Morphing Structures Research Articles

Shape morphing of 2D lattice structures from localized contra-rotations

The morphing of structure and materials from localized, self-equilibrated actuation loads is limited by Saint-Venant’s principle: Deformations typically decay rapidly from the actuation region, so that changes in shape for the entire structure are negligible. Materials and structures with unusual combinations of elastic properties may induce competitions between different deformation modes over longer decay distances, thereby overcoming this limitation. Here we push this principle to the extreme to generate shape morphing in large 2D lattice structures. We consider planar triangular lattice made of “meta-elements” with unusual combinations of axial, shear and flexural stiffness. We show, using finite element models, that localized contra-rotations on the center nodes can morph the entire structure in bending, provided that adequate combinations of elastic properties are selected. We use the global curvature as a measure of this deformation to establish precise design guidelines for morphing. We finally propose physical embodiments of these meta-elements and lattice structures which we fabricated using laser cutting, and which tested using servo-motors to impose contra-rotations on the two center nodes. The results validate our models and the design guidelines: planar lattice can morph in bending with significant curvatures, especially when the size of the structure is small. In comparison, similar lattice structures made of regular beams show no morphing, with all the deformation localized near the center nodes. These findings may lead to new strategies to actuate morphing materials and structures, with applications in aerospace or robotics.

Customized deformation behavior of morphing wing through reversibly assembled multi-stable metamaterials

The geometry of multi-stable metamaterials, will change by the transition from one stable state to another. Shape morphing wings consisted of multi-stable metamaterials have capability to deform as desired, attributed to the programmable mechanical properties of architectured materials. In this study, to fabricate large-scale shape morphing structures, multi-stable unit cells with reversible connections were designed, printed and assembled. The mechanical properties and deformation capability were examined for multi-stable metamaterials with different geometrical parameters (e.g. width, thickness of beams). The deformation sequence for one assembled column consisting of identical multi-stable unit cells was found unpredictable, but could be tailored into a predictable manner by slightly adjusting beam geometry. To realize the customized deformation profile, the overall design domain of shape morphing structures was discretized into independent sub-regions. By enforcing deformation on sub-regions via the precise control of mechanical actuators that fixed with corresponding columns, the assembled shape morphing structures formed the targeted deformation. Also, the deformation feasibility was also demonstrated after incorporating voids or nondeformable functional elements within the assembled metamaterials platform. This study had provided practical solution for the design and fabrication of metamaterial-based shape morphing structures, and would shed light on future innovation of morphing aircraft.

Adaptive robust constraint-following control for morphing quadrotor UAV with uncertainty: A segmented modeling approach

During morphing, changes in a quadrotor UAV’s center of gravity and inertia contribute to unstable flight. Various uncertainties also impact its performance. In modeling, considering inertia and length variations due to morphing increases complexity. In control, detailed knowledge of uncertainties, such as parameter variability, is often needed. We propose a segmented modeling approach to obtain the quadrotor UAV model under morphing condition, along with an adaptive robust control to handle uncertainties within the system. The quadrotor UAV is innovatively segmented into three subsystems. Using the Udwadia–Kalaba (U–K) equation’s cascading and clustering features, we transform desired trajectories into constraints and integrate them with structural morphing constraints. This provides a direct analytical solution for constraint forces, which is immediately applicable to subsequent control design. This control consists of a nominal control part and an adaptive robust control part. Additionally, we only require that the uncertainty is bounded. The designed adaptation law is leaky, and adaptive parameters are adjusted based on the system’s performance to compensate for uncertainties within the system. The efficacy of the proposed modeling and control approaches is validated through simulation results.

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.

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.

Transparent Structures with a Fast De‐Stiffening Functionality

The majority of natural organisms interact with their environments with a degree of mechanical adaptability that allows them to carry out a variety of tasks and adapt to changing circumstances. Human‐made structures, however, lack this versatility and are normally designed to fulfill a certain load‐carrying requirement. This causes limitations in performance, efficiency, and safety. The aim of this article is to present rapid de‐stiffening in the response of conventional structures, without compromising the load‐bearing capacity. This has been achieved by developing an active interface using an interconnected nanostructured metallic network. A very fast heating rate with an average of ≈45 °C s−1 under 4.8 V excitation while retaining transparency of 67% is demonstrated. The embedded metallic network in a thermoplastic matrix has been deployed as an active interface, in a conventional transparent multilayered structure. Upon activation, it provides a rapid (i.e., 2 s after activation) mechanical de‐stiffening capability. The results from finite element modeling have been found to be in good agreements with those from experiments. The rapid reversible stiffness tuning demonstrated here can be implemented in variety of multilayered structures with a wide range of applications in robotics, morphing and deployable structures, active damping, and active impact safety systems.

A Magnet‐Driven Soft Bistable Actuator

AbstractBistable morphing structures are widely used as actuation mechanisms in soft actuators, soft robotics, energy absorbers, mechanical computers, optical lenses, metamaterials, and flexible electronics. However, untethered actuators, repetitive actuators, and hybrid‐assembly (containing in‐plane‐assembly and out‐of‐plane‐assembly) actuators remain challenging to realize using existing bistable structures, which hinders the novel application of such actuators in research, engineering, and daily life. This problem is solved by fabricating a magnet‐driven soft bistable actuator (MSBA) unit. The self‐buckling of the circular polydimethylsiloxane (PDMS) sheet ensures the bistability of the actuator and allows it to operate as an independent unit, free of external constraints. The reorientation of neodymium‐iron‐boron (NdFeB) microparticles embedded in the PDMS sheet enables the dome‐shaped actuators to exhibit repetitive snapping under the stimulus of a direction‐switching magnetic field. The potential of this MSBA unit in bionics, electronics, and biomechanics applications is demonstrated in systematic studies involving modification of the buckling deflection and magnetic moment density. The MSBA unit exhibits excellent performance in hybrid designs and intelligent systems.

A comprehensive formulation for determining static characteristics of mosaic multi-stable composite laminates under large deformation and large rotation

Multi-stable composite laminates are composite materials that exhibit multi-stable states, making them highly suitable for use in morphing structures. These materials are capable of maintaining each stable state without expending any energy. As a result, they are used extensively in numerous applications and garnered the interest of scholars and aerospace organizations. In the context of practical applications, such as morphing structures, it is insufficient for designers to rely solely on common bi-stable composite laminates that exhibit large deformations and medium rotations to achieve their desired objectives. Consequently, based on the objectives of the design, there are two potential resolutions to address this limitation. A designer may utilize mosaic multi-stable composite laminates to achieve a morphing structure that exhibits high flexibility, significant deformation, and substantial rotation. The utilization of a series connection between a bi-stable composite laminate and a symmetric composite laminate results in the formation of a mosaic bi-stable composite laminate with variable stiffness. Furthermore, the amalgamation of two asymmetric composite laminates with inverted orientations engenders a mosaic tri-stable composite laminate. The present research examines the static characteristics of mosaic bi-stable and tri-stable composite laminates. It also seeks to analyze the factors affecting the behavior of these types of laminates. A geometrically exact model was formulated for this objective. Apart from the geometrically exact model, a widely used and uncomplicated model relying on the conventional Classical Laminated-Plate Theory (CLPT) and Von-Karman nonlinear strains was employed. The proposed models were validated through finite element simulations. The system's static equations were derived using the virtual work principle and the Rayleigh-Ritz method. The present study examines and explores quasi-static snap-through behavior between stable states through the application of concentrated forces. The findings indicate a high level of concurrence between the outcomes derived from the geometrically exact model and the finite element analyses, particularly in composite laminates exhibiting significant deformations and rotations.

Bio-inspired facile strategy for programmable osmosis-driven shape-morphing elastomer composite structures.

Achieving programmable and reversible deformations of soft materials is a long-standing goal for various applications in soft robotics, flexible electronics and many other fields. Swelling-induced shape morphing has been intensively studied as one of the potential mechanisms. However, achieving an extremely large swelling ratio (>1000% in volume) remains challenging with existing swellable soft materials (e.g., hydrogels and water-swellable rubbers). Inspired by the shape change enabled by the osmosis-driven swelling in living organisms, herein, we report a polymer composite system composed of fine sodium chloride (NaCl) particles embedded in Ecoflex00-10 polymer. This Ecoflex00-10/NaCl polymer composite can achieve controllable volumetric swelling up to 3000% while maintaining a relatively high elastic stiffness. We demonstrate that this swellable polymer composite can serve as an active component to drive the shape morphing of various structures. By controlling the geometric design and the fraction of the NaCl particle, morphing structures capable of deforming sequentially are created. Finally, by encapsulating 3D printed polymer composite patterns using water-permeable PDMS membrane, a programmable braille with visual and tactile regulation is demonstrated for the purpose of information encryption. Our study provides a facile approach to generate customizable shape-morphing structures, aiming to broaden the range of techniques and applications for morphing devices.

Error analysis and correction method of multi-core fiber sensing

To meet the application requirements of accurate shape sensing for biomedical robotics and flexible morphing structure of aircraft etc, the error analysis and correction method for multi-core fiber is proposed. First, the relationship between the central wavelength shift and curvature of the multi-core fiber is analyzed which is based on the principle of multi-core fiber shape sensing, and a temperature decoupling method was researched. Considering the influence of the fiber structural parameters on curvature sensing, which is simulated by using the Monte Carlo method, and the simulation results show a strong influence among them. Next, to reduce the sensing errors introduced by the structural parameters, an error correction method based on regularized multilayer perceptron (MLP) networks is investigated, the proposed method does not require precise structural parameters of the multi-core fiber. Finally, some experiments with different curvatures are carried out, the results showed that the maximum root mean square error (RMSE) decreases from 2.03 m−1 to 0.007 m−1, and the minimum RMSE decreases from 0.01 m−1 to 0.001 m−1. The method this paper proposed has potential applications in shape sensing in the fields of biomedical engineering and aerospace.

Nonlinear Vibration Analysis of Bistable Morphing Composite Laminated Shell Based on High-Dimensional Dynamical Model

The bistable morphing composite laminated shell presents promising potential for aerospace morphing structures design, as it is capable of shape-changing under small energy inputs and maintaining two stable states without external loading. The bistable nonlinearity is distinct from the typical geometrical nonlinearity, as it arises from thermal residual stresses that cannot be equalized. During the derivation of a three-degree-of-freedom nonlinear dynamic model, Sanders’ nonlinear strain is incorporated into the strain–displacement relationship, while thermal residual stresses are taken into account in the constitutive relationship. The nonlinear dynamic model effectively captures the snap-through phenomena with orthogonal asymmetry in bistable morphing composite laminated shells. In order to reveal the resonance response and chaotic characteristics due to the interaction of vibrations between degrees of freedom, high-dimensional nonlinear dynamical model is derived by multiple scales method based on the 1:1:1 internal resonance relationship. The resonance response curves reflect the parametric influence law of the dynamical system stability. The nonlinear dynamic behaviors are described by the bifurcation diagrams and the maximum Lyapunov exponent. The significant motions under particular excitation conditions are visualized by phase portraits, time histories and Poincaré maps.

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.

Multiscale Heterogeneous Polymer Composites for High Stiffness 4D Printed Electrically Controllable Multifunctional Structures.

4D printing is an emerging field where 3D printing techniques are used to pattern stimuli-responsive materials to create morphing structures, with time serving as the fourth dimension. However, current materials utilized for 4D printing are typically soft, exhibiting an elastic modulus (E) range of 10-4 to 10MPa during shape change. This restricts the scalability, actuation stress, and load-bearing capabilities of the resulting structures. To overcome these limitations, multiscale heterogeneous polymer composites are introduced as a novel category of stiff, thermally responsive 4D printed materials. These inks exhibit an E that is four orders of magnitude greater than that of existing 4D printed materials and offer tunable electrical conductivities for simultaneous Joule heating actuation and self-sensing capabilities. Utilizing electrically controllable bilayers as building blocks, a flat geometry that morphs into a 3D self-standing lifting robot is designed and printed, setting new records for weight-normalized load lifted and actuation stress when compared to other 3D printed actuators. Furthermore, this ink palette is employed to create and print planar lattice structures that transform into various self-supporting complex 3D shapes. Finally these inks are integrated into a 4D printed electrically controlled multigait crawling robotic lattice structure that can carry 144 times its own weight.

Shape Morphing of Tubular Structures with Tailorable Mechanical Properties

Tubular structures are in high demand in robotics, medicine, and electronics. They are expected to match different shapes under loading and simultaneously exhibit certain mechanical behavior, e.g., specific radial strength and local flexibility, that poses a complex engineering design task. Herein, strategies to achieve programmable shape morphing in patterned tubular structures are explored, whose mechanical properties for all types of deformation modes can be tailored on demand. The general design problem is formulated, and the programmable response for fundamental—expansion, bending, and twisting—modes activated by tension and pressurization is demonstrated. The design problem for expansion modes is solved analytically; the numerical results agree well with the experimental data for stereolithography three‐dimensional printed cellular tubes. The effects of loading and boundary conditions on the deformed shapes and the structural mechanical response are analyzed. Algorithm‐based design strategies are proposed to achieve quantitative and automatic design for complex deformation modes. The possible use of the proposed structures is also discussed with respect to several applications. The findings pave the way for multifunctional tubular structures by exploring the pluridimensional space of the geometric parameters of metamaterial patterns.

Multishape Programming of Shape Memory Polymer Assemblies Fabricated by Vat Photopolymerization-Based 3D Printing and Interfacial Welding.

The combination of three-dimensional (3D) printing and shape memory polymers (SMP) enables programmable shape morphing of complex 3D structures, which is commonly termed four-dimensional (4D) printing. The process requirements of vat photopolymerization-based 3D printing impose limitations on the molecular structure design of SMPs, making it challenging to achieve triple- or multiple-shaped memory effects. Herein, we printed SMPs with different Tg values and obtained an SMP assembly through interfacial welding. The welding process is facilitated by the dynamic exchange of hindered urethane bonds at the interface. The resulting SMP assembly exhibits a quadruple shape memory effect, enabling programmable sequential deformation. The advantage of this approach is that the molecular design and the corresponding thermodynamic properties of different welding SMP components can be independently adjusted, enabling a greater range of shape and functional variations in the final 3D SMP assembly.

Design and Characterization of Deformable Superstructures Based on Amine-Acrylate Liquid Crystal Elastomers.

Deformable superstructures are man-made materials with large deformation properties that surpass those of natural materials. However, traditional deformable superstructures generally use conventional materials as substrates, limiting their applications in multi-mode reconfigurable robots and space-expandable morphing structures. In this work, amine-acrylate-based liquid crystal elastomers (LCEs) are used as deformable superstructures substrate to provide high driving stress and strain. By changing the molar ratio of amine to acrylate, the thermal and mechanical properties of the LCEs are modified. The LCE with a ratio of 0.9 exhibited improved polymerization degree, elongation at break, and toughness. Besides an anisotropic finite deformation model based on hyperelastic theory is developed for the LCEs to capture the configuration variation under temperature activation. Built upon these findings, an LCE-based paper-cutting structure with negative Poisson's ratio and a 2D lattice superstructure model are combined, processed, and molded by laser cutting. The developed superstructure is pre-programmed to the configuration required for service conditions, and the deformation processes are analyzed using both experimental and finite element methods. This study is expected to advance the application of deformable superstructures and LCEs in the fields of defense and military, aerospace, and bionic robotics.

Molecular investigation on temperature-dependent mechanical properties of PMMA/CNT nanocomposite

Carbon nanotube (CNT)-reinforced poly (methyl methacrylate) (PMMA) composite is subjected to changing temperature levels when used in aerospace field, which leads to the morphing structure and changing properties, and even structural failure. In this paper, the temperature effect on the structure and properties of PMMA/CNT nanocomposite with different CNT volume fractions is investigated using molecular dynamics (MD) simulation. It is measured that with increasing temperature from 100 to 500 K, the longitudinal, transverse, and shear moduli of PMMA/CNT nanocomposite decrease by 30 %, 45 %, and 62 %, respectively, while the coefficient of thermal expansion (CTE) increases by 27 %. It is found that the atom distribution becomes more dispersed and the nanocomposite structure turns to looser, which lead to the weakened properties of the nanocomposite. Based on the MD results, the efficiency parameters of PMMA/CNT nanocomposite are derived using extended rule of mixtures (EROM), which are used to predict the mechanical properties of nanocomposite at different temperatures. The revealed temperature-dependent mechanical properties and the underlying mechanisms contribute to the understanding of performance changes of PMMA/CNT nanocomposite under the temperature effect, which provide references for the application of composite materials in the aerospace field where the changing temperatures are of highly concern.

Liquid Crystal Elastomer-Liquid Metal Composite: Ultrafast, Untethered, and Programmable Actuation by Induction Heating.

Liquid crystal elastomers (LCEs) are a class of stimuli-responsive materials that have been intensively studied for applications including artificial muscles, shape morphing structures, and soft robotics due to their capability of large, programmable, and fully reversible actuation strains. To fully take advantage of LCEs, rapid, untethered, and programmable actuation methods are highly desirable. Here, a liquid crystal elastomer-liquid metal (LCE-LM) composite is reported, which enables ultrafast and programmable actuations by eddy current induction heating. The composite consists of LM sandwiched between two LCE layers printed via direct ink writing (DIW). When subjected to a high-frequency alternating magnetic field, the composite is actuated in milliseconds. By moving the magnetic field, the eddy current is spatially controlled for selective actuation. Additionally, sequential actuation is achievable by programming the LM thickness distribution in a sample. With these capabilities, the LCE-LM composite is further exploited for multimodal deformation of a pop-up structure, on-ground omnidirectional robotic motion, and in-water targeted object manipulation and crawling.

Fatigue performance evaluation of bistable composites at different combinations of loading and environmental conditions

Bistable composite laminates have large-scale applications in morphing and energy-harvesting structures, but their fatigue performance remains largely unexplored. This study investigates the stiffness and damage progression and evaluates bistable performance to develop protocols for long-term applications. We analyze the effects of displacement-controlled fully reversible high cycle fatigue-loading on stiffness, damage, curvature, and snap-through load in the out-of-plane loading direction at eight different combinations of parameters with frequency from 1 to 10 Hz, two boundary conditions, and temperature from 22°C to 150°C up to 3 to 10 million cycles. Stiffness and damage evolution analysis demonstrate the first two stages in out-of-plane fatigue loading. The study proposes a damage definition in terms of load adapting with two fatigue damage models: (1) Shiri Model and (2) Wu Model, while both models exhibit reasonable accuracy in predicting damage for the first two stages despite deviating at the final cycle due to assuming this cycle as the final failure cycle. Of the two models, the Shiri model provided a smaller range of model parameter values, 0.22 and 0.43, for parameters p and q, respectively, which reflects adjustability to different test conditions by maintaining a moderate range. Specimens encountered no final failure by fiber breakage and did not lose bistability for any combination. Curvature and snap-through load measurements have not substantially changed due to fatigue loading. These findings confirm application protocols with a broad range of parameters for which the laminates can operate without significant fatigue damage and maintain their bistable performance for an infinite lifetime.

Analysis of clustered cable-actuation strategies of V-Expander tensegrity structures

This study presents an analysis method to design cable-actuated clustered V-Expander tensegrity elementary cells based on the nonlinear tensegrity statics. Clustered actuation takes advantage of the presence of cable elements in a tensegrity structure by allowing cables to run over frictionless joints. The study first provides the nonlinear static equations of clustered tensegrity structures. Then, it introduces the topology of V-Expander tensegrity elementary cells, which vary in complexity and aspect ratio. To achieve cable actuation, specific sets of cables are chosen from the complete pool of cables to serve as the active elements of V-Expander cells. During actuation, the length of these active cables decreases. The actuation efficiency of each specific choice of active cable is computed to find the optimal actuation strategy. The proposed approach can be utilized to analyze and design other types of cable-driven tensegrity structures, with applications to morphing structures and soft robots.