Snap-through Instability Research Articles

Nonlinear thermal stability and snap-through buckling of temperature-dependent geometrically imperfect graded nanobeams on nonlinear elastic foundation

In this research, thermal postbuckling and nonlinear thermal bending of size-dependent functionally graded (FG) perfect/imperfect nanobeams in-contact with a nonlinear elastic foundation and exposed to thermal loading are first scrutinized. The second objective of this research is to investigate snap-through instability in a thermally postbuckled FG nanobeam due to uniform lateral load. The geometrical imperfection of the nanobeam is taken into account. Thermo-mechanical material properties are temperature-dependent and are assumed to vary continuously throughout the nanobeam thickness on the basis of the power-law model. The nonlinear equilibrium equations are derived according to the Euler-Bernoulli beam theory in conjunction with the nonlinear von-Karman assumptions based on the nonlocal elasticity theory. Using Chebyshev polynomial of the first kind, Ritz method is utilized into the principle of virtual displacement to form nonlocal governing equations. Three different methodologies, including direct displacement control approach, Newton-Raphson iterative method, and cylindrical arch-length scheme are utilized to investigate the nonlinear thermal stability curves and snap-through phenomenon through limit points of a thermally postbuckled FG nanobeam. The primary purpose of this research is to explore the influences of the nonlocal parameter, nonlinear elastic foundation coefficients, power-law index, imperfection amplitude as well as the different types of boundary conditions on the nonlinear thermal stability and snap-through phenomenon of the FG nanobeam.

Adhesion-force micro-scale study of desiccating granular material

Experiments on five-, four-, three- and two-wet-hydrophilic-grain clusters were performed to investigate evolution of adhesion of granular media during drying on the micro-scale. The experiments show that the adhesion-force of a cluster initially grows at most to three times the original value before decreasing to zero by the end of evaporation. The adhesion-force is composed of capillary pressure force acting over the liquid/solid contact surface area, and surface tension forces acting over the three-phase contact perimeter length. This is in contrast with most macro-scale phenomenological models, in which the only desaturation process variables affecting strength are suction and saturation. Both the contact surface area and contact perimeter length are reduced to zero upon complete liquid evaporation. The morphology of an evaporating water body evolves through slow flow controlled by evaporation rate, interrupted by various modes of fast air entry, which are non-equilibrium jumps of liquid/gas interfaces (Haines jumps). The instabilities involve large adhesion force discontinuities and substantial water mass reconfiguration with water flow in an extremely short time, which makes the process transient. The reconfigurations can reduce the original multi-grain water clusters to four-, three- and two-grain clusters by way of three different instability modes: of thin-sheet instability, or meniscus snap-through instability, depending on the sign of the Gauss curvature of the liquid surface, or finally, for two-grain bridges only, a liquid wire pinch-off. For larger meso-scale assemblies, however, the global adhesion-force evolution is little affected by the jumps. The air entries are potential sites for drying cracks. The (approximately) calculated capillary pressure for two- and three-grain clusters, in no cases is seen to reach high values, predicted from water retention curves.

Electrically tunable fast and reversible structural coloration of two-dimensional photonic crystals

Photonic crystals (PCs) can regulate the propagation of light through them and show visible structural coloration when illuminated by white light. We achieve fast (response time less than 1 s) and reversible structural coloration of two dimensional (2D) PCs by integrating them with a dielectric elastomer actuator (DEA). For the in-plane actuation mode of DEA, we study the diffraction angle dependent structural coloration of 2D PCs vertically illuminated by white light under different actuation voltages experimentally and theoretically. We also optimize the DEA by considering its snap-through instability and actuation performance in our theoretical model. Furthermore, we first demonstrate that the out-of-plane actuation mode of DEA can also effectively tune the structural coloration of integrated 2D PCs. The tunable 2D PCs realized by DEA have applications in color changeable soft skin for camouflage and smart optical devices, such as adjustable optical grating.

Electrostatic arch micro-tweezers

This paper presents a novel electrostatic micro-tweezers to manipulate particles with diameters up to 14 μm. The tweezers consist of two grip-arms mounted to an electrostatically actuated initially curved micro-beam. It exploits bistable equilibria, resulting from a snap-through instability, to close the separation distance between the two arms allowing them to grasp a large range of objects. The tweezers offer further control beyond the snap-through point, via electrostatic actuation, to increase pressure on larger objects or grasp smaller objects. The tweezers are fabricated in a p-type Silicon on Insulator (SOI) wafer. Euler-Bernoulli beam theory is utilized to derive the governing equation of motion taking into account the arms' rotary inertia and the electrostatic fringing field. A reduced-order model (ROM) is developed utilizing two, three and five symmetric modes in a Galerkin expansion. A finite element model (FEM) is also developed to validate the ROM and to study the arm tips' separation as a function of actuation voltage. The five-mode ROM is found to be convergent and accurate except in the vicinity of the snap-through saddle-node bifurcation. Our analysis shows that the tweezers can manipulate micro-particles with diameters ranging from 5 to 12μm with an operating voltage range limited by the snap-back voltage 100.2V and the pull-in voltage 153.2V.

Mechanics of Chiral Honeycomb Architectures With Phase Transformations

Abstract The mechanics of phase transforming cellular materials (PXCMs) with three different chiral honeycomb architectures, viz., hexachiral, tetra-anti-chiral, and tetra-chiral, are investigated under quasi-static loading/unloading. Each PXCM comprises interconnected unit cells consisting of tape springs rigidly affixed to circular nodes that can rotate and/or translate. The phase change is associated with snap-through instability due to bending of the tape springs and corresponds to sudden changes in the geometry of the unit cells from one stable configuration to another stable (or metastable) configuration during loading/unloading. When compared with similar chiral materials with flat ligaments, the chiral PXCMs exhibit a significantly higher energy dissipation in quasi-static experiments. The hexachiral PXCM was selected for detailed parametric analysis with finite element simulations including 21 models constructed to investigate the effects of PXCM geometry on phase change and energy dissipation. An analytical formalism is developed to predict the minimum compressive load required to induce phase transformation and snap-through. The formalism predictions are compared with those from finite element simulations. An Ashby plot is developed in which the energy dissipated per unit volume versus work conjugate plateau stress of the H-PXCM is compared with other energy absorbing materials.

Nonlinear Bending Analysis of Functionally Graded CNT-Reinforced Shallow Arches Placed on Elastic Foundations

This research explores the nonlinear bending behaviors of functionally graded carbon nanotube-reinforced (FG-CNTR) shallow arches with unmovable simply supported ends and clamped–clamped ends; these arches are subjected to a uniform radial pressure and rest on a nonlinear elastic foundation. The temperature-dependent material properties of the arches are considered. Within the framework of Reddy shear deformation theory possessing von Karman nonlinearity, the motion equations and boundary conditions for the FG-CNTR arches are determined by the Euler–Lagrange variational principle. Then, a two-step perturbation technique is adopted to determine the load–deflection relationship analytically. To verify the validity of the developed model and related perturbation solutions, a numerical investigation is conducted for shallow arches with five distribution patterns of carbon nanotube (CNT) reinforcements uniaxially aligned in the axial direction. Finally, the influences of various factors, including the elastic foundation, layout type, and volume fraction of CNTs and geometric factors, on the nonlinear behaviors of FG-CNTR shallow arches are examined. The obtained results show that the load–deflection curves exhibit less snap-through instability as the CNT volume fraction increases. The transverse shear stress versus the thickness of FG-CNTR shallow arches is markedly affected by the layout type and content of reinforcements.

Delayed electromechanical instability of a viscoelastic dielectric elastomer balloon.

When a dielectric elastomer (DE) balloon is subjected to electromechanical loading, instability may happen. In recent experiments, it has been shown that the instability configuration of a DE balloon under electromechanical loading can be very different from that only subjected to mechanical load. It has also been observed in the experiments that the electromechanical instability phenomena of a DE balloon can be highly time-dependent. In this article, we adopt a nonlinear viscoelastic model for the DE membrane to investigate the time-dependent electromechanical instability of a DE balloon. Using the model, we show that under a constant electromechanical loading, a DE balloon may gradually evolve from a convex shape to a non-convex shape with bulging out in the centre, and compressive hoop stress can also gradually develop the balloon, resulting in wrinkles as observed in the experiments. We have further shown that the snap-through instability phenomenon of the DE balloon also greatly depends on the ramping rate of the applied voltage.

Dynamic pull-in instability and snap-through buckling of initially curved microbeams under the effect of squeeze-film damping, mechanical shock and axial force

This research investigates the dynamic behavior of microelectromechanical systems (MEMS) containing curved electrodes, under a combined loading of electrostatic force, axial force, mechanical shock loading and squeeze-film damping (SQFD). The dynamic governing equation of a curved microbeam (micro-arch) is solved by utilizing a nonlinear finite element method, while the effect of the fluid film damping on the microbeam is modeled by the nonlinear Reynolds equation. The response of the micro-arch under different loading conditions and the influence of the MEMS device parameters on its behavior are studied and discussed in detail. In particular, the snap-through and pull-in instabilities of the curved microbeam are thoroughly investigated, and the maximum deflections of the micro-arch subjected to different types of loadings are analyzed. Finally, the phase diagram of the curved beam under various loading conditions is presented for guiding the design and analysis of the MEMS in the future.

Nonlinear Snap-Through Instability of FGM Shallow Micro-Arches with Integrated Surface Piezoelectric Layers Based on Modified Couple Stress Theory

Based on the modified couple stress theory, an attempt is made in this study to analyze the nonlinear snap-through instability of shallow sandwich arches. The microstructure-dependent functionally graded material (FGM) arch with surface bonded piezoelectric actuator layers is analyzed. The piezo-FGM sandwich arch is subjected to uniform transverse pressure load in thermo-electrical environment. All material properties of the FGM micro arch are assumed to be temperature- and position-dependent. The governing equilibrium equations of the piezo-FGM sandwich arch are established with the aid of virtual displacement principle and the uncoupled thermoelacticity theory. The obtained governing differential equations are based on the first-order shear deformation shallow arch theory of the Timoshenko and von Kármán nonlinear assumptions. These equilibrium equations contain three coupled ordinary differential equations in terms of displacements. The nondimensional governing equations are solved for the cases of piezo-FGM sandwich arches with simply supported and clamped boundary conditions by using the two-step perturbation technique. Analytical closed-form solutions are derived to give the deflected shape of the piezo-FGM sandwich arch with immovable ends. Comparison is made with the existing results for the cases of FGM arch without couple stress and piezoelectric layers, where good agreement is obtained. The nonlinear behavior of the sandwich arches is highly affected by the couple stress, piezoelectric layers, temperature change, volume fraction index, and geometrical properties of the arch.

Temperature-tunable time-dependent snapping of viscoelastic metastructures with snap-through instabilities

3D-printed metastructures and metamaterials with snap-through instabilities have been extensively investigated in recent years. However, most of the previous research has been limited to the analysis of their elastic response. This paper focuses on the time-dependent mechanics of 3D-printed viscoelastic metastructures with snap-through instabilities. Due to viscoelastic relaxation, a regime called pseudo-bistability can be observed: a previously deformed 3D-printed metastructure can appear to be temporarily bistable before snapping back to its undeformed configuration after a critical time. Experiments with 3D-printed samples and finite element simulations demonstrate that the critical time can be tuned by adjusting the temperature. While the time-dependent snapping causes a change in the overall height in the case of single layer metastructure, experimental and finite element results show that the same type of time-dependent snapping can also be used to obtain an internal reconfiguration when the overall height of a multilayer metastructure is constrained to remain constant. Because of the possibility of tuning the critical time for a given sample by varying the external temperature, harnessing the pseudo-bistable mechanics of these viscoelastic metastructures gives new opportunities towards the development of novel reconfigurable metastructures with programmable response and properties for applications in soft robotics or impact protection.

Snap-through and stiffness adaptation of a multi-stable Kirigami composite module

Multi-stable composite laminates have been used to create adaptive and shape-morphing structures for many applications. However, it remains challenging to use these composites to obtain complicated shape changes and mechanical property adaptations. This study proposes a “Kirigami composite” concept to help address this challenge. By strategically placing slit cuts into the composite laminate with carefully designed fiber layout, one can release the internal constraints and significantly enrich the achievable shapes and adaptive functions. This study focuses on the elementary Kirigami composite module consisting of a single slit cut and two bistable patches. Experiments and finite element simulations show that this Kirigami module exhibits four different stable equilibria and its snap-through instability originates from a rapid “run-away” growth of surface curvature inversions due to connecting tab. This study also investigates a stiffness adaptation function. These results can be used for creating more sophisticated Kirigami composite structures with multiple patches and cuts.

Bi-stability of pressurized electrically actuated flat micro-plates

Despite the usual belief that only curved micro-structures can behave bi-stably, recently, it has been substantiated that flat micro-structure can also experience this type of behavior. In this way, the present paper aims to investigate snapping behavior in pressurized 2-D flat micro-electro-mechanical plates with a rectangular shape. To this end, a size-dependent and geometric non-linear thin plate model based on the modified couple stress theory is employed. The governing equilibrium equations as well as their corresponding boundary conditions are obtained using the principle of the minimum total potential energy. Employing an efficient Galerkin's discretization procedure, the instability thresholds of the system are determined by vanishing the first and the second variations of the total potential energy expression of the system. The present findings for non-pressurized systems are verified by those published in previous studies. Furthermore, the results concerning the cases under the differential pressures are validated through direct comparison with those extracted from 3-D finite element simulations carried out in COMSOL Multiphysics commercial software. Results reveal that flat micro-plates may experience snap-through instability when they are subjected to some certain values of the differential pressure in the opposite direction of the electrical field. To find the conditions in which a flat micro-plate may face with the snapping behavior, a large number of systems with different material and geometric properties are analyzed. Employing this detailed parametric study, snapping criteria which provide the combination of the system properties and the level of the applied pressure required for prompting snap-through instability are then introduced.

Nonlinear deformation and bifurcation of a soft cantilever induced by acoustic radiation force

We theoretically and numerically demonstrate that the nonlinear bending deformation of a soft cantilever can be induced by acoustic radiation force when a plane ultrasonic wave impinges on it. The acoustic radiation force arises from the acoustic momentum change at the top and bottom interfaces of the soft cantilever, which is unevenly distributed at the interfaces and deformation curvature dependent. As the acoustic radiation force varies nonlinearly with the deformation of the cantilever, there exist multiple equilibrium configurations of the cantilever at a given incident ultrasonic wave (with fixed amplitude and frequency). This phenomenon is confirmed by both theoretical prediction and numerical simulation. Furthermore, by changing the pressure amplitude or the frequency of the incident wave, the deformation of the cantilever is able to switch from one equilibrium configuration to another equilibrium configuration discontinuously due to the snap-through instability. These nonlinear deformation and multistable switch performance of the system show promising potential applications in the fields of soft robotics, microfluidics and biomedicine and so on.

Analysis of Nonlinear Vibration and Instability of Electrostatically Actuated Fluid-Conveying Micro Beams

Based on the Euler beam theory and a Galerkin formulation using natural modes, the nonlinear vibration behavior and stability of electrostatic driving fluid-conveying micro (straight or curved) beams are studied in the paper. The focus of this study is on the critical coupling of fluidic, mechanical and electrostatic effects in the nonlinear system. Under these effects, micro devices may exhibit (dynamic) snap-through or/and pull-in instabilities. Our study reveals, for the first time, the effects of the velocity of the inner fluid on the bifurcation diagrams for complex nonlinear systems. It is also found that fluid can be utilized to efficiently tune the frequency of straight beams over a wide range. For curved beams, the tuning can be achieved easily by adjusting the voltage. These findings are beneficial in many applications of the electrostatic microelectronic mechanical systems (MEMS). In addition, phase plane analyses are performed in this study, and more complicated phase portraits for different initial conditions are obtained as well. It is found that the homoclinic connections on the phase plane are directly related to the dynamic snap-through or dynamic pull-in instabilities; and the periodic orbits are directly related to the periodic motions of micro beams. These findings can provide reasonable explanations for the experimentally-observed phenomena for micro sensors, and are beneficial to the optimization design of MEMS.

Phase transition and optimal actuation of active bilayer structures

Active bilayer structures have great potential applications in the fields of drug delivery, soft robots and actuators. In this paper, we have investigated the phase transition and optimal actuation of bilayer structures under biaxial active strains. A theoretical model is developed to predict the bending curvature of the bilayer in the large deformation regime, instead of the traditional Timoshenko’s buckling solution. A Riks path-following procedure in the finite element method is utilized to trace the active-strain induced snap-through instability to identify the phase boundaries of bistability in the bilayer. The phase transition diagram from bistability to monostability and the general requisites to generate a snap-through instability by varying active strains are thoroughly discussed based on the bending curvature and energy landscape from simulations. Using the average curvature to characterize the actuation efficiency, we find that the anisotropy of active strains can be utilized to tune the bending angle and configuration of bilayer structures. The presented model and the obtained phase diagram provide a potential guidance for future design of high-performance bilayer-based actuators and machines in a broad range of applications.

Mode II dominant fracture of layered composite beams and wide-plates: a homogenized structural approach

Brittle delamination fracture under Mode II dominant conditions in unidirectional composite and layered beams and wide-plates is studied using a homogenized structural model based on a zigzag approach. The model captures the unstable propagation of cracks, snap-back and snap-through instabilities, the effects of the interaction of multiple cracks on the macrostructural response and of the layered structure on the energy release rate. The layered structure and the delaminations are described by introducing local enrichments, in the form of zigzag functions and cohesive interfaces, to a classical first-order shear deformation plate theory. The model applies to layers with principal material directions parallel to the geometrical axes, depends on only three displacement variables and the solution of specific problems requires only in-plane discretization, for any numbers of layers and delaminations. Closed form solutions are derived for the energy release rate in bi-material beams and applications are presented to homogeneous, bi-material and layered, simply supported and cantilever, bend-beams, with one and two delaminations.

Digital logic for soft devices

Although soft devices (grippers, actuators, and elementary robots) are rapidly becoming an integral part of the broad field of robotics, autonomy for completely soft devices has only begun to be developed. Adaptation of conventional systems of control to soft devices requires hard valves and electronic controls. This paper describes completely soft pneumatic digital logic gates having a physical scale appropriate for use with current (macroscopic) soft actuators. Each digital logic gate utilizes a single bistable valve-the pneumatic equivalent of a Schmitt trigger-which relies on the snap-through instability of a hemispherical membrane to kink internal tubes and operates with binary high/low input and output pressures. Soft, pneumatic NOT, AND, and OR digital logic gates-which generate known pneumatic outputs as a function of one, or multiple, pneumatic inputs-allow fabrication of digital logic circuits for a set-reset latch, two-bit shift register, leading-edge detector, digital-to-analog converter (DAC), and toggle switch. The DAC and toggle switch, in turn, can control and power a soft actuator (demonstrated using a pneu-net gripper). These macroscale soft digital logic gates are scalable to high volumes of airflow, do not consume power at steady state, and can be reconfigured to achieve multiple functionalities from a single design (including configurations that receive inputs from the environment and from human users). This work represents a step toward a strategy to develop autonomous control-one not involving an electronic interface or hard components-for soft devices.

Response characterization of multistable shallow domes with cosine-curved profile

The multistable elastic behavior of a shallow dome with a cosine-curved profile is investigated in this work. The dome exhibits snap-through instability and could be used as a building block for energy dissipation mechanism in structures subjected to cyclic loading and high deformation demands. Numerical and experimental studies were carried on the geometric and material properties of the cosine-curved domes (CCD) under concentrated load at the apex. Finite element analyses (FEA), validated by experimental tests on 3D printed specimens, were conducted to study the controlling geometric and material properties of the CCD. Three types of response were recognized and discussed based on the force- and strain energy-displacement curves. Limitations on the geometric parameters that govern the recoverability of the original shape and the stability state upon load removal are also identified. In addition, empirical relations to estimate the limit-point load and displacement, and to characterize the snap-through response were developed. Good agreement was observed using the determined limits on the geometric parameters and the developed relations with the results from FEA and experimental tests.

Architected materials for tailorable shear behavior with energy dissipation

A class of architected materials is proposed for tailorable shear behavior and high energy dissipation. Inclined beams with elastic snap-through instabilities define the microstructure of the proposed materials, which display a ‘twinkling’ phenomenon that converts strain energy to dynamic motions, resulting in rate-independent energy dissipation. The design concepts were experimentally validated using 3D printed prototypes under both half- and full-cycle shear deformation conditions, and shown to respond in rate-independent sequential snap-through transitions with large energy dissipation in the elastic regime. Numerical simulations and analytical analyses show that predictable material behavior and tunable shear properties can be designed through the microstructure’s geometry. The proposed materials fill the need of dissipating energy under shear deformations in a recoverable and rate-independent manner.

Programmable Deformations of Networked Inflated Dielectric Elastomer Actuators

Soft actuators play an indispensable role in producing motions of soft robots. Dielectric elastomer actuators coupled with a fluid/air mass have proved to undergo considerable voltage-induced deformation. To achieve large deformation, a dominant way is to trigger snap-through instability, but the induced instantaneous deformation is not continuously stable, resulting in a limited space for control. This paper proposes a network of inflated dielectric elastomer actuators, interconnected via a chamber, with the advantages to be not only highly deformable but also continuously controllable. Herein, the snap-through instability is suppressed by the initial in-plane prestretch (set to be 3), and the networked design enlarges the actuation range by modulating the inner pressure to postpone material failures. With a large and continuous actuation space, an array of the networked actuators can present programmable deformations. We investigate how to compute the required input voltages for programming desired deformations. We further carry out experiments to show different deformation patterns. This paper represents an important step toward the integration and network of numerous soft actuators, and the potential applications may span shape display and distributed actuation for soft robots.