Bistable Structures Research Articles

Hydrothermal effect on Bi-stability of composite cylindrical shell

Bi-stable composite cylindrical shells have attracted many attentions due to their lightness, simple structure, high packaging efficiency, high specific strength and stiffness. However, the anti-symmetric cylindrical shell is susceptible to the effect of ambient temperature and humidity. In this paper, an analytical model of shell structure considering hydrothermal effect was built, and its strain energy expressions were derived. Based on the minimum energy principle, the effects of moist and heat on the bi-stability of cylindrical shell structure were analyzed. In addition, the finite element model of the anti-symmetric cylindrical shell was established to simulate its stable configurations. This study could provide reference for the practical application of bi-stable structure.

Architected metamaterials with tailored 3D buckling mechanisms at the microscale

Attaining architected structures with unprecedented properties not found in natural materials is a long-sought goal for both materials science and additive manufacturing. Improving the mechanical behavior of engineered materials such as auxetics for bioengineering applications or bistable structures for mechanical actuation depends on the buckling mechanisms governing their response. Despite the fact that the design principles for two-dimensional buckling have been elucidated in previous studies, comprehending three dimensional buckling mechanisms is still tenuous. In this study, we aim to illuminate the buckling mechanisms governing the response of three-dimensional structures at the microscale, providing the critical guidelines for the design of novel metamaterials. In addition, finite element analysis and in-situ SEM — microindentation experiments are performed to investigate how scale effects affect the design principles to architect a controlled 3D buckling mechanism and reflect the mechanical response to the deformation of the structure in-situ. Our findings elicit the design process of tailored three dimensional buckling structures based on the geometric architecture instead of the behavior of the bulk material, while setting a broader framework to fabricate and characterize these structures at the microscale.

Optical-Dielectric Duple Bistable Switches: Photoluminescence of Reversible Phase Transition Molecular Material.

Molecular optical-dielectric duple bistable switches are photoelectric (dielectric and fluorescent) multifunctional materials that can simultaneously convert optical and electrical signals in one device for seamless integration. However, exploring optical-dielectric duple channels of dielectric and photoluminescence is still a bigger challenge than single dielectric or photoluminescence bistable ones, which are hardly reported but probably will be heavily researched owing to the new generation artificial intelligence development needs in the future. Herein, a new optical-dielectric duple bistable switches material, [(CH3 )3 NCH2 CH3 ]2 MnCl4 (I), was obtained by a simple method for volatilization of solvents. Variable temperature single crystal X-ray analysis indicates that material I has a reversible bistable structure (order-disorder structure phase transition) corresponding to switching "ON'' and "OFF''. Unlike the single dielectric bistable structures that were previously reported, material I also own bistable features in terms of fluorescence property. This material enriches the specific examples of photoelectric duple function switch materials and facilitates the development of required devices.

Magnetic actuation bionic robotic gripper with bistable morphing structure

Soft robotics is an emerging research field that uses deformable materials or structures to fabricate compliant and adaptable systems through simple integrated mechanisms, thereby, enabling biomimetic behaviour. The Venus flytrap has the characteristics of excellent responsiveness and deformability, making it a promising inspirational model for the development of soft robotics. This paper presents a novel robotic gripper that mimics the trapping motion of the Venus flytrap. This gripper was implemented by exploiting a combination of bistable anti-symmetric shells and magnetic actuation. Two cylindrical shells constructed from carbon-fibre-reinforced polymer act as compliant fingers that can transform between two stable configurations based on external actuation. An applied clamped boundary condition reduces the actuation force required to trigger the morphing process. A novel non-contact magnetic actuation method with excellent responsiveness is proposed to actuate the compliant finger. The robotic gripper is designed to be lightweight and compact with high gripping force. Experiments and simulations were performed to analyse the gripping motion and measure the actuation force. The width of the clamped edge is the main factor influencing gripper performance as it relates to actuation force. The results of our analysis demonstrate that the proposed flytrap-inspired design with a bistable structure can be used to implement a novel robotic gripper controlled by a magnetic field.

Voltage-actuated snap-through in bistable piezoelectric thin films: a computational study

Bistable piezoelectric structures exhibit snap-through motions in response to applied voltage and play important roles in achieving functions such as fast actuation and structural morphing. However, modeling the nonlinear snap-through behaviors in such structures remains a challenge. In this paper, we develop a theoretical framework to model the voltage-actuated snap-through in bistable piezoelectric composites. Based on a revised continuum theory capable of characterizing the coupled finite deformation and electric field in piezoelectric materials, we establish a universal nonlinear finite element framework where the unknowns are the displacement and a scalar factor characterizing the magnitude of the applied voltage. By using the traditional Riks method, a supplementary arc-length equation related to the increment of the displacement and the scalar factor is constructed to complete the linearized incremental equation. A general solution scheme for obtaining the increments of all unknowns is developed, which enables automatic tracing of the nonmonotonic equilibrium path evolution. The feasibility and efficiency of this numerical method were demonstrated by the voltage-actuated snap-through phenomena for several bistable piezoelectric structures, including a simply-supported bilayer beam, a 3D square bilayer plate with free ends and a 3D constrained circular bilayer plate. This method will benefit the numerical design of high-performance bistable piezoelectric structures.

Mechanics of bistable cross-shaped structures through loading-path controlled 3D assembly

Morphable three-dimensional (3D) structures capable of reversible shape changes between distinct geometric configurations have widespread applications in many important engineering areas. Recent advances in mechanically-guided 3D assembly provided a powerful approach to achieve morphable 3D mesostructures in a broad set of high-performance materials, over length scales from several micrometers to tens of centimeters. This approach relies on prestrained elastomer substrates released with different sequences to trigger the stabilization of distinct 3D buckling modes in specially engineered 2D precursor structures. Many of the reported 2D precursor structures are constructed with ribbon components that incorporate creases with reduced stiffness at strategic locations. The design of crease geometries and crease locations is essential to the structural bistability through this loading-path approach, which requires the development of a theory to serve as the design basis. This paper presents a finite-deformation model to analyze the stability of different buckling modes induced during the simultaneous and sequential compressions of structures with cross-shaped ribbon geometries, a very representative class of precursor patterns. By introducing a perturbation method to obtain an analytic solution to the deformed configuration of a uniform beam, a theoretical model is developed to predict the postbuckling deformations in cross-shaped ribbon structures with a prescribed number of creases. Based on the analyses of the strain-energy landscape, a stability coefficient is proposed to evaluate the bistability of cross-shaped ribbon structures. The developed model is validated by finite element analyses (FEA) and experimental measurements of structures with a broad range of cross-shaped geometries. This model allows the construction of design diagrams to identify the bistability for a variety of geometric parameters, including the normalized width and location of each crease in the cross-shaped patterns. These results elucidate how to select the various design parameters to achieve bistable 3D structures through the loading-path approach. Furthermore, the developed model is extended to the bistability analyses of precursor structures with generalized cross patterns and cross-shaped patterns consisting of locally stiffened elements. This study offers a theoretical reference for the design of ribbon-shaped mesostructures to achieve diverse morphable microelectronic devices.

Multistable Cylindrical Mechanical Metastructures: Theoretical and Experimental Studies

An innovative bistable energy-absorbing cylindrical shell structure composed of multiple unit cells is presented in this paper. The structural parameters of the single-layer cylindrical shell structure that produces bistable characteristics are expounded both analytically and numerically. The influence of the number of circumferential cells and the size parameters of the cell ligament on the structure’s macroscopic mechanical response was analyzed. A series of cylindrical shell structures with various size parameters were fabricated using a stereolithography apparatus (SLA). Uniaxial loading and unloading experiments were conducted to achieve force–displacement relationships. Deformation of the structural multistable phase transition response was discussed based on experimental and finite element simulation results. The results show that the proposed innovative single-layer cylindrical shell structure will stabilize at two different positions under certain parameters. The multilayer cylindrical shell exhibits different force–displacement response curves under loading and unloading, and these curves enclose a closed area. In addition, this structure can be cyclically loaded and unloaded, thanks to its good stability and reproducibility, making it attractive in applications requiring repetitive energy absorption.

Nonlinear dynamics of shape memory alloys actuated bistable beams

The phenomenon of bi-stable behaviour has been widely used in the structural design, as it can provide large deformation by switching between two stable equilibrium positions. This paper aims to investigate the intrinsic nonlinear dynamic characteristics of an actively controlled bistable beam using a simplified spring-mass model. The dynamic model for an active (heated) SMA wire driven bistable beam is established based on a polynomial constitutive equation to describe the thermomechanical behaviour of the shape memory alloy. The actively controlled bistable beams are designed, fabricated and experimentally tested to achieve the morphing behaviour snapping-through form one position to another. The results obtained from the experimental testing and the theoretical simulation are compared to validate the proposed model. Dynamic behaviour of the proposed SMA wires actuated bistable beam under varying external excitation is investigated to show the influence of the thermomechanical loadings. Analysis of the experimental data and simulation results shows that the SMA wires actuated bistable structure can be well-performed for the bistable switching. It also approved that the different behaviours of the system, including periodic responses, complex responses and chaos can be accurately predicted using the proposed simplified model.

Characterization of bistable mechanisms for microrobotics and mesorobotics

The use of mechanical bistable structures in the design of microrobots and mesorobots has many advantages especially for flexible robotic structures. However, depending on the used fabrication technology, the adequacy of theoretical and experimental mechanical behaviors can vary widely. In this paper, we present the manufacturing results of bistable structures made with two extensively used contemporary technologies: MEMS and FDM additive manufacturing. Key issues of these fabrication technologies are discussed in the context of microrobotics and mesorobotics applications.

A component coupling approach to dynamic analysis of a buckled, bistable vibration energy harvester structure

Over the past ten years, the energy harvesting community has focused on bistable structures as a means of broadening the working frequency range and, by extension, the effective efficiency of vibration-based power scavenging systems. In the current study, a new method is implemented to statically and dynamically analyze a bistable buckled, multi-component coupled structure designed specifically for low-frequency (< 30 Hz) vibration energy harvesting. First, the system is divided into its individual components and the governing equations for each part are developed based on Euler–Bernoulli beam theory. These governing equations are then solved in one single system of equations by applying geometrical and force-moment boundary conditions at the connections. Solving the nonlinear static equations gives the critical buckling loads, as well as the exact static, post-buckled configuration of the system about which the dynamic response is formulated. The natural frequencies and mode shapes of the system are obtained by solving the free vibration case of the linearized buckled structure, which are then used as spatial functions in a Galerkin approach to discretize the nonlinear partial differential equations of the coupled system. To validate the modeling approach, the obtained results are compared with the ones captured from both finite element analysis model and the experimental setup, which shows good agreement between them. Furthermore, the amplitude-frequency response of the system and snap-through regime with the variation of various parameters, including exciting frequency, base vibration and buckling loads are investigated based on the developed model. It is shown that for a weakly buckled configuration, bistable motion can be captured for a wide range of frequencies, which is crucial for the performance of energy harvesting devices.

3D printing of twisting and rotational bistable structures with tuning elements

Three-dimensional (3D) printing is ideal for the fabrication of various customized 3D components with fine details and material-design complexities. However, most components fabricated so far have been static structures with fixed shapes and functions. Here we introduce bistability to 3D printing to realize highly-controlled, reconfigurable structures. Particularly, we demonstrate 3D printing of twisting and rotational bistable structures. To this end, we have introduced special joints to construct twisting and rotational structures without post-assembly. Bistability produces a well-defined energy diagram, which is important for precise motion control and reconfigurable structures. Therefore, these bistable structures can be useful for simplified motion control in actuators or for mechanical switches. Moreover, we demonstrate tunable bistable components exploiting shape memory polymers. We can readjust the bistability-energy diagram (barrier height, slope, displacement, symmetry) after printing and achieve tunable bistability. This tunability can significantly increase the use of bistable structures in various 3D-printed components.

On stochastic dynamic analysis and assessment of bistable structures

This paper investigates some basic issues on the stochastic dynamic analysis and assessment of bistable structures from an applications perspective, illustrated with a classical spring–mass–rod structure. A complete Lagrangian-description-based Monte Carlo simulation and an Eulerian-description-based Fokker–Planck equation analysis are implemented, respectively, to capture the evolution process of the physical response probability density function, with special focus on the dynamics under the statistical steady state condition. A comparison of these two methods outlines their capabilities. As a representative example, quantitative counting and statistical analysis of the number and amplitudes of snapping-through of the structure indicate that physical quantities for structural assessment may show certain statistical regularities under the statistical steady state condition, which can be utilized efficiently to reduce the efforts of structural assessment without loss of precision.

Design of Specific Properties for Bistable Structures Based on Pre-stress and Localization Reinforcement

Design of Specific Properties for Bistable Structures Based on Pre-stress and Localization Reinforcement

Snap-through Bifurcation Analysis of Compliant Bistable Structures

Snap-through Bifurcation Analysis of Compliant Bistable Structures

Multistable Thermal Actuators Via Multimaterial 4D Printing

Abstract3D printing of smart materials, called “four‐dimensional” (4D) printing, adds active, responsive functions to 3D‐printed structures. Shape memory polymers (SMPs) can be employed as an active material in 4D printing, and this could be useful for a wide range of potential applications. New design for 4D printing is presented here by introducing SMPs into rotational multistable structures. Two different digital SMPs are employed to enable large‐angle, thermal actuation in a controlled manner. It is started with bistable structures and then extending them to quadristable ones. In this design, by adjusting the thickness of SMP beams, a balance is controlled between the energy barrier and shape memory force, and this can enable controlled thermal actuation. Especially, one can control the activation time for thermal actuation. Multistable structures can simplify actuation and motion control without complicated control systems. Therefore, by adopting multistable structures in 4D printing, one can potentially enable precisely controlled, large‐magnitude, rapid actuation beyond the material capability of SMPs. These multistable structures do not require heating in the programming stage and this significantly simplifies the actuation procedure. This work provides new physical insights into 3D‐printable, active structures, and could be useful for various smart actuators responding to the environmental stimuli.

Magneto-sensitive bistable soft actuators: Experiments, simulations, and applications

Bistable structures featuring two stable states have been widely applied in designing fast and high-force-output actuators under various types of stimuli, such as mechanical force, swelling, thermal expansion, and so on. In this paper, we designed a magneto-actuated mechanism to realize the reversible shape transition between two curved stable configurations of a buckled beam using magneto actuation. The beam is composed of a silicone elastomer matrix with embedded micro-sized iron particles. The magnetic response of these iron particles endows the composite beam with the ability to snap from one stable shape to the other when the magnitude of the surrounding magnetic field exceeds the threshold value. By separately analyzing the electric-magnetic field and the magnetic-mechanical field, we formulate a simple and efficient computational method to numerically predict the critical current on the onset of snap-through. The computational and experimental critical currents show good agreement for different material and geometrical parameters, including the thickness of the beams, iron particle mixing ratios of the material, and the distances of the beam to the electromagnet. The proof-of-concept design is demonstrated to be efficient in the application of a magneto-responsive soft switch and a catapult for ejecting small objects, providing new insights into designing contactless, low-voltage-actuated bistable structures.

Mechanical characteristics of the bistable origami hypar

This letter explores the mechanical behavior of the origami hyperbolic paraboloid or hypar which is a bistable thin sheet structure with symmetric stable states. We use experiments to evaluate the global and local behaviors of the structure, which are unique from other bistable origami systems. In theory, for the hypar to reconfigure between the stable states, the thin sheet which is initially patterned with acute and reflex folds needs to fully flatten. However, we find that axial stretching as well as two distinctly different buckling patterns in the origami can allow for portions of the sheet to remain folded during the reconfiguration. The spacing of folds in the hypar, the resulting buckling characteristics, the stretching of the sheet, and the local material nonlinearity at the fold lines all have significant effects on the force–displacement response of the system. The work gives insight to these phenomena which are often omitted in the testing and modeling of more conventional origami-inspired systems. We reinforce our understanding of the hypar behavior by establishing an analytical model that can simulate the kinematics, the buckling, and the force–displacement behavior of the structure. The letter also discusses topics for future extension and introduces hypar chains where multiple hypars are connected in series to achieve multistability.

Computational modelling of the transformation of bistable scissor structures with geometrical imperfections

In many applications structures need to be easily moveable, or assembled at high speed on unprepared sites. For this purpose, preassembled deployable structures, which consist of beam elements connected by hinges, are highly effective. Intended geometric incompatibilities between the members are introduced for instantaneous structural stability after deployment. In such bistable scissor structures, these incompatibilities result in the bending of some specific members that are under compression with a controlled snap-through behaviour. The main goal of this contribution is to qualitatively and quantitatively discuss the behaviour of bistable scissor structures during deployment. To do this, a 3D nonlinear structural model is proposed to simulate the deployment, including explicitly geometrical imperfections in a stochastic approach. The originality of this contribution is (i) the implementation of gravity, (ii) the geometrical imperfections and (iii) the extension of the numerical model to complex deployable structures. Bounds on geometrical tolerances on several uncertain parameters (length of the beams, eccentricity of the pivot points, hinge misalignment and finite hinge stiffness) are proposed based on non-linear finite element simulations on a single module transformation. The computational tool is then applied to structures consisting of multiple modules and the influence of geometrical imperfections is characterized.

Analysis of broadband characteristics of two degree of freedom bistable piezoelectric energy harvester

In order to broaden the working frequency band of the piezoelectric energy harvester and improve the energy harvesting efficiency, a new two degree of freedom bistable piezoelectric vibration energy harvester is designed in this paper. It consists of a basic cantilever beam, a mass, a piezoelectric cantilever beam and magnets. The equivalent model of the system is established using lumped parameter method, and the two degree of freedom bistable motion equation is established considering the influence of electromechanical coupling. Using Matlab, the motion equation is calculated, and the curve of the system voltage with time and frequency is obtained. The voltage output characteristics of the system under bistable vibration and the influence of the stiffness and the mass of the basic cantilever beam on the output performance of the system are analyzed. Under the excitation of 0.3 g simple harmonics, the two degree of freedom bistable piezoelectric energy harvester is experimented using one-way frequency-increasing sweep. The results show that the maximum output voltage of the two resonance band of the energy harvester is 26 V and 13 V. Compared with the single degree of freedom bistable structure, the frequency band is widened by 10 Hz. In addition, reducing the stiffness of the basic cantilever beam and increasing the mass of mass block are all beneficial to broadening the working band of the harvester.

Bioinspired Electrically Activated Soft Bistable Actuators

AbstractMovement and morphing in biological systems provide insights into the materials and mechanisms that may enable the development of advanced engineering structures. The nastic motion of plants in response to environmental stimuli, e.g., the rapid closure of the Venus flytrap's leaves, utilizes snap‐through instabilities originating from anisotropic deformation of plant tissues. In contrast, ballistic tongue projection of chameleon is attributed to direct mechanical energy transformation by stretching elastic tissues in advance of rapid projection to achieve higher speed and power output. Here, a bioinspired trilayered bistable all‐polymer laminate containing dielectric elastomers (DEs) is reported, which double as both structural and active materials. It is demonstrated that the prestress and laminating strategy induces tunable bistability, while the electromechanical response of the DE film enables reversible shape transition and morphing. Electrical actuation of bistable structures obviates the need for continuous application of electric field to sustain their transformed state. The experimental results are qualitatively consistent with our theoretical analyses of prestrain‐dependent shape and bistability.