Snap-through Instability Research Articles

Pressure-induced instability and its coupled aeroelasticity of inflated pillow

A floating air weapon system (such as airborne floating mines) plays an important role in modern air defense operations. This paper focuses on aeroelastic characteristics of airborne floating mine named inflated pillow. Firstly, the dynamic deployable process of the pillow and characteristics of the local instability of the edge are studied, and the evolution mechanism of wrinkles and kinks is analyzed. Secondly, in the cruising stage, the fluid-structural-thermal coupling analysis is performed on the pillow, and the aeroelastic characteristics are studied. Thirdly, the shape-preserving effect of the inflated pillow during the “negative pressure” slow landing stage is evaluated. It is found that when the wind velocity is higher, the pillow has a collapsed instability (surface extrusion and contact), and when the wind velocity is lower, snap-through instability occurs. Finally, for the collapsed instability, a carbon fiber skeleton is added to discrete the large global collapsed fold into small local folds, thus achieving shape-preserving effect of pillow. For snap-through instability, the critical internal pressure and different shape evolution under different wind velocity are evaluated. Through the analysis of the mechanical mechanism and control of the structural morphological evolution, it provides theoretical guidance for the application of the curved shell structure in floating air weapon system.

Snap-through instability of slightly curved beams under sinusoidal loading based on nonlocal elasticity theory

The nonlinear behavior of thin-walled, sinusoidal, slightly curved beams with pinned ends under lateral sinusoidal loading is considered numerically, based on Eringen’s nonlocal elasticity theory and the Euler-Bernoulli beam theory. Geometrically nonlinear governing differential equations are solved by using the finite difference method and the displacement-controlled Newton-Raphson method. The influences of the nonlocal parameter, the initial curvature, and the span of the slightly curved beam on the buckling values are examined. Unlike the relevant previous studies, it is stated in this study that the values of these parameters must remain within certain limits in order to have purely snap-through buckling behavior. Moreover; the graphs of the deformed shapes of the slightly curved beams, the internal forces and the horizontal support reactions corresponding to the various phases of the equilibrium paths (including the prebuckling, buckling and postbuckling stages) are drawn for various values of the nonlocal parameter and the effect of the nonlocal parameter on these graphs are investigated in detail. The study contains insightful results and concluding remarks improving the comprehension of the snap-through phenomenon of the slightly curved beams under lateral loading.

Nonlinear elasticity of biological basement membrane revealed by rapid inflation and deflation

Basement membrane (BM) is a thin layer of extracellular matrix that surrounds most animal tissues, serving as a physical barrier while allowing nutrient exchange. Although they have important roles in tissue structural integrity, physical properties of BMs remain largely uncharacterized, which limits our understanding of their mechanical functions. Here, we perform pressure-controlled inflation and deflation to directly measure the nonlinear mechanics of BMs in situ. We show that the BMs behave as a permeable, hyperelastic material whose mechanical properties and permeability can be measured in a model-independent manner. Furthermore, we find that BMs exhibit a remarkable nonlinear stiffening behavior, in contrast to the reconstituted Matrigel. This nonlinear stiffening behavior helps the BMs to avoid the snap-through instability (or structural softening) widely observed during the inflation of most elastomeric balloons and thus maintain sufficient confining stress to the enclosed tissues during their growth.

Delayed bifurcation in 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.

Soft dielectric elastomer tubes in an electric field

Soft dielectric elastomers with high relative permittivity, very low modulus and high electric breakdown strength have emerged as promising materials for various applications as sensors, actuators and in energy harvesting and soft robotics. We study the intricate deformation behaviour of a soft dielectric elastomer tube of finite length and closed ends, that carries a dead load, is internally pressurised by an injected fluid and has a high electric potential applied across its walls. As for soft tubes in the absence of a potential, this electro-hyperelastic problem involving very large deformations, exhibits a multitude of possibilities, including homogeneous deformation, inhomogeneous bifurcation, snap-through instabilities and post bifurcation behaviour in the form of propagation of axisymmetric bulges. We develop a coupled Finite Element procedure for the situation where the domains of the mechanical and electrostatic problems coincide. The procedure can handle volume flow rate controlled electro-elastic problems. We use it to study the many aspects of the deformation behaviour and limitations placed by competing failure mechanisms on practical utilisation of the large areal strains and axial actuations that can be produced. If electrical breakdown can be avoided by ingenious design of loading sequences, the large volume increase in the tube due to the triggering of instabilities can be harnessed and has far-reaching technological implications.

Modal analysis of post-buckled beams undergoing stable transitions between remote equilibria

Post-buckled structures are prone to snap-through instabilities when external loading causes the structure to lose local stability and jump to a remote equilibrium. However, using piezoelectric actuation, structures can undergo entirely stable transitions between remote equilibria, thereby avoiding snap-through. This paper investigates the linearized vibrational properties of post-buckled beams along these stable transition paths. Numerical results are calculated using an elastica model with allowances for piezoelectric actuation. The model is non-dimensionalized to provide a general view of how the natural frequencies and corresponding mode shapes evolve during stable transitions. Results are presented for two types of stable transitions—one in which the transition is accomplished by changing the external load under a constant actuation level, and one in which the actuation levels are changed without external loading. Results show that the first four natural frequencies of the beam undergo complicated changes during a stable transition. Results also indicate that the first two mode shapes tend to be asymmetric and localized during the early and later stages of the transition. Yet, during the middle of the transition, when the static configuration of the beam is an anti-symmetric “S” shape, the first two mode shapes are symmetric and global. The natural frequencies and modes predicted by the numerical model are validated with a series of experiments.

Elastocaloric heat pump with specific cooling power of 20.9 W g–1 exploiting snap-through instability and strain-induced crystallization

Conventional refrigeration relies on hazardous agents, contributing to global warming. Soft, cheap, biodegradable solid-state elastocaloric cooling based on natural rubber offers an environmentally friendly alternative. However, no such practical cooler has been developed, as conventional soft elastocaloric designs are not fast enough to ensure adiabaticity. Here, we combine snap-through instability with strain-induced crystallization and achieve a sub-100 ms quasi-adiabatic cycling, which is 30 times faster than previous designs. Negligible heat exchange in expansion/contraction stages combined with the latent heat of phase transitions results in a giant elastocaloric crystallization effect. The rubber-based all-soft heat pump enables a specific cooling power of 20.9 W g–1, a heat flux of 256 mW cm–2, a coefficient of performance of 4.7 and a single-stage temperature span between hot and cold reservoirs of 7.9 K (full adiabatic temperature change of rubber membrane exceeding 23 K). The pump permits a compact all-soft voltage-actuated set-up, opening up the opportunity of a viable plug-in-ready cooling device.

Quantifying the equilibrium swelling responses and swelling-induced snap-through of heterogeneous spherical hydrogels

We employ the finite deformation theory to analyze the inhomogeneous large deformation of a heterogeneous spherical hydrogel subjected to chemo-mechanical loadings. The heterogeneous spherical hydrogel is composed of two concentric spherical hydrogel layers with different material properties. The Gent model is employed for the free energy function of the polymer stretching part in order to tackle the effect of the limiting chain extensibility. The heterogeneous spherical hydrogel is assumed to be perfectly bonded at the interface and is traction free at the external surface. At the internal surface, two boundary conditions are considered: one is internally fixed and the other is internally pressurized. Numerical examples are performed to describe the nonlinear behaviors of a heterogeneous spherical hydrogel when subjected to the swelling and mechanical loadings. For internally fixed case, numerical results show that the limiting chain extensibility and the initial swelling ratio have significant effect on the actuation deformation of a heterogeneous spherical hydrogel. For internally pressurized case, we find that the swelling-induced snap-through instability can be triggered under specified conditions. It is shown that the chemo-mechanical behaviors of the heterogeneous spherical hydrogels can be adjusted by tuning the material properties and the initial swelling ratios.

Topologically switchable behavior induced by an elastic instability in a phononic waveguide

While topological insulators have been widely studied, they typically appear in configurations and properties that are set once a structure is fabricated. As such, there is significant interest in developing topologically tunable or switchable concepts. In this work, we demonstrate that geometric nonlinearity in the form of an elastic snap-through instability can be exploited to switch the topological properties of a Timoshenko arch beam unit cell. We first demonstrate that the phonon band structure can be tuned using geometric nonlinearity and large displacement to reveal the existence of a topological phase transition point. To make this concept fully stable under the removal of the applied force, we then demonstrate the emergence of a bistable unit cell by varying the parameters of the unit cell. In doing so, we show that the bistability of the arch beam unit cell can be harnessed to design a switch that controls the topological nature of an interface between two different 1D phononic crystals.

Anomalous inflation of a nematic balloon

Inflation of an elastomer balloon is one of the most classical and important problems in the field of nonlinear elasticity. Many intriguing phenomena associated with the inflation of elastomer balloons such as snap-through instability and bulge propagation have been often observed and intensively studied. In this article, we report a new phenomenon during the inflation of a cylindrical balloon made from nematic elastomer. We found in the experiment that with a small increment of inflating pressure, the balloon contracts significantly along its axial direction while expands in its radial direction. With further increase of the pressure, the balloon expands mainly in the radial direction while maintains its length almost unchanged. Finally, the balloon expands both in the radial and axial directions abruptly with a tiny increase of inflating pressure, often leading to rupture of the balloon. The inflation behavior of the nematic balloon can be changed when it is subjected to an additional axial load. To quantitatively understand the experiments, we adopt a quasi-convex free energy function of nematic elastomer to derive the relationship between the inflating pressure and its deformation state. We have shown that the anomalous inflation of the nematic balloon is closely associated with the soft elasticity of the nematic elastomer. Our theoretical predictions agree with experimental measurements well with only two material parameters separately determined by uniaxial tension test of nematic elastomer.

Inflatable soft jumper inspired by shell snapping.

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.

Tuning the load-deflection curve of beams via densely distributed edge cracks: Analytic modeling and solutions

Tuning load-deflection curves is of significant importance in advanced structural design. In this paper, by introducing densely distributed edge cracks artificially, the N-shaped load-deflection curve with snap-through instability is realized in the axially pre-compressed, simply supported beam made of tough material under transverse uniform pressure. A simple mechanics model is established based on the Bernoulli-Euler beam theory with large rotations, which enables a satisfactory description of quasi-static opening and closing of the edge cracks. A second-order nonlinear differential equation that governs the quasi-static evolution of the envelope of densely distributed edge cracks is derived, which exceptionally yields an analytic solution expressed in terms of incomplete elliptic integrals. Computational results show that the realization of N-shaped pressure-deflection curves is mainly attributed to the competition between edge-crack opening induced softening and axial force releasing induced stiffening. Parametric analysis indicates that the shape of pressure-deflection curve is sensitive to the edge-crack length, which provides a useful means to tune the load-deflection curve of beams made of tough materials on the structural level.

Plant Movements as Concept Generators for the Development of Biomimetic Compliant Mechanisms.

Plant movements are of increasing interest for biomimetic approaches where hinge-free compliant mechanisms (flexible structures) for applications, for example, in architecture, soft robotics, and medicine are developed. In this article, we first concisely summarize the knowledge on plant movement principles and show how the different modes of actuation, that is, the driving forces of motion, can be used in biomimetic approaches for the development of motile technical systems. We then emphasize on current developments and breakthroughs in the field, that is, the technical implementation of plant movement principles through additive manufacturing, the development of structures capable of tracking movements (tropisms), and the development of structures that can perform multiple movement steps. Regarding the additive manufacturing section, we present original results on the successful transfer of several plant movement principles into 3D printed hygroscopic shape-changing structures ("4D printing"). The resulting systems include edge growth-driven actuation (as known from the petals of the lily flower), bending scale-like structures with functional bilayer setups (inspired from pinecones), modular aperture architectures (as can be similarly seen in moss peristomes), snap-through elastic instability actuation (as known from Venus flytrap snap-traps), and origami-like curved-folding kinematic amplification (inspired by the carnivorous waterwheel plant). Our novel biomimetic compliant mechanisms highlight the feasibility of modern printing techniques for designing and developing versatile tailored motion responses for technical applications. We then focus on persisting challenges in the field, that is, how to speed-boost intrinsically slow hydraulically actuated structures and how to achieve functional resilience and robustness, before we propose the establishment of a motion design catalog in the conclusion.

A double-side electrically-actuated arch microbeam for pressure sensing applications

In this study, we consider a pressure sensor whose main component is a clamped-clamped shallow arched microbeam. Two fixed electrodes are used to actuate the microbeam in the transverse direction. The lower electrode is powered by a combination of DC and AC voltages sources to excite the microbeam (drive mode). The upper electrode is polarized with a DC voltage and used to detect the change in the capacitance resulting from the transverse vibrations of the microbeam (sense mode). We formulate a fully-coupled multi-physics model of the electrically-actuated shallow arch microbeam combining the nonlinear Euler-Bernoulli beam theory with the nonlinear Reynolds equation governing the surrounding fluid domains (drive and sense zones). The model captures the inherent nonlinear physical aspects including the mid-plane stretching, the squeeze film damping, and fringing field effect. We validate the developed model by quantitatively comparing our nonlinear frequency-response against existing experimental results. We conduct static analysis to identify the occurrence of snap-through and pull-in instability for different initial midpoint rises. The coupled eigenvalue problem is also solved to compute the damped natural frequencies along with their corresponding beam and fluid mode shapes. The obtained natural frequencies are in good agreement with those reported in the literature. High sensitivity of the natural frequency to pressure variations is observed when decreasing the gap distance separating the microbeam from the fixed electrodes and reducing the initial midpoint rise of the curved microbeam.We also investigate the effect of breaking the symmetry of the microstructure on its dynamic response by introducing a slight perturbation in the mass distribution. The stability analysis reveals the occurrence of a new period doubling bifurcation point. Of interest, the location of this bifurcation point is observed to be sensitive to the pressure of the surrounding fluid medium. As such, we propose to exploit this nonlinear feature for design enhancement of the pressure sensor.

Effects of strain stiffening and electrostriction on tunable elastic waves in compressible dielectric elastomer laminates

This paper presents an electromechanical analysis of the nonlinear static response and the superimposed small-amplitude wave characteristics in an infinite periodic compressible dielectric elastomer (DE) laminate subjected to electrostatic excitations and prestress in the thickness direction. The enriched Gent material model is employed to account for the effects of strain stiffening and electrostriction of the DE laminate. The theory of nonlinear electroelasticity and related linearized incremental theory are exploited to derive the governing equations of nonlinear response and the dispersion relations of incremental shear and longitudinal waves. Numerical results reveal that the snap-through instability of a Gent DE laminate resulting from geometrical and material nonlinearities can be used to achieve a sharp transition in the position and width of wave band gaps. Furthermore, the influence of material properties (including Gent constants, the second strain invariant and electrostrictive parameters) and that of prestress on the snap-through instability and the electrostatic tunability of band gaps for both shear and longitudinal waves are discussed in detail. The electrostrictive effect and prestress are beneficial to stabilizing the periodic DE laminate. Depending on whether the snap-through instability occurs or not, a continuous variation or a sharp transition in wave band gaps can be realized by varying the electric stimuli. Our numerical findings are expected to provide a solid guidance for the design and manufacture of soft DE wave devices with tunable band structures.

Lumped Parameter Modeling and Snap-Through Stability Analysis of Planar Hydraulically Amplified Dielectric Elastomer Actuators

AbstractIn this paper, we established an analytical model that avoids extensive numerical computation for the analysis of a hydraulically amplified dielectric elastomer actuator. This actuator comprises a thin elastomer shell filled with an incompressible dielectric fluid coupled with a pair of electrodes placed in the central area. Application of high voltage on the electrodes inflates the actuator due to the induced Maxwell stress that pressurizes the incompressible dielectric fluid. The lumped parameter model predicts the stable functional region and the snap-through instability in the actuator. The model was compared with multi-physics finite element models that considered both linear elastic and nonlinear Mooney–Rivlin materials. The proposed model showed good agreement in the estimation of the actuation strain and the hydrostatic pressure as a function of voltage when compared to the finite element results. The average error in the axial and radial actuation using the proposed analytical model and nonlinear finite element method models was 1.62% and 3.42%, respectively. This shows the model strength in the estimation of the actuator states and the critical voltage to avoid snap-through instability, required in applications such as control algorithms.

Hill-top branching: Its asymptotically expanded and visually solved bifurcation equations

Hill-top branching (HTB) is an exceptional stability problem in which the bifurcation point (BP) coincides exactly with a limit point (LP). In such cases, snap-through and branching instability occur simultaneously. Then, HTB is often obscured in snap-through behavior and is often overlooked in stability design. The compound instability is in fact not well realized in the community of computational mechanics, when the rank deficiency and number of negative eigenvalues of the stiffness matrix are carelessly examined. No report of the relevant literature has established diagnosis of path branching or proposed a branch-switching procedure. Furthermore, few HTB models are available in the literature.This report proposes a set of asymptotic bifurcation equations to address this academically important and exciting issue. There might be a single or two critical eigenvectors of the singular stiffness matrix. Higher-derivatives of the stiffness matrix with respect to nodal displacements can be computed exactly using hyper-dual numbers (HDNs). The resulting simultaneous equations can be solved visually using graphical tools available in popular mathematical software packages such as MATLAB®. From the locations of existing real roots displayed on a graphic monitor, the crossover situation of path branching is visually clear above and below the hill-top. For the present study, three HTB examples are computed to verify the proposed algorithm strategy using HDNs and graphical tools. The obtained numerical results show excellent agreement with analytical and finite element predictions. The proposed asymptotically expanded and visually solved bifurcation equations reliably diagnose asymmetric and unstable symmetric HTB in structural stability problems and function well in computational engineering problems.

Changing the critical snap-through loads of post-buckled beams using piezoelectric actuation

Post-buckled and curved structures experience snap-through instabilities when external loads from mechanical, fluid, or thermal environments result in a loss of local stability and a dramatic jump to a remote stable equilibrium. Fatigue caused by snap-through is a concern in many engineered systems because of the large stress reversals involved. This paper studies the extent to which the strategic placement and actuation of piezoelectric materials bonded to clamped-clamped post-buckled beams can influence the loads at which snap-through occurs. The electromechanical system is modeled using elastica theory with extensions to account for the influence of piezoelectric actuation on the structure. Static equilibrium positions and their stability are computed across a large configuration space using numerical integration and a shooting method. The results indicate that the effect of piezoelectric actuation on critical snap-through load depends on the degree to which the beam is buckled, the location of the external load, the placement of the piezoelectric material, and the applied actuation voltage. Experiments are performed to validate the numerical results and provide a physical demonstration of changing snap-through loads with piezoelectric actuation. Experimental results demonstrate that critical snap-through loads can be altered by factors ranging from 0.4 to 2.0, and numerical results indicate that even larger changes to snap-through loads are physically realizable.

Geometrically nonlinear behavior of lattice domes coupled with local Eulerian instability

Abstract Structural analysis is an intricate subject when nonlinearities occur. They make the structural behavior complex and may have important consequences in the design choice as well. Especially for lattice domes, as snap-through phenomena and local Eulerian instabilities generally affect the structural response, linear analysis is not enough. In this paper, a semi-analytical formulation is used in order to study the geometrically nonlinear behavior of lattice domes subject to vertical loads. The formulation is derived from the equilibrium equations written in the deformed configuration, considering large displacements and taking also into account local buckling conditions. The resulted system of equations, being strongly nonlinear, has been solved by means of a numerical procedure, based on a mixed load-displacement control scheme, leading to the evaluation of the complete equilibrium path. The influence of geometrical parameters on the critical load multiplier and shape of the load-displacement curve is also discussed. In particular, a complex equilibrium path for a sixteen-member five-node lattice structure is analyzed, which is characterized by several branches which can generate ‘snapping’ conditions.

Engineer Energy Dissipation in 3D Graphene Nanolattice Via Reversible Snap-Through Instability

Abstract Carbon micro/nanolattice materials, defined as three-dimensional (3D) architected metamaterials made of micro/nanoscale carbon constituents, have demonstrated exceptional mechanical properties, including ultrahigh specific strength, stiffness, and extensive deformability through experiments and simulations. The ductility of these carbon micro/nanolattices is also important for robust performance. In this work, we present a novel design of using reversible snap-through instability to engineer energy dissipation in 3D graphene nanolattices. Inspired by the shell structure of flexible straws, we construct a type of graphene counterpart via topological design and demonstrate its associated snap-through instability through molecular dynamics (MD) simulations. One-dimensional (1D) straw-like carbon nanotube (SCNT) and 3D graphene nanolattices are constructed from a unit cell. These graphene nanolattices possess multiple stable states and are elastically reconfigurable. A theoretical model of the 1D bi-stable element chain is adopted to understand the collective deformation behavior of the nanolattice. Reversible pseudoplastic behavior with a finite hysteresis loop is predicted and further validated via MD. Enhanced by these novel energy dissipation mechanisms, the 3D graphene nanolattice shows good tolerance of crack-like flaws and is predicted to approach a specific energy dissipation of 233 kJ/kg in a loading cycle with no permanent damage (one order higher than the energy absorbed by carbon steel at failure, 16 kJ/kg). This study provides a novel mechanism for 3D carbon nanolattice to dissipate energy with no accumulative damage and improve resistance to fracture, broadening the promising application of 3D carbon in energy absorption and programmable materials.