Bistable Units Research Articles

Large-stroke snap-through instability in the axial direction of a bi-stable structure with high slenderness

Mechanical snap-through instability of bi-stable structures may find many practical applications such as state switching and energy transforming. Although there exist diverse bi-stable structures capable of snap-through instability, it is still difficult for a structure with high slenderness to undergo the axial snap-through instability with a large stroke. Here, an elastic structure with high slenderness is simply constructed by a finite number of identical, conventional bi-stable units with relatively low slenderness in series connection. For realizing the axial snap-through instability with a large stroke, common scissors mechanisms are further introduced as rigid constraints to guarantee the synchronous snap-through instability of these bi-stable units. The global feature of the large-stroke snap-through instability realized here is robust and even insusceptible to the local out-of-synchronization of individual units. The present design provides a simple and feasible way to achieve the large-stroke snap-through instability of slender structures, which is expected to be particularly useful for state switching and energy transforming in narrow spaces.

Synthesis of a highly programmable multistable Kresling origami-inspired unit cell

Multistable origami structures have been exploited for mechanical property tailoring, deployable robotic arms, wave propagation tuning and others, due to its ability to possess multiple stable states with distinct properties. Traditionally these structures are made by assembling bistable unit cells, which results in a significant increase in the size and weight of the system when larger number of stable states are required. Recently, researchers have uncovered a third stable state in the Kresling origami pattern. Although this is an advancement over the bistable unit cell, there is an unexplored opportunity for more systematically expanding the design space of Kresling unit cells to possess many more stable configurations (>>2) and enhance its programmable multistability. In this research, we seek to develop a methodology for the design of a Kresling origami-inspired unit cell that can be easily programmed to achieve up to 10 stable configurations, with the potential to achieve even more. We exploit the rich kinematics of the Kresling origami-inspired unit cell, that arise from its coupled translational and rotational deployment, and propose the strategic integration of tensile elements to realize multiple stable states. Analytically, we study the unstretched length values (defined to be the precise length between the string “slacked” and “tensioned” configurations) of the strings that yield the distinct number of stable states. We present the potential energy profiles with its corresponding force-displacement plots for the bistable, tristable, quadstable, pentastable and decastable unit cells. Moreover, we show that by simply adjusting the unstretched length of the strings we can program and tune the number of stable states of the unit cell. Tristable and pentastable unit cell prototypes are designed and experimentally tested to validate the proposed methodology. Lastly, a study is performed on the mechanical property tailoring capabilities of two unit cells assembled in series. The results show that the decastable unit cell assembly can achieve up to 55 discrete values of equivalent stiffness, while the bistable one can only achieve 3. For the bistable unit cell assembly to match this number, it will require 54 unit cells in series, which will significantly increase the size and weight of the structural system. These findings show that the modular structure will have more programmable capabilities, while maintaining its size and weight at a minimum, as the number of stable states per unit cell is increased.

Topological edge states in reconfigurable multi-stable mechanical metamaterials

Multi-stable mechanical structures find cutting-edge applications across various domains due to their reconfigurability, which offers innovative possibilities for engineering and technology advancements. This study explores the emergence of topological states in a one-dimensional chain-like multi-stable mechanical metamaterial composed of bistable units through a combination of mechanical and optical experiments. Drawing inspiration from the SSH (Su-Schrieffer-Heeger) model in condensed matter physics, we leverage the unique mechanical properties of the reconfigurable ligament-oscillator metamaterial to engineer a system with coexisting topological phases. Based on the one-dimensional periodic bistable chain, there is an exponential decay diffusion of elastic energy from both end boundaries towards the interior of the body. Experimental characterizations demonstrate the existence of stable topological phases within the reconfigurable multi-stable mechanical metamaterial. The findings underscore the potential of reconfigurable mechanical metamaterials as versatile platforms for flexibly exploring and manipulating topological phenomena, with applications ranging from impact resistance to energy harvesting and information processing.

Easy-to-actuate multi-compatible truss structures with prescribed reconfiguration

Multi-stable structures attract great interest because they possess special energy landscapes with domains of attraction around the stable states. Consequently, multi-stable structures have the potential to achieve prescribed reconfiguration with only a few lightweight actuators (such as shape-memory alloy springs), and do not need constant actuation to be locked at a stable state. However, most existing multi-stability designs are based on assembling bi-stable unit cells, which contain multitudes of distractive stable states, diminishing the feasibility of reconfiguration actuation. Another type is by introducing prestress together with kinematic symmetry or nonlinearity to achieve multi-stability, but the resultant structure often suffers the lack of stiffness. To help address these challenges, we firstly introduce the constraints that a truss structure is simultaneously compatible at multiple (more than two) prescribed states. Then, we solve for the design of multi-stable truss structures, named multi-compatible structures in this paper, where redundant stable states are limited. Secondly, we explore minimum energy paths connecting the designed stable states, and compute for a simple and inaccurate pulling actuation guiding the structure to transform along the computed paths. Finally, we fabricated four prototypes to demonstrate that prescribed reconfigurations with easy-actuation have been achieved and applied a quadra-stable structure to the design of a variable stiffness gripper. Altogether, our full-cycle design approach contains multi-stability design, stiffness design, minimum-energy-path finding, and pulling actuation design, which highlights the potential for designing morphing structures with lightweight actuation for practical applications.

Reconfigurable origami-inspired multistable metamorphous structures.

Origami-inspired metamorphous structures can adjust their shapes and mechanical behaviors according to operational requirements. However, they are typically composed of nonrigid origami, where required facet deformation complicates actuation and makes them highly material dependent. In this study, we present a type of origami metamorphous structure composed of modular bistable units, each of which is a rigid origami. The elasticity within the origami creases and switching of mountain and valley crease lines enable it to have bistability. The resultant metamorphous structure has multistability, allowing it to switch among multifarious configurations with programmable profiles. This concept was validated by potential energy analysis and experiments. Using this concept, we developed a robotic limb capable of both lifting and gripping through configuration changes. Furthermore, we used the origami units to construct a metamaterial whose properties could change with the variation of configurations. These examples demonstrate the concept's remarkable versatility and potential for many applications.

Reprogrammable Mechanics via Individually Switchable Bistable Unit Cells in a Prestrained Chiral Metamaterial

AbstractArchitected materials exhibit unique properties and functionalities based on the geometric arrangement of their constituent materials. In most cases, these parameters are fixed, requiring that the system be redesigned and reconstructed if different properties are desired. Both stimuli‐responsive materials and modular designs have been used to enable re‐programmable properties in the past, but often have limitations, such as the need for a continuous application of external stimuli or power, or unwanted global morphing. In this study, a locally stable anti‐tetra chiral (LSAT) metamaterial is introduced consisting of independently multistable units that can deform and change state without inducing changes in the global morphology. Adjacent cells are only weakly coupled, allowing the collective metamaterial to be switched between many different possible states. Local bistability enables re‐programmable heterogeneity, such as the snapping of cells along an edge or diagonally within the architected material. Utilizing finite element analysis (FEA), the influence of key geometric parameters on the re‐programmability of the metamaterials is systematically investigated. The effect of these parameters on properties such as shear stiffness, Poisson's ratio, and vibration are also investigated using experimental prototypes. This re‐programmable metamaterial promises to expand the design space for mechanical systems, with potential applications in non‐traditional computation, robotic actuation, and adaptive structures.

On the limit behavior of lattice-type metamaterials with bi-stable mechanisms

This paper explores 2D lattice-type metamaterials featuring bi-stable unit cells and predefined symmetry configurations. Our investigation delves into the emergence of phase-transition patterns and probes the limit behavior of these lattice arrangements. We develop a macroscale generalized standard material model based on a quasi-convexified free energy framework and validate it through a specific lattice configuration – a 1D chain of bi-stable elements – where the relaxed free energy is analytically derived.To assess the limit behavior of the analyzed lattices, we elucidate the connection between energy release and topology at the microscale. This insight aids in identifying lattice configurations yielding high extrinsic energy dissipation density. We introduce the concept of dissipation efficiency and quantify it across all examined lattices under different loading conditions. Transverse loads prevail in the studied configurations and exhibit a detrimental effect by diminishing extrinsic energy dissipation during metamaterial phase transitions. To facilitate a comprehensive numerical assessment of diverse lattice configurations, we employ a surrogate model of the bistable element. This approach enables an efficient evaluation of sampling volumes constituted by numerous unit cells.

A Flexibly Function‐Oriented Assembly Mechanical Metamaterial

AbstractBased on the snap‐through instability, the pursuit for mechanical metamaterials with flexible functional applications and the ability to combine with information has been the Holy Grail for structural scientists. Here, the function/application‐oriented bistable unit motifs (UMs) are developed by an elaborately architectural design inspired by the hind leg of the frog in jumping, and a corresponding assembled strategy is proposed. Three functional applications derived from their progressive evolutions. The first is the construction of on‐demand assemblable mechanical curves, including multi‐stage vibration isolation, recoverable energy absorption, and energy dissipation along with integrated vibration isolation and energy dissipation characteristics. The second is the development of mechanic and temperature double pattern encryption strategy using bistability and shape memory programmability, resulting in 4n encryption and decryption modes for n‐bit encryption devices. Finally, five non‐volatile basic mechanical logic gates and a universal combinatorial half‐adder are built, affording guidance to unconventional computing devices with logic functions.

Intrinsically Multistable Soft Actuator Driven by Mixed-Mode Snap-Through Instabilities.

Actuators utilizing snap-through instabilities are widely investigated for high-performance fast actuators and shape reconfigurable structures owing to their rapid response and limited reliance on continuous energy input. However, prevailing approaches typically involve a combination of multiple bistable actuator units and achieving multistability within a single actuator unit still remains an open challenge. Here, a soft actuator is presented that uses shape memory alloy (SMA) and mixed-mode elastic instabilities to achieve intrinsically multistable shape reconfiguration. The multistable actuator unit consists of six stable states, including two pure bendingstates and four bend-twist states. The actuator is composed of a pre-stretched elastic membrane placed between two elastomeric frames embedded with SMA coils. By controlling the sequence and duration of SMA activation, the actuator is capable of rapid transition between all six stable states within hundreds of milliseconds. Principles of energy minimization are used to identify actuation sequences for various types of stable state transitions. Bendingand twisting angles corresponding to various prestretch ratios are recorded based on parameterizations of the actuator's geometry. To demonstrate its application in practical conditions, the multistable actuator is used to perform visual inspection in a confined space, light source tracking during photovoltaic energy harvesting, and agilecrawling.

Topology optimization design of recoverable bistable structures for energy absorption with embedded shape memory alloys

In this work, multistable mechanical metamaterials with recoverable capabilities are designed for high energy absorption and resistance to repetitive impacts. Based on the known curved beam with energy dissipation characteristics, the shape memory alloys (SMAs) curved beam is added and optimized to achieve recoverability of the bi-layer beam structure. To simultaneously achieve bistable characteristics and recoverability in the designed metamaterial, the optimization model is formulated to maximize the energy absorption capacity of the structure while constraining the peak and valley forces. To solve this complex and highly nonlinear topological optimization problem with stringent constraints, the topological design of the SMAs layer is represented using a limited number of design variables along with the material-field series expansion strategy, and the optimization problem is subsequently solved using a non-gradient-based optimization algorithm. Finite element simulation results demonstrated that the optimized design possesses a substantial capacity for energy absorption. Additionally, the design structure can recover to its initial state from buckling induced by the initial load by regulating the external temperature. Different multistable metamaterials, including those designed to prevent repetitive impacts, have been further developed based on the designed recoverable high-energy-absorbing bistable unit cells, utilizing combinations of varying energy absorption capacities.

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.

An adaptive metastructure concept using bistable composite laminates

Concepts involving adaptive and morphing structures offer us the possibility to realise shape transformation with each shape imparting an individual functionality. There is an increased demand in the design of structural components that are suitable for diverse operational conditions rather than limited to a unique one. However, most concepts of shape adaptive structures require a “holding force” or a continuous supply of energy to maintain a targeted 3D shape. As a result, structures that can lead to desired shape transformation with self-locking capabilities are more desirable.In this work, the concept of multistability is employed to demonstrate a novel class of metastructures that can tackle this challenge. The metastructure is constructed with a periodic arrangement of bistable unit cells made of highly anisotropic composite laminates. Each unit cell comprises multi-sectioned rectangular composite plates exhibiting bistable behaviour due to the thermal residual stresses engendered during the cool-down process from curing to room temperature. To analyse the proposed metastructure, a finite element model has been developed at three hierarchical levels: a plate level, a unit cell level, and a lattice level. At the plate level, a corresponding semi-analytical model using the Rayleigh–Ritz method has also been formulated to validate the finite element models. By carefully tuning the size and spacing of the unit cell, a desired response of the metastructure can be achieved. Additionally, by changing the ply layup and the fibre orientation of each layer of constituent composite plates, conflicting requirements, including load-carrying, shape-adaptive and lightweight, at the same time can be addressed simultaneously. From an extensive parametric study, few designs have been selected for its application in a load-carrying morphing structure.

Thermally active programmable metamaterials with holey tilted struts

Bistable transition is often applied in the design of microstructures in metamaterials. In this study, we introduce a series of strategically placed holes in the tilted struts, and observe, through numerical and experimental analysis, an effect of the perforation on the snap-through buckling behavior of the structure. By infilling the holes with thermal-sensitive polymer bars, we realize actively tuning the local stiffness of the holey struts, thereby enabling a means to switch the metamaterial between bistable and monostable states. Furthermore, we propose a multi-stable metamaterial by stacking bistable units with different arrange of infilled and empty holes. The designed metamaterial demonstrates a progressive restoration from the deformed shape to its original shape as the environment temperature reaches up to certain values. These findings highlight the potential of holey-type bistable metamaterials in the design of actuators, deployable structures, and reusable energy absorbers.

Finding transition state and minimum energy path of bistable elastic continua through energy landscape explorations

Mechanical bistable structures have two stable equilibria and can transit between them under external stimuli. Due to their unique behaviors such as snap-through and substantial shape changes, bistable structures exhibit unprecedented properties compared to conventional structures and thus have found applications in various fields such as soft robots, morphing wings and logic units. To quantitatively predict the performance of bistable structures in these applications, it is desirable to acquire information about the minimum energy barrier and an energy-efficient transition path between the two stable states. However, there is still a general lack of efficient methodologies to obtain this information, particularly for elastic continua with complicated, unintuitive transition paths. To overcome this challenge, here we integrate energy landscape exploration algorithms into finite element method (FEM). We first utilize the binary image transition state search (BITSS) method to identify the saddle point and then perform nudged elastic band (NEB) calculations with an initial guess based on the BITSS results to find the minimum energy path (MEP). This integrated strategy greatly helps the convergence of MEP calculations, which are highly nonlinear. Two representative cases are studied, including bistable buckled beams and a bistable unit of mechanical metamaterials, and the numerical results agree well with the previous works. Importantly, we numerically predict the complicated MEP of an asymmetric bistable unit of mechanical metamaterials and use experiments to demonstrate that following this MEP leads to successful transition between stable states while intuitive uniaxial compression fails to do so. Our work provides an effective numerical platform for identifying the minimum energy barrier and energy-efficient transition path of a bistable continuum, which can offer valuable guidance to the design of actuators, damping structures, energy harvesters, and mechanical metamaterials.

Bistable reconfigurable origami metamaterials with high load-bearing and low state-switching forces

Bistable shape-reconfigurable metamaterials can achieve large morphological changes under a relatively low state-switching force and can maintain the configuration autonomously after removing the force. However, the state-switching force and the load-bearing forces are usually coupled in the same direction, resulting in low loadability at the deployed state. Here we separate the load-bearing direction and the state-switching direction of bistable unit, and combine the directional folding feature of origami to design a shape-reconfigurable metamaterial with high bearing force and low switching force, named mechanical relay metamaterial. The feasibility of the design concept is first validated experimentally. The bearing force of the mechanical relay metamaterial is at least 4 times the switching force and 100 times the gravity of self-weight. Then the geometric design domain of the unit is derived by spherical trigonometry. Finally, the effect of geometric parameters on the load carrying capacity of the unit is investigated by finite element simulations, and the optimal geometric parameters are determined. This work provides an effective solution for bistable shape-reconfigurable metamaterials with high bearing force and low switching force.

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.

Programming metastable transition sequences in digital mechanical materials

The realization of unconventional computing methods in soft matter has inspired the creation of mechanological systems capable of processing information. These systems often utilize bistable mechanisms that serve as mechanically abstracted bits to perform digital logic operations. Yet, the input of such operations often requires manual control of complex cyclic loading to reach a desired configuration. This research presents a method to design digital mechanical materials that can enter a programmable sequence of metastable configurations through simple displacement-controlled inputs. Interactions between serially connected bistable units enable the transition and reset behavior of mechanical bits. An analytical model using the principle of minimum total potential energy of a single bit is presented to articulate systematic ways to tune the critical force thresholds and displacements of metastable transition sequences. This work elucidates how the application of a prescribed displacement allows for novel resetting behavior that enables simultaneous transitions of multiple bits. By combining the principles of deterministic transition sequences and mechanical computing, a mechanical analog to digital conversion (ADC) material system is introduced that digitizes a continuous force stimulus into binary configurations that perform computations within the mechanical material based on the applied load. The mechanical ADC establishes a foundation for the integration of environmental sensing, information processing, and response in a soft material system.

Quasipotentials for coupled escape problems and the gate-height bifurcation.

The escape statistics of a gradient dynamical system perturbed by noise can be estimated using properties of the associated potential landscape. More generally, the Freidlin and Wentzell quasipotential (QP) can be used for similar purposes, but computing this is nontrivial and it is only defined relative to some starting point. In this paper we focus on computing quasipotentials for coupled bistable units, numerically solving a Hamilton- Jacobi-Bellman type problem. We analyze noise induced transitions using the QP in cases where there is no potential for the coupled system. Gates (points on the boundary of basin of attraction that have minimal QP relative to that attractor) are used to understand the escape rates from the basin, but these gates can undergo a global change as coupling strength is changed. Such a global gate-height bifurcation is a generic qualitative transition in the escape properties of parametrized nongradient dynamical systems for small noise.

Flows in Straws: Viscous Flows in One-Dimensional Metamaterial

The authors study the interaction between a viscous flow and a one-dimensional mechanical metamaterial composed of bistable unit cells, much like a drinking straw. Their twofold model shows excellent agreement with experimental results. While prior studies have focused on tailoring unit-cell structure to obtain a desired multistable behavior, here the viscous fluid allows tuning of rate-dependent properties and nonlocal interaction between unit cells. The ability to manipulate both structural and nonlocal rate-related properties points to the development of smart materials with tunable kinetic relations, large reversible deformations, and tailored dynamic properties.

Topological transformability and reprogrammability of multistable mechanical metamaterials

Concepts from quantum topological states of matter have been extensively utilized in the past decade to create mechanical metamaterials with topologically protected features, such as one-way edge states and topologically polarized elasticity. Maxwell lattices represent a class of topological mechanical metamaterials that exhibit distinct robust mechanical properties at edges/interfaces when they are topologically polarized. Realizing topological phase transitions in these materials would enable on-and-off switching of these edge states, opening opportunities to program mechanical response and wave propagation. However, such transitions are extremely challenging to experimentally control in Maxwell topological metamaterials due to mechanical and geometric constraints. Here we create a Maxwell lattice with bistable units to implement synchronized transitions between topological states and demonstrate dramatically different stiffnesses as the lattice transforms between topological phases both theoretically and experimentally. By combining multistability with topological phase transitions, this metamaterial not only exhibits topologically protected mechanical properties that swiftly and reversibly change, but also offers a rich design space for innovating mechanical computing architectures and reprogrammable neuromorphic metamaterials. Moreover, we design and fabricate a topological Maxwell lattice using multimaterial 3D printing and demonstrate the potential for miniaturization via additive manufacturing. These design principles are applicable to transformable topological metamaterials for a variety of tasks such as switchable energy absorption, impact mitigation, wave tailoring, neuromorphic metamaterials, and controlled morphing systems.