Almost all pneumatic and hydraulic actuators useful for mesoscale functions rely on hard valves for control. This article describes a soft, elastomeric valve that contains a bistable membrane, which acts as a mechanical “switch” to control air flow. A structural instability—often called “snap-through”—enables rapid transition between two stable states of the membrane. The snap-upward pressure, Δ P 1 (kilopascals), of the membrane differs from the snap-downward pressure, Δ P 2 (kilopascals). The values Δ P 1 and Δ P 2 can be designed by changing the geometry and the material of the membrane. The valve does not require power to remain in either “open” or “closed” states (although switching does require energy), can be designed to be bistable, and can remain in either state without further applied pressure. When integrated in a feedback pneumatic circuit, the valve functions as a pneumatic oscillator (between the pressures Δ P 1 and Δ P 2 ), generating periodic motion using air from a single source of constant pressure. The valve, as a component of pneumatic circuits, enables (i) a gripper to grasp a ball autonomously and (ii) autonomous earthworm-like locomotion using an air source of constant pressure. These valves are fabricated using straightforward molding and offer a way of integrating simple control and logic functions directly into soft actuators and robots.

A soft, bistable valve for autonomous control of soft actuators

Snap‐through bistability is often observed in nature (e.g., fast snapping to closure of Venus flytrap) and the life (e.g., bottle caps and hair clippers). Recently, harnessing bistability and multistability in different structures and soft materials has attracted growing interest for high‐performance soft actuators and soft robots. They have demonstrated broad and unique applications in high‐speed locomotion on land and under water, adaptive sensing and fast grasping, shape reconfiguration, electronics‐free controls with a single input, and logic computation. Here, an overview of integrating bistable and multistable structures with soft actuating materials for diverse soft actuators and soft/flexible robots is given. The mechanics‐guided structural design principles for five categories of basic bistable elements from 1D to 3D (i.e., constrained beams, curved plates, dome shells, compliant mechanisms of linkages with flexible hinges and deformable origami, and balloon structures) are first presented, alongside brief discussions of typical soft actuating materials (i.e., fluidic elastomers and stimuli‐responsive materials such as electro‐, photo‐, thermo‐, magnetic‐, and hydro‐responsive polymers). Following that, integrating these soft materials with each category of bistable elements for soft bistable and multistable actuators and their diverse robotic applications are discussed. To conclude, perspectives on the challenges and opportunities in this emerging field are considered.

Bistable and Multistable Actuators for Soft Robots: Structures, Materials, and Functionalities

Fluidic soft actuators are enlarging the robotics toolbox by providing flexible elements that can display highly complex deformations. Although these actuators are adaptable and inherently safe, their actuation speed is typically slow because the influx of fluid is limited by viscous forces. To overcome this limitation and realize soft actuators capable of rapid movements, we focused on spherical caps that exhibit isochoric snapping when pressurized under volume-controlled conditions. First, we noted that this snap-through instability leads to both a sudden release of energy and a fast cap displacement. Inspired by these findings, we investigated the response of actuators that comprise such spherical caps as building blocks and observed the same isochoric snapping mechanism upon inflation. Last, we demonstrated that this instability can be exploited to make these actuators jump even when inflated at a slow rate. Our study provides the foundation for the design of an emerging class of fluidic soft devices that can convert a slow input signal into a fast output deformation.

/pdf/inflatable-soft-jumper-inspired-by-shell-snapping-40iiqb5vps.pdf

Inflatable soft jumper inspired by shell snapping.

Miniaturization has been the driving force of scientific and technological advances over recent decades. Recently, flexibility has gained significant interest, particularly in miniaturization approaches for biomedical devices, wearable sensing technologies, and drug delivery. Flexible microfluidics is an emerging area that impacts upon a range of research areas including chemistry, electronics, biology, and medicine. Various materials with flexibility and stretchability have been used in flexible microfluidics. Flexible microchannels allow for strong fluid-structure interactions. Thus, they behave in a different way from rigid microchannels with fluid passing through them. This unique behaviour introduces new characteristics that can be deployed in microfluidic applications and functions such as valving, pumping, mixing, and separation. To date, a specialised review of flexible microfluidics that considers both the fundamentals and applications is missing in the literature. This review aims to provide a comprehensive summary including: (i) Materials used for fabrication of flexible microfluidics, (ii) basics and roles of flexibility on microfluidic functions, (iii) applications of flexible microfluidics in wearable electronics and biology, and (iv) future perspectives of flexible microfluidics. The review provides researchers and engineers with an extensive and updated understanding of the principles and applications of flexible microfluidics.

Flexible Microfluidics: Fundamentals, Recent Developments, and Applications.

On virus growth and form

Critical phenomena are well understood in a wide range of physical systems. The dynamics of snap-through instabilities, a widespread phenomenon in their own right, are now shown to display critical scaling properties.

Critical slowing down in purely elastic 'snap-through' instabilities

We study elastic snap-through induced by a control parameter that evolves dynamically. In particular, we study an elastic arch subject to an end-shortening that evolves linearly with time, i.e. at a constant rate. For large end-shortening the arch is bistable but, below a critical end-shortening, the arch becomes monostable. We study when and how the arch transitions between states and show that the end-shortening at which the fast ‘snap’ happens depends on the rate at which the end-shortening is reduced. This delay in snap-through is a consequence of delayed bifurcation and occurs even in the perfectly elastic case when viscous (and viscoelastic) effects are negligible. We present the results of numerical simulations to determine the magnitude of this delay (and the associated time lag) as the loading rate and the importance of external viscous damping vary. We also present an asymptotic analysis of the geometrically-nonlinear problem that reduces the salient dynamics to that of an ordinary differential equation; the form of this reduced equation is generic for snap-through instabilities in which the relevant control parameter is ramped linearly in time. Moreover, this asymptotic reduction allows us to derive analytical results for the delay observed in snap-through that are in good agreement with the results of our simulations. Finally, we discuss scaling laws for the delay that should be expected in other examples of delayed bifurcation in elastic instabilities.

Delayed bifurcation in elastic snap-through instabilities

We present a detailed asymptotic analysis of the point indentation of an unpressurized, spherical elastic shell. Previous analyses of this classic problem have assumed that for sufficiently large indentation depths, such a shell deforms by ‘mirror buckling’—a portion of the shell inverts to become a spherical cap with equal but opposite curvature to the undeformed shell. The energy of deformation is then localized in a ridge in which the deformed and undeformed portions of the shell join together, commonly referred to as Pogorelov's ridge. Rather than using an energy formulation, we revisit this problem from the point of view of the shallow shell equations and perform an asymptotic analysis that exploits the largeness of the indentation depth. This reveals first that the stress profile associated with mirror buckling is singular as the indenter is approached. This consequence of point indentation means that mirror buckling must be modified to incorporate the shell's bending stiffness close to the indenter and gives rise to an intricate asymptotic structure with seven different spatial regions. This is in contrast with the three regions (mirror-buckled, ridge and undeformed) that are usually assumed and yields new insight into the large compressive hoop stress that ultimately causes the secondary buckling of the shell.

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2015.0732

The shallow shell approach to Pogorelov's problem and the breakdown of 'mirror buckling'.

We present a detailed asymptotic analysis of the point indentation of an unpressurized, spherical elastic shell. Previous analyses of this classic problem have assumed that for sufficiently large indentation depths, such a shell deforms by `mirror buckling' --- a portion of the shell inverts to become a spherical cap with equal but opposite curvature to the undeformed shell. The energy of deformation is then localized in a ridge in which the deformed and undeformed portions of the shell join together, commonly referred to as Pogorelov's ridge. Rather than using an energy formulation, we revisit this problem from the point of view of the shallow shell equations and perform an asymptotic analysis that exploits the largeness of the indentation depth. This reveals first that the stress profile associated with mirror buckling is singular as the indenter is approached. This consequence of point indentation means that mirror buckling must be modified to incorporate the shell's bending stiffness close to the indenter and gives rise to an intricate asymptotic structure with seven different spatial regions. This is in contrast with the three regions (mirror-buckled, ridge and undeformed) that are usually assumed and yields new insight into the large compressive hoop stress that ultimately causes the shell to buckle azimuthally.

The shallow shell approach to Pogorelov's problem and the breakdown of `mirror buckling'

Snap-through is a striking instability in which an elastic object rapidly jumps from one state to another. It is seen in the leaves of the Venus flytrap plant and umbrellas flipping on a windy day among many other examples. Similar structures that snap-through are used to generate fast motions in soft robotics, switches in micro-scale electronics and artificial heart valves. Despite the ubiquity of snap-through in nature and engineering, its dynamics is usually only understood qualitatively. In this thesis we develop analytical understanding of this dynamics, focussing on how the mathematical structure underlying the snap-through transition controls the timescale of instability. We begin by considering the dynamics of 'pull-in' instabilities in microelectromechanical systems (MEMS) - a type of snap-through caused by electrostatic forces in which the motions are dominated by fluid damping. Using a lumped-parameter model, we show that the observed time delay near the pull-in transition is a type of critical slowing down - a so-called 'bottleneck' due to the 'ghost' of a saddle-node bifurcation. We obtain a scaling law describing this slowing down, and, in the process, unify a large range of experiments and simulations that exhibit delay phenomena during pull-in. We also investigate the pull-in dynamics of MEMS microbeams, extending the lumped-parameter approach to incorporate the details of the beam geometry. This provides a model system in which to understand snap-through of a continuous elastic structure due to external loading. We develop a perturbation method that systematically exploits the proximity to pull-in to reduce the governing equations to a simpler evolution equation, with a structure that highlights the saddle-node bifurcation. This allows us to analyse the bottleneck dynamics in detail, which we compare with previous experimental and numerical data. The remainder of the thesis is concerned with the dynamics of snap-through in macroscopic systems. In particular, we explore the extent to which dissipation is required to explain anomalously slow snap-through. Considering an elastic arch as an archetype of a snapping system, we use the perturbation method developed earlier to show that two bottleneck regimes are possible, depending delicately on the relative importance of external damping. In particular, we show that critical slowing down occurs even in the absence of damping, leading to a new scaling law for the snap-through time that is confirmed by elastica simulations and experiments. In many real systems material viscoelasticity is present to some degree. Finally, we examine how this influences the snap-through dynamics of a simple truss-like structure. We present a regime diagram that characterises when the timescale of snap-through is controlled by viscous, elastic or viscoelastic effects.

Ghosts and bottlenecks in elastic snap-through

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