used to identify actuation sequences for various types of stable state transitions. Bending and twisting angles corresponding to various prestretch ratios are recorded based on parameterizations of the actuator's geometry. To demonstrate its application in practical conditions, the multistable actuator is used to perform visual inspection in a confined space, light source tracking during photovoltaic energy harvesting, and agile crawling.

Buckling mediated by mobile localized elastic excitations.

Experiments reveal that structural transitions in thin sheets are mediated by the passage of transient and stable mobile localized elastic excitations. These "crumples" or "d-cones" nucleate, propagate, interact, annihilate, and escape. Much of the dynamics occurs on millisecond time scales. Nucleation sites correspond to regions where generators of the ideal unstretched surface converge. Additional stable intermediate states illustrate two forms of quasistatic inter-crumple interaction through ridges or valleys. These interactions create pairs from which extended patterns may be constructed in larger specimens. The onset of localized transient deformation with increasing sheet size is correlated with a characteristic stable crumple size, whose measured scaling with thickness is consistent with prior theory and experiment for localized elastic features in thin sheets. We offer a new theoretical justification of this scaling.

A rapid-response soft end effector inspired by the hummingbird beak.

Biology is a wellspring of inspiration in engineering design. This paper delves into the application of elastic instabilities-commonly used in biological systems to facilitate swift movement-as a power-amplification mechanism for soft robots. Specifically, inspired by the nonlinear mechanics of the hummingbird beak-and shedding further light on it-we design, build and test a novel, rapid-response, soft end effector. The hummingbird beak embodies the capacity for swift movement, achieving closure in less than [Formula: see text]. Previous work demonstrated that rapid movement is achieved through snap-through deformations, induced by muscular actuation of the beak's root. Using nonlinear finite element simulations coupled with continuation algorithms, we unveil a representative portion of the equilibrium manifold of the beak-inspired structure. The exploration involves the application of a sequence of rotations as exerted by the hummingbird muscles. Specific emphasis is placed on pinpointing and tailoring the position along the manifold of the saddle-node bifurcation at which the onset of elastic instability triggers dynamic snap-through. We show the critical importance of the intermediate rotation input in the sequence, as it results in the accumulation of elastic energy that is then explosively released as kinetic energy upon snap-through. Informed by our numerical studies, we conduct experimental testing on a prototype end effector fabricated using a compliant material (thermoplastic polyurethane). The experimental results support the trends observed in the numerical simulations and demonstrate the effectiveness of the bio-inspired design. Specifically, we measure the energy transferred by the soft end effector to a pendulum, varying the input levels in the sequence of prescribed rotations. Additionally, we demonstrate a potential robotic application in scenarios demanding explosive action. From a mechanics perspective, our work sheds light on how pre-stress fields can enable swift movement in soft robotic systems with the potential to facilitate high input-to-output energy efficiency.

Explainable Artificial Intelligence to Investigate the Contribution of Design Variables to the Static Characteristics of Bistable Composite Laminates.

Material properties, geometrical dimensions, and environmental conditions can greatly influence the characteristics of bistable composite laminates. In the current work, to understand how each input feature contributes to the curvatures of the stable equilibrium shapes of bistable laminates and the snap-through force to change these configurations, the correlation between these inputs and outputs is studied using a novel explainable artificial intelligence (XAI) approach called SHapley Additive exPlanations (SHAP). SHAP is employed to explain the contribution and importance of the features influencing the curvatures and the snap-through force since XAI models change the data into a form that is more convenient for users to understand and interpret. The principle of minimum energy and the Rayleigh-Ritz method is applied to obtain the responses of the bistable laminates used as the input datasets in SHAP. SHAP effectively evaluates the importance of the input variables to the parameters. The results show that the transverse thermal expansion coefficient and moisture variation have the most impact on the model's output for the transverse curvatures and snap-through force. The eXtreme Gradient Boosting (XGBoost) and Finite Element (FM) methods are also employed to identify the feature importance and validate the theoretical approach, respectively.

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.

Investigation into Mode Localization of Electrostatically Coupled Shallow Microbeams for Potential Sensing Applications.

With the constant need for the development of smart devices, Micro-Electro-Mechanical Systems (MEMS) based smart sensors have been developed to detect hazard materials, micro-particles or even toxic substances. Identifying small particles using such micro-engineering technology requires designing sensors with high sensitivity, selectivity and ease of integration with other electronic components. Nevertheless, the available detection mechanism designs are still juvenile and need more innovative ideas to be even more competitive. Therefore, this work aims to introduce a novel, smart and innovative micro-sensor design consisting of two weakly electrostatically coupled microbeams (both serving as sensors) and electrically excited using a stationary electrode assuming a dc/ac electric signal. The sensor design can be tuned from straight to eventually initially curved microbeams. Such an arrangement would develop certain nonlinear phenomena, such as the snap-through motion. This behavior would portray certain mode veering/mode crossing and ultimately mode localization and it would certainly lead in increasing the sensitivity of the mode-localized based sensing mechanism. These can be achieved by tracking the change in the resonance frequencies of the two microbeams as the coupling control parameter is varied. To this extent, a nonlinear model of the design is presented, and then a reduced-order model considering all geometric and electrical nonlinearities is established. A Long-Time Integration (LTI) method is utilized to solve the static and dynamics of the coupled resonators under primary lower-order and higher-order resonances, respectively. It is shown that the system can display veering and mode coupling in the vicinity of the primary resonances of both beams. Such detected modal interactions lead to an increase in the sensitivity of the sensor design. In addition, the use of two different beam's configurations in one device uncovered a possibility of using this design in detecting two potential substances at the same time using the two interacting resonant peaks.

Finite Element Analysis of Crack Propagation in Adhesive Joints with Notched Adherends.

The adherends notching technique has been the subject of a few recent studies and consists of tailoring the geometry of the adjoined layers to mitigate the bondline peak stresses and enhance the joint strength. In the present study, we explored the effect of the adherends notching technique on crack propagation using finite element (FE) simulations based on the cohesive zone model (CZM) of fracture. Double cantilever beam (DCB) adhesive joints subjected to quasistatic loading were considered as a model material system. An array of equally spaced notches was placed on the faying sides of the adherends, oriented perpendicularly to the direction of crack growth. A parametric investigation was carried out to ascertain the role of the notches and the input cohesive properties on various performance metrics, e.g., load-displacement response and dissipated energy. The proposed notching strategy promotes an unstable crack pinning/depinning process, which effectively delays crack growth and increases the effective work of fracture. Additionally, we found that the overall behaviour is tunable by changing geometric (i.e., notch spacing and depth) and bondline material properties.

Fast Thermal Actuators for Soft Robotics.

Thermal actuation is a common actuation method for soft robots. However, a major limitation is the relatively slow actuation speed. Here we report significant increase in the actuation speed of a bimorph thermal actuator by harnessing the snap-through instability. The actuator is made of silver nanowire/polydimethylsiloxane composite. The snap-through instability is enabled by simply applying an offset displacement to part of the actuator structure. The effects of thermal conductivity of the composite, offset displacement, and actuation frequency on the actuator speed are investigated using both experiments and finite element analysis. The actuator yields a bending speed as high as 28.7 cm-1/s, 10 times that without the snap-through instability. A fast crawling robot with locomotion speed of 1.04 body length per second and a biomimetic Venus flytrap were demonstrated to illustrate the promising potential of the fast bimorph thermal actuators for soft robotic applications.

Self-offloading therapeutic footwear using compliant snap-through arches.

In diabetic peripheral neuropathy, offloading high-plantar-pressure areas using statically offloaded customized insoles or expensive sensors and actuators are commonly-followed treatment procedures. In this article, we propose the concept of dynamically self-offloading therapeutic footwear that operates mechanically without using sensors and actuators. We achieve this by using an array of snapping arches. When a load higher than a bespoke value is applied, these arches enter negative-stiffness regime and offload the high-pressure region by snapping to a different shape. They again return to their initial shape when the load disappears. Thus, they serve as both sensors and actuators that get actuated by person's body weight. We present an analytical method to compute the switching load and the switchback time of such arches and use them to customize the footwear according to the person's body weight, gait speed, and foot size. We identify the high-pressure regions from the clinical data and place the arches such that these high-pressure regions get dynamically offloaded, and the pressure gets redistributed to other regions. We considered 200 kPa as a limiting pressure to prevent the prolonged effects of high plantar pressure. To check the efficacy of the concept, a complete 3D-printed prototype made of thermoplastic polyurethane was tested and compared with barefoot and in-shoe plantar pressure for subjects recruited at a clinical facility. We notice that the self-offloading insole shows the plantar pressure reduction at all the foot regions, and significant offloading of 57% is observed at the forefoot region.

Programming Soft Shape-Morphing Systems by Harnessing Strain Mismatch and Snap-Through Bistability: A Review.

Multi-modal and controllable shape-morphing constitutes the cornerstone of the functionalization of soft actuators/robots. Involving heterogeneity through material layout is a widely used strategy to generate internal mismatches in active morphing structures. Once triggered by external stimuli, the entire structure undergoes cooperative deformation by minimizing the potential energy. However, the intrinsic limitation of soft materials emerges when it comes to applications such as soft actuators or load-bearing structures that require fast response and large output force. Many researchers have explored the use of the structural principle of snap-through bistability as the morphing mechanisms. Bistable or multi-stable mechanical systems possess more than one local energy minimum and are capable of resting in any of these equilibrium states without external forces. The snap-through motion could overcome energy barriers to switch among these stable or metastable states with dramatically distinct geometries. Attributed to the energy storage and release mechanism, such snap-through transition is quite highly efficient, accompanied by fast response speed, large displacement magnitude, high manipulation strength, and moderate driving force. For example, the shape-morphing timescale of conventional hydrogel systems is usually tens of minutes, while the activation time of hydrogel actuators using the elastic snapping instability strategy can be reduced to below 1 s. By rationally embedding stimuli-responsive inclusions to offer the required trigger energy, various controllable snap-through actuations could be achieved. This review summarizes the current shape-morphing programming strategies based on mismatch strain induced by material heterogeneity, with emphasis on how to leverage snap-through bistability to broaden the applications of the shape-morphing structures in soft robotics and mechanical metamaterials.

Improving Energy Harvesting from Bridge Vibration Excited by Moving Vehicles with a Bi-Stable Harvester.

To monitor the health status of the bridge, many sensors are needed to be mounted on it. Converting bridge vibration energy to electrical energy is considered as a potential solution to the problem of providing reliable electric power to these sensors. The objective of this work is to present an operable strategy for improving the electric energy output of a piezoelectric energy harvester installed on a bridge by introducing bi-stable characteristics. A bi-stable harvester is proposed. By adjusting the tip and fixed magnets, different types of potential energy can be generated, and then the harvester can exhibit the linear, mono-stable and bi-stable characteristics. In the bi-stable state, the harvester triggers snap-through motions easily and generates large outputs. The corresponding prototype was fabricated, and the experiment was carried out to validate the advantage of the bi-stable energy harvester. The experiment results show that the bi-stable energy harvester outperforms the classical linear harvester over the whole range of vehicle speed. As the vehicle speed exceeds a critical one, the snap-through motion will happen, which is beneficial to enhancing the electricity output. This conceptual design may provide guidance for promoting the performance of bridge energy harvesting.