Multistable Structures Research Articles

A multistable composite hinge structure

A composite tape-spring (CTS) structure is a thin-walled open slit tube with fibres oriented at ±45°, which is stable in both extended and coiled configurations. The governing factors of its bistability include composite constitutive behaviour, initial geometrical proportions, and geometrically non-linear structural behaviour. Its bistable principle can be employed to produce a flexible multistable hinge structure with tailorable stability. This is achieved by introducing variable stiffness design within a cylindrical shell structure, where folding stability is dependent on central functional patch region, and then connected to linking ploy regions. Thus, a novel multistable composite hinge structure can be designed with positive Gaussian curvature deformation, and its multistability is highly tailorable: a lengthy one-dimensional mechanical arm can be designed to coil and fold multiple times to enable large folding ratio. An analytical model was established based on the strain energy principle, in order to determine effects from functional tape length; the typical structural stability and stable configurations were then predicted with respect to regional length of the functional layer. It is found that the stability of a multistable composite hinge structure is dependent on geometry and combination of both the functional patch region, and connecting ploy region; the stable criteria are then proposed and show good agreement with experimental observations and FE analysis. These enrich the diversities of functional deployable structures to benefit novel requirements for various deployable mechanisms, and enable customised design, as well as smart driving for flexible and multifunctional mechanical composite hinge applications.

Buckling-induced sound production in the aeroelastic tymbals of Yponomeuta

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

The study on the properties of a metamaterial composed of star-shaped auxetic and curved-beam multi-stable structure

This article presents the design of a new metamaterial with adjustable Poisson’s ratio and multi-stability, which combines two common metamaterial structures: star-shaped auxetic and multi-stability. The range of negative Poisson’s ratio variation for the unit structure is 0.2433. The negative Poisson’s ratio shows an increasing trend followed by a decrease with the increase in compression displacement. The peak compression displacement is 12 mm, and the peak negative Poisson’s ratio is −0.1499. Simultaneously, the structure exhibits good shape memory properties, with a shape memory recovery ratio of R rx = 94.18% in the y-axis direction and R ry = 91.20% in the x-axis direction. The shape memory recovery time is 35.10 s. The combination of experimental testing and finite element analysis was employed to verify the functionality of the adjustable Poisson’s ratio in the structure. Special attention was given to investigating the structural parameters such as the type of curved-beam, the angle of the star-shaped structure, the width of the star-shaped structure, and the connection method for their effects on the shape memory effect and the range, peak value, and peak compression displacement of the negative Poisson’s ratio in the unit structure. Based on the characteristics of the novel metamaterial, including a significant increase in stiffness upon compression and controllable deformation sequence, it can be used as a buffering device in protective engineering and civil engineering applications.

2-D multistable structures under shear: equilibrium configurations, transition patterns, and boundary effects

2-D multistable structures under shear: equilibrium configurations, transition patterns, and boundary effects

Investigations on the dynamic snap-through of MFC bonded self-resetting bistable laminates

Unsymmetric composite laminates having two stable equilibrium configurations have been studied extensively in the recent past due to their potential applications in morphing structures. Surface bonded Macro Fiber Composites (MFC) actuators have been considered as a viable solution to trigger the snap-through transition in bistable laminates. Although MFC bonded bistable laminates are widely used in morphing applications, they might require considerably high voltage inputs to achieve the required levels of actuation control during the shape transition. As a solution, other possible energy sources can be combined with active MFC patches to reduce the snap-through energy required from the single source of MFC actuation. In this work, we examine the dynamic behavior of bistable composite plates actuated using MFC actuators, where external vibration energy has been used to assist with the MFC-controlled actuation between stable states. A refined semi-analytical model based on the Rayleigh–Ritz formulation has been proposed, where the membrane energy and the bending energy are separately evaluated. Bending components are directly evaluated using the approximated transverse displacement functions, whereas the membrane components are evaluated separately by combining compatibility conditions and equilibrium equations. Results from the proposed semi-analytical framework are compared with a full geometrically nonlinear finite element framework and necessary experimental observations. The results show a significant reduction in the snap-through energy demand on MFC layers where external dynamic excitation assists the snap-through process. Additionally, a parametric study is performed using variable stiffness (VS) fiber orientation parameters, achieving bistable laminate-MFC configurations that lower snap-through requirements through the proposed morphing strategy. Thus, the study offers to aid a multi-efficient snap-through strategy for the morphing of multistable composite structures.

A rapid and automated computational approach to the design of multistable soft actuators

We develop an automated computational modeling framework for rapid gradient-based design of multistable soft mechanical structures composed of non-identical bistable unit cells with appropriate geometric parameterization. This framework includes a custom isogeometric analysis-based continuum mechanics solver that is robust and end-to-end differentiable, which enables geometric and material optimization to achieve a desired multistability pattern. We apply this numerical modeling approach in two dimensions to design a variety of multistable structures, accounting for various geometric and material constraints. Our framework demonstrates consistent agreement with experimental results, and robust performance in designing for multistability, which facilities soft actuator design with high precision and reliability.

Assembled mechanical metamaterials with integrated functionalities of programmable multistability and multitransition behaviors.

Mechanical metamaterials with integrated functionalities can simultaneously fulfill multiple design requirements through design consolidation, which is highly desirable for weight-sensitive and space-constrained applications. Despite the extensive research on multistable metamaterials, their integration with other functionalities, such as vibration isolation, sensing, and hierarchical energy absorption, remains largely untapped. Here, we report a novel class of mechanical metamaterial featuring programmable multistability and function-oriented multitransition behaviors. This integration is realized through a novel assembly-based design concept that incorporates interchangeable contact block (CB) units into a classical bistable structure. By varying the position, number, and shape of CB units, we can obtain a spectrum of function-oriented transition behaviors, offering reconfigurability through unit replacement. To ensure the rational design of CB, we employ a comprehensive approach that combines theoretical analysis, numerical simulations, and experimental validation to investigate the nonlinear behaviors of these assembled metamaterials, including snap-through instability and contact behaviors. Additionally, we explore design strategies such as 2D arraying and 3D extension to achieve programmable multistability. Furthermore, we demonstrate the versatility of these assembled mechanical metamaterials by constructing digital materials with scalability, reconfigurability, and multidirectionality. The proposed assembly-based design concept breaks new ground in engineering multistable structures with integrated functionalities for deployable structures, robotics, and beyond.

Effect of Filament Color and Fused Deposition Modeling/Fused Filament Fabrication Process on the Development of Bistability in Switchable Bistable Squares

Abstract Switchable multistable structures (SMS) are additively manufactured metamaterials. SMS are printed in polylactic acid, a shape memory polymer, and pre-strain is stored in bilayers during fused deposition modeling 3D printing process that encode different stable states can be activated above the glass transition temperature (Tg). Eight filament colors were used to 3D print sample squares. A hot water bath was used to determine sample bistability or monostability. Differential scanning calorimetry determined the Tg and melting temperature, (Tm). Thermogravimetric analysis was used to investigate colored filament thermal stability. The viscoelasticity of colored filament was investigated with melt rheology and the crystallinity of the printed samples was studied with X-ray diffraction. Filament color was an indicator of bistability and colors with lower Tm values tended to be bistable. Polyethylene terephthalate glycol SMS exhibited the shape memory effect but did not show bistability with the given print parameters. Bistability is achieved when the difference between the pre-strain of the bilayers is less than the energy needed to snap the sample to a given state. The relationship between monostability, self-snapping back to a favored state, and bistability is explained by a series of mathematical equations. Future work includes printing pre-strain relationship and the molecular level impact.

Highly stable glucose oxidase polynanogel@MXene/chitosan electrochemical biosensor based on a multi-stable interface structure for glucose detection

It is a challenging and meaningful task to design an enzyme electrochemical biosensor that can maintain high sensitivity while improving stability. In this study, we constructed an enzyme electrochemical biosensor by preparing nanocomposites with multi-stable interface structures. Specifically, the nanocomposite (PGOx@MXene/CS) was prepared by efficient electrostatic assembly of GOx polynanogel (PGOx) onto MXene nanosheets. PGOx could enhance enzyme stability, while the extensive the large specific surface area of MXene could realize the efficient loading of nanocapsules (PGOx) and catalyze the decomposition of toxic intermediate H2O2, thereby reducing its influence on the stability of enzyme. The linear range of the constructed glucose sensor was 0.03–16.5 mM, the sensitivity was 48.98 μA mM−1·cm−2, and the detection limit was 3.1 μM. After 200 cycles, the current still remained at 85.83% of the initial current value. The high sensitivity, excellent selectivity and great reproducibility verified the effectiveness of the system we constructed. The multi-stable enzyme electrochemical biosensor had a wide application prospect in stable and continuous blood glucose detection.

Influence of actuation sequence on the snap-through process of composite multi-stable structures

In this paper, the impact of the actuation sequence on the snap-through process of a composite multi-stable structure composed of regular triangular modules was investigated. Using ABAQUS finite element simulation software, a finite element (FE) model of laminated plates was established, actuation points was selected on its surface, and bending moment loads were applied in different actuation sequences to induce the snap-behaviors of the structure. Based on the minimum load value for driving structure deforms, the actuation sequence laws of multi-stable structures were obtained. The most efficient and feasible actuation path for transitioning between different steady states was also achieved. It’s proved that the actuation paths are reasonable and feasible by the loading experiment. The research results of this paper can provide references for the design of multi-stable structures and the application modes of driving forces.

Modular Design of Multistable Pneumatic Structures from a Flat Pattern of Air Pouches

We introduce a novel family of structures that can be inflated from a plane to form a three-dimensional surface using articulated straight pouches with inextensible membranes. Specifically, we propose a modular design using a quadrangle surrounded by four slender pouches, whose inflation causes the surface to form a saddle shape. Then we show a fabrication method using heated nylon films with heat adhesives separated by paper mask patterns inside. We first show a geometric model to explain and predict the out-of-plane deformation and the bi-stability effect inherited in this structure. Through a geometric analysis and an elastic simulation of a pouch, we show that lowering the width-length ratio of pouches reduces the imperfection of shapes. We further propose a method for controlling the height of saddles using concentric patterns. We then extend structural modules into multiple-grid systems and identify the multistable behaviors of the overall structure.

Machine learning-based design and optimization of double curved beams for multi-stable honeycomb structures

Curved beams with bistable and negative stiffness properties can be used to design multi-stable metamaterials or honeycomb structures. Consequently, the deformation patterns and mechanical properties of curved beams under load have attracted many attentions. However, due to the nonlinear characteristics of variable thickness double curved beams, it is impossible to exhaust all possible structural forms through experimental and theoretical approaches. This paper presents a machine learning (ML) method for designing and optimizing double curved beam structures. The ML model is used to establish the underlying mapping relationship between thickness parameters and mechanical properties. After optimizing the double curved beam in different directions, the optimal thickness distributions of the backward snapping force and energy absorption are obtained. Double curved beams with optimal thickness distributions are used to construct multi-stable honeycomb structures, demonstrating the optimization process from single cell structure to periodic structure. Under the same mass, compared to the constant thickness honeycomb structure, the optimized variable thickness honeycomb structures exhibit a 140% increase in backward snapping force and a 57% increase in energy absorption. The objective of this study is to utilize machine learning technique to obtain a general approach for optimizing model of ‘multi-parameter input’ to ‘single-parameter output’, which is valuable for guiding the optimization and design of metamaterial structures in the future. This paper is a good case study of the mechanical structure performance optimization, whose implementation path is given detailly in appendix. Other disciplines with similar optimization goals can also use this method to carry out researches.

Generative optimization of bistable plates with deep learning

Bistate plates have found extensive applications in the domains of smart structures and energy harvesting devices. Most bistable curved plates are characterized by a constant thickness profile. Regrettably, due to the inherent complexity of this problem, relatively little attention has been devoted to this area. In this study, we demonstrate how deep learning can facilitate the discovery of novel plate profiles that cater to multiple objectives, including maximizing stiffness, forward snapping force, and backward snapping force. Our proposed approach is distinguished by its efficiency in terms of low computational energy consumption and high effectiveness. It holds promise for future applications in the design and optimization of multistable structures with diverse objectives, addressing the requirements of various fields.

Connecting the branches of multistable non-Euclidean origami by crease stretching.

Non-Euclidean origami is a promising technique for designing multistable deployable structures folded from nonplanar developable surfaces. The impossibility of flat foldability inherent to non-Euclidean origami results in two disconnected solution branches each with the same angular deficiency but opposite handedness. We show that these regions can be connected via "crease stretching," wherein the creases exhibit extensibility in addition to torsional stiffness. We further reveal that crease stretching acts as an energy storage method capable of passive deployment and control. Specifically, we show that in a Miura-Ori system with a single stretchable crease, this is achieved via two unique, easy to realize, equilibrium folding pathways for a certain wide set of parameters. In particular, we demonstrate that this connection mostly preserves the stable states of the non-Euclidean system, while resulting in a third stable state enabled only by the interaction of crease torsion and stretching. Finally, we show that this simplified model can be used as an efficient and robust tool for inverse design of multistable origami based on closed-form predictions that yield the system parameters required to attain multiple, desired stable shapes. This facilitates the implementation of multistable origami for applications in architecture materials, robotics, and deployable structures.

Coned disk spring with friction or restraint at its edges: Explicit solution and experimental study

The behavior of a coned disk spring can be significantly affected by friction or restraint, yet the existing theoretical solutions cannot fully capture these influences. The limitation is particularly problematic for analyzing the behavior of coned disk springs with bi-stability. This paper proposes an explicit solution that can predict the behavior of the coned disk spring under these boundary conditions. The solution considers detailed influences of friction and restraint at the edges of the coned disk spring on its moment equilibrium and location of the neutral fiber. The theoretical results are validated using existing literature, FE analysis, and a series of tests. The theoretical solution confirms that the friction force at the edge of the coned spring significantly affects the axial response of the spring but not its bending moment or distribution of tangential stress. The bending moment and overall behavior of the coned disk spring are, on the other hand, very sensitive to restraints in radial directions. The proposed explicit solution shows good accuracy for coned disk springs with restrained radial stretching and rotation. The solution is particularly useful for coned disk springs in multistable structures and metamaterials.

Nonlinear dynamics of a compact and multistable mechanical energy harvester

The use of smart materials as transducers in mechanical energy harvesting systems has gained significant attention in recent years. Despite the numerous proposed solutions in the literature, challenges still exist in terms of their implementation within limited spaces while maintaining optimal performance. This paper addresses these challenges through the concepts of compactness and space-efficient design, as well as the incorporation of nonlinear characteristics and additional degrees-of-freedom. A multistable dual beam nonlinear structure featuring two magnetic interactions and two piezoelectric transducers is presented. A reduced order model with 2-degrees-of-freedom is established based on the harvester structure in order to capture the essential qualitative characteristics of the system. Stability analysis demonstrates that the combination of two nonlinear magnetic interactions furnish unprecedented multistable characteristics to this type of harvester. A framework using a nonlinear dynamics perspective is established to analyze multistable systems based on energy harvesting purposes. Different dynamical and stability characteristics are determined by the differences in the system stiffness ratio. Parametric analyses are carried out classifying regions of high performance in the external excitation parameter space. These regions are associated with rich and complex dynamics. Finally, a comprehensive comparison is conducted between the proposed harvester and the classical bistable harvester, revealing improvements in performance across nearly all relevant conditions. These findings highlight the enhanced capabilities of the proposed harvester design, solidifying its potential of application in diverse energy harvesting scenarios.

Identifying the energy threshold for multistable tensegrity structures using a Mountain Pass algorithm

Multistable tensegrity structures are able to switch between equilibrium configurations and maintain these states with no additional energy input; as a result, they have found applications in reconfigurable robotics and deployable structures. However, the actuation strategy for multistable tensegrity structures to transform from one stable state to another remains unknown. In this work, we propose a method to identify a transition route between the known stable states of multistable tensegrity structures. The least-energy threshold and the transformation route formed by a series of deformed position point vectors are obtained. The method is based on the Conjugate Peak Refinement (CPR) method, which is one of the Mountain Pass Algorithms. To capture the fact that cable members could go slack during the transition route, a slack cable model is adapted into the CPR method so that the accurate energy state of the tensegrity structure is derived. The algorithms are successfully applied to examples of 3D multistable tensegrity structures from the literature. The work in this paper provides a minimum energy threshold between stable states, a measure of its shock sensitivity, and a reference actuation strategy to transform between the stable states of multistable tensegrity structures.

Multi-Stability of the Extensible Origami Structures.

Multi-stable structures and metamaterials with more than two stable states are widely applied in diversified engineering applications. Non-rigid foldable origami patterns have provided an effective way of designing multi-stable structures. But most of them have only two stable states and therefore require a combination of many units to achieve multi-stability. Here, a series of extensible origami structures are proposed with generic multi-stability based on non-rigid wrapping origami. Through a kinematic analysis and experiments, it is demonstrate that a sequential folding among different layers of the structures is created to generate a continuous rigid origami range and several discrete rigid origami states, which consequently leads to the multi-stability of the extensible origami structures. Moreover, the effects of design parameters on the mechanical properties of the structures are investigated by numerical simulation, enabling properties programmability upon specific needs. This study thus paves a new pathway for the development of novel multi-stable origami structures.

Static and dynamic nonlinear behavior of a multistable structural system consisting of two coupled von Mises trusses

Recent years have witnessed a growing interest in multistable structures. In most cases it is attained by a sequence of bistable elements. However, little is known on their nonlinear static and dynamic responses. In this work a detailed static and dynamic nonlinear analysis of a multistable structural system consisting of two coupled bistable von Mises trusses is conducted to enlighten the complex behavior of these systems. For this, the exact nonlinear equilibrium equations and equations of motion in their dimensionless forms are obtained through the principle of stationary potential energy and Hamilton’s principle, respectively, considering a linear elastic material. Using continuation algorithms, the nonlinear equilibrium paths are obtained. The stability of each configuration is analyzed using the principle of minimum potential energy. Multiple equilibrium paths of the coupled system are identified, leading to several coexisting stable and unstable solutions, bifurcations and potential wells which are closely connected to the symmetries of the system. It is shown that the number of coexisting solutions increases exponentially with the number of bistable units. The effect of unavoidable imperfections is also clarified. The nonlinear dynamics and bifurcations of the system under harmonic forcing and static pre-load are then studied. Bifurcation diagrams, Poincaré maps and cross-sections of the basins of attraction are used to study the influence of coexisting attractors due to multiple potential wells, resonances and bifurcations. The coexisting responses can merge giving rise to several types of cross-well motions, the threshold value being closely connected with the limit point load of the coupled system. The increase in coexisting solutions leads to increasingly complex basins of attraction with broad fractal regions. On the one hand, the complexity of the bifurcation scenarios seems valuable in several applications to encode information, to respond to external forcing and to switch between different states. On the other hand, multiple attractors and their fractal basins can lead to the loss of global stability and dynamic integrity due to the small uncorrupted basins surrounding each attractor. Thus, the knowledge of the static and dynamic behavior of multistable systems is of great significance to either inducing or avoiding this phenomenon or making use of it.

Programmable Multi-stable Structure Based on Cosine Beam

Mechanical metamaterials with multi-stable properties are an emerging field of interest. In this paper, we present a novel 3D bi-stable cell element with negative stiffness characteristics designed based on a cosine-curved beam. Static compression simulations were performed for the single-cell model and the series model. Using “E” and “F” states as programming units, five array models were designed to analyze the stiffness variation rules. Dynamic simulations were conducted to compare the energy absorption rate and collision force of the model with variable stiffness. The conclusion shows that the structure has multi-stable and negative stiffness characteristics, and its stiffness can be adjusted in the range of 113.0 to 197.6 N/mm. Additionally, the energy absorption rate can be adjusted in the range of 8% to 65%. This study has made the structure configurable after manufacturing, breaking through the application limitations of predefined objects, and broadening its application prospects.