Elastic Energy Storage Research Articles

A high-entropy alloy showing gigapascal superelastic stress and nearly temperature-independent modulus.

High-performance superelastic materials with a combination of high superelastic stress, large elastic recovery strain, and stable elastic modulus over a wide temperature range are highly desired for a variety of technological applications. Unfortunately, it is difficult to achieve these multi-functionalities simultaneously because most superelastic materials have to encounter the modulus softening effect and the limited superelastic stress, whereas most Elinvar-type materials show small elastic strain limit. Here, we report a (TiZrHf)44Ni25Cu15Co10Nb6 high-entropy alloy that meets all these requirements. This alloy also shows good cyclic stability, thermally-stable capacity for elastic energy storage, high micro-hardness and good corrosion resistance, allowing it to operate stably in hostile environments. We show that its multi-functionalities stem from a natural composite microstructure, containing a highly-distorted matrix phase with strain glass transition and various structural and compositional heterogeneities from micro- to nano-scale. Our findings may provide insight into designing high-entropy alloys with unconventional and technologically-important functional properties.

Experimental Research on Characterizing Elastic–Plastic Mixed‐Mode Crack Extension Based on Ultimate Elastic Strain Energy Storage

ABSTRACTThis paper proposes a new insight into describing elastic–plastic mixed‐mode crack extension based on ultimate elastic strain energy storage (ESES). The experimental fixture and specimen are specially designed and processed, and a series of experiments of mixed‐mode I–II crack extension are conducted with different loading angles. It is found that the ultimate ESES invariably decreases as the crack length increases during mixed‐mode crack extension with different loading angles, whereas the ultimate elastic strain energy storage release rate (ESESRR) is demonstrated to be stable in various loading angles. Moreover, the magnitude of the initial ultimate ESES can measure the difficulty of crack initiation, and its value is affected by loading conditions and specimen shape. Eventually, the theoretical and experimental values of the ultimate ESESRR fit well by excluding three nonnegligible physical factors. Therefore, the ultimate ESESRR provides a new perspective to characterize mixed‐mode I–II crack extension in elastic–plastic materials.

Shear localisation controls the dynamics of earthquakes

Earthquakes are produced by the propagation of rapid slip along tectonic faults. The propagation dynamics is governed by a balance between elastic stored energy in the surrounding rock, and dissipated energy at the propagating tip of the slipping patch. Energy dissipation is dictated by the mechanical behaviour of the fault, which is itself the result of feedbacks between thermo-hydro-mechanical processes acting at the mm to sub-mm scale. Here, we numerically simulate shear ruptures using a dual scale approach, allowing us to couple a sub-mm description of inner fault processes and km-scale elastodynamics, and show that the sudden localisation of shear strain within a shear zone leads to the emergence of classical cracks driven by a constant fracture energy. The fracture energy associated to strain localisation is substantially smaller than that predicted in theoretical and numerical models assuming uniform shearing within the shear zone. We show the existence of a unique scaling law between the localised shearing width and the rupture speed. Our results indicate that earthquakes are likely to be systematically associated to extreme strain localisation.

A stick-slip piezoelectric actuator with large stepping displacement

Piezoelectric actuators have gained widespread attention for their quick response, low energy consumption, and resistance to electromagnetic interference. However, current piezoelectric actuators face challenges in achieving large stepping displacement within compact spaces owing to the small output of individual piezoelectric elements. To address this issue, a stick-slip piezoelectric actuator based on the lever and triangular coupling amplification principle is proposed in this study. The improved lever and triangular amplification mechanisms significantly enhance the forward displacement during the stick stage. Owing to the unique slender flexible driving foot design of the triangular amplification section, the coupled triangular amplification mechanism can store elastic potential energy during the stick stage without compromising structural compactness. This energy is then released during the slip stage to counteract the sliding friction, enabling the actuator to achieve a sudden increase in characteristics. The displacement amplification effect of the flexible hinge mechanism is examined through theoretical calculations and simulations. The experimental results confirm that the proposed actuator can achieve large stepping displacement and high stepping performance factors under low-frequency conditions. Specifically, at a voltage of 100 V and frequency of 10 Hz, the stepping displacement and stepping performance factor reached 144 μm and 1.44 μm/V, respectively. Owing to the increased stepping displacement, the actuator achieved a maximum speed of 99.1 mm/s at 800 Hz. These features demonstrate the tremendous potential of the proposed actuator in various applications.

Multifunctional Phase Change Films with High Mechanical Strength, Thermally Induced Switchable Adhesion, and Shape Recoverability for Infrared Stealth.

The application of organic solid-liquid phase change materials (PCMs) is limited for the leakage problem after phase change and high rigidity. In this work, a novel flexible solid-solid PCM (DXPCM) was synthesized using a block copolymerization process with polyethylene glycol (PEG) as the energy storage segment. The phase transition temperature (from 36.2 to 49.4 °C) and enthalpy (from 83.27 to 123.35 J/g) of DXPCM could be changed through adjusting the molecular weight of PEG. The introduction of hard chain segments endowed DXPCM with excellent flexibility, foldability, and mechanical properties at room temperature. The large number of internal hydrogen bonds and π-π stacking provided DXPCM with interesting thermally induced switchable adhesion and recyclability. The storage and release of elastic potential energy ensured that DXPCM could recover its original shape after being deformed by external forces. It is worth mentioning that DXPCM exhibits excellent infrared stealth capability as it can absorb and release latent heat for a long period of time. In conclusion, this work developed a novel solid-solid phase change film with high mechanical strength, thermally induced switchable adhesion, and shape recovery capability, which has great potential for application in infrared stealth.

4D printing of biodegradable intestinal drug delivery devices with shape-memory effect.

Expanding devices designed to physically facilitate the permeation of drugs across the gastrointestinal mucosa are gaining attention for the oral delivery of therapeutic macromolecules. The ideal system should be biodegradable with latex-like properties, allowing it to withstand gut movement without breaking prematurely and preventing intestinal obstruction or damage. A highly foldable and elastic device is desirable because it can fit into commercial capsules by being compressed into confined spaces. However, this compression has limits due to the device's tendency to spring back to its original shape driven by stored elastic energy after deformation. This challenge can be addressed by using shape-memory polymers. In this work, we report a photo-crosslinkable resin suitable for 3D printing by digital light processing that yields an elastomer with latex-like properties, shape-recovery at body temperature, and degradation within 6h under simulated intestinal conditions. Thermal shape-memory was conferred by adding stearyl(acrylate) to poly(β-aminoester)-based inks, achieving high elasticity (>700%) and strength (>7.5MPa), along with strain-hardening properties.

Foldable piecewise linear origami that approximates curved tile origami

Curved origami featuring curved tiles can store elastic energy and bias the structure toward a desired shape when subjected to appropriate constraints. Without constraints, however, a curved origami structure generally has infinitely many degrees of freedom. For engineering applications in which a particular folding motion is desired, a great many constraints have to be introduced. One natural strategy to reduce degrees of freedom is to discretize curved origami into piecewise linear origami while closely approximating the desired curved folding motion. Then, as we show, the degrees of freedom are vastly reduced (typically to one DoF in cases where the folding angle at the crease is not trivial, and excluding overall rigid body motions). In this paper we present a Lagrangian approach for constructing curved origami structures which is complementary to our approach in Liu and James (2024). Then, we generalize this approach to allow quite general curved creases. We outline a way to discretize curved crease patterns and present two optimization methods to refine these patterns. Our approach ensures that the deformed piecewise linear origami closely matches the folding angles and crease configurations of the curved origami. Piecewise linear origami structures that approximate curved origami offer promising potential for architectural and robotic design applications. They also give an efficient way to design desired smooth structures by optimizing finite-dimensional piecewise linear structures.

Ultrahigh Elastic Energy Storage in Nanocrystalline Alloys with Martensite Nanodomains.

Elastic materials that store and release elastic energy play pivotal roles in both macro and micro mechanical systems. Uniting high elastic energy density and efficiency is crucial for emerging technologies such as artificial muscles, hopping robots, and unmanned aerial vehicle catapults, yet it remains a significant challenge. Here, a nanocrystalline structure embedded with elliptical martensite nanodomains in ferroelastic alloys wasutilized to enable high yield strength, large recoverable strain, and low energy dissipation simultaneously. As a result, the designed Ti-Ni-V alloys demonstrate ultrahigh energy density (>40 MJ m-3) with ultrahigh efficiency (>93%) and exceptional durability. This concept, which combines nano-sized embryos to minimize energy dissipation of psuedo-elasticity and employs a fine-grained structure to enhance yield strength, can be applied to other ferroelastic materials. Furthermore, it holds promise for the development of phase transformation-involved functionalities such as high-performance dielectric energy storage, ultralow-hysteresis magnetostrain, and high-efficiency solid-state caloriccooling.

Stability‐Enhanced Variable Stiffness Metamaterial with Controllable Force‐Transferring Path

AbstractSelf‐contact variable stiffness (SVS) metamaterial offers specific patterns of elastic strain energy storage by changing its force‐transferring path. The change of the elastic strain energy storage patterns further influences the stiffness variation of the SVS metamaterials. However, challenges still arise because typically fabricated SVS metamaterials inevitably contain structural irregularities, eccentricities, and defects. These microstructural imperfections impede the stable generation of designed strain energy storage patterns in the metamaterial, implying that the SVS metamaterials cannot achieve expected stiffness variations. To address this burning question, an SVS metamaterial/meta‐structure design paradigm with eccentric unit designs is proposed, which can realize both stable stiffness variations and high load‐bearing. The theoretical, simulation, and experimental results demonstrate that the SVS chain meta‐structure achieves ≈110 times stiffness variation between the low and high loading conditions. Its load‐bearing can reach more than 1500 N when the meta‐structure falls into the high stiffness stage. Furthermore, some typical functions are demonstrated using the stability‐enhanced SVS metamaterial, including customized mechanical protections for human joints and information transformation regulated by remote mechanical input signals. The results can provide a useful solution for generating a more feasible stability‐enhanced SVS metamaterial/meta‐structure and promote their potential applications in aerospace, medical devices, and robotics.

Comparison of Experimental and Numerical Investigation of Mono-Composite and Metal Leaf Spring

The automotive industry is increasingly focused on reducing vehicle weight, leading to the widespread adoption of composite materials with high strength-to-weight ratios in both aviation and automotive sectors. These materials are gradually replacing traditional options like steel. Leaf springs, one of the oldest and most common suspension components, continue to be widely used in vehicles. This study aims to replace conventional multi-leaf steel springs with mono-composite leaf springs while preserving the same load-carrying capacity and stiffness. Composite materials, such as glass fiber and epoxy resin, provide advantages including higher elastic strain energy storage, superior strength-to-weight ratios, and enhanced corrosion resistance compared to steel. Consequently, the weight of leaf springs can be reduced without sacrificing performance. The steel and mono-composite leaf springs were modeled using Catia software, and their performance was evaluated using ANSYS 15.0 software.

Failure behaviors of anisotropic shale with a circular cavity subjected to uniaxial compression

Layered rock formations are frequently encountered during the excavation of underground structures. The stability of such structures is influenced not only by the stress concentration caused by the cavities in the strata but also by the anisotropy of the layered rock mass. The interaction between them can lead to critical structural failure, such as rupture, collapse, or significant deformation within the adjacent rock mass, thereby jeopardizing operational safety. However, the coupling law and mechanism between the stress concentration resulting from the cavities and the anisotropy of a layered rock mass remain unclear. In this study, a uniaxial compression test was performed on shale specimens containing a circular hole to investigate the effects of layer inclination and circular holes on the mechanical properties, elastic energy storage, and failure behaviors of these specimens. The failure mechanism of the rock surrounding the hole was analyzed on the basis of the single plane of weakness theory and the Kirsch solution. The test results indicated pronounced anisotropy in the compressive strength, elastic modulus, and elastic strain energy of the specimens, with distinct “V”, “M” and “U”-shaped patterns correlated with varying layer inclination angles. In addition, the combined effect of stress concentration and layer inclination resulted in different failure types, which were classified into four groups according to their failure behavior. Theoretical analysis revealed that failure around circular holes in layered rock is affected by a range of variables, such as layer inclination, layer strength, lateral pressure coefficient, azimuth, and loading stress.

Effects of Inertial Flywheel Training vs. Accentuated Eccentric Loading Training on Strength, Power, and Speed in Well-Trained Male College Sprinters.

This study aimed to evaluate and compare the effects of inertial flywheel training and accentuated eccentric loading training on the neuromuscular performance of well-trained male college sprinters. Fourteen sprinters were recruited and randomly assigned to either the flywheel training (FWT, n = 7) group or the accentuated eccentric loading training (AELT, n = 7) group. The FWT group completed four sets of 2 + 7 repetitions of flywheel squats, whereas the AELT group performed four sets of seven repetitions of barbell squats (concentric/eccentric: 80%/120% 1RM). Both groups underwent an eight-week squat training program, with two sessions per week. A two-way repeated ANOVA analysis was used to find differences between the two groups and between the two testing times (pre-test vs. post-test). The results indicated significant improvements in all measured variables for the FWT group: 1RM (5.0%, ES = 1.28), CMJ (13.3%, ES = 5.42), SJ (6.0%, ES = 2.94), EUR (6.5%, ES = 4.42), SLJ (2.9%, ES = 1.77), and 30 m sprint (-3.4%, ES = -2.80); and for the AELT group: 1RM (6.3%, ES = 2.53), CMJ (7.4%, ES = 3.44), SJ (6.4%, ES = 2.21), SLJ (2.2%, ES = 1.20), and 30 m sprint (-3.0%, ES = -1.84), with the exception of EUR (0.9%, ES = 0.63, p = 0.134), showing no significant difference. In addition, no significant interaction effects between group and time were observed for 1RM back squat, SJ, SLJ, and 30 m sprint (p > 0.05). Conversely, a significant interaction effect between group and time was observed for both CMJ and EUR (p < 0.001); post hoc analysis revealed that the improvements in CMJ and EUR were significantly greater in the FWT group compared to the AELT group (p < 0.001). These findings indicate that both FWT and AELT are effective at enhancing lower-body strength, power, and speed in well-trained male college sprinters, with FWT being particularly more effective in promoting elastic energy storage and the full utilization of the stretch-shortening cycle.

A coupled crystal inelasticity-phase field model for crack growth in polycrystalline nitinol microstructures

Abstract This paper introduces a comprehensive computational framework, comprising a finite deformation crystal inelasticity constitutive model and phase field model, for modeling crack growth in superelastic nitinol polycrystalline microstructures. The crystal inelasticity model represents crystal stretching and lattice rotation from elastic mechanisms, as well as local inelastic deformation due to austenite-martensite phase transformation. The phase field formulation decomposes the Helmholtz free energy density into stored elastic energy, phase transformation energy, and crack surface energy components. The elastic energy accounts for tension-compression asymmetry with the formation of the crack through a spectral decomposition. Kinetic Monte Carlo simulations generate equilibrium area fractions of different surface orientations, which serve as weights for the surface energy. An adaptive wavelet-enhanced hierarchical finite element (FE) model is introduced to alleviate high computational overhead in phase field crack simulations. Simulations with the coupled inelasticity phase field model are conducted under various loading conditions including Mode-I tension, a quasi-static Kalthoff experiment, and cyclic loading of polycrystalline microstructures. Crack propagation is effectively predicted by this model, providing valuable insights into the material mechanical behavior with growing cracks.

Kinematic synthesis and mechanism design of a six-bar jumping leg for elastic energy storage and release based on dead points

Small jumping robots widely adopt complex catapult mechanisms. This paper presents a novel jumping strategy using dead point instead of traditional catapult mechanisms, achieving efficient energy storage and release without increasing mechanical complexity. Single degree-of-freedom (DOF) planar six-bar linkages are widely used in bionic mechanism design due to their simple control and strong design flexibility. However, their complex configuration and numerous parameters make it challenging to carry out multi-objective and multi-constraint designs. In this paper, a design method of single DOF six-bar linkages based on dead-point constraints is proposed to design a frog-inspired leg mechanism. By enumerating the basic configuration atlas and using a stepwise closed-loop method, initial value screening is completed to improve the efficiency of objective function optimization. The dead-point constraints are simplified with graphical geometric properties. The resulting mechanism satisfies multiple objectives and constraints, including shape, motion posture and trajectory, demonstrating the feasibility of the method. Simulations and experiments confirmed the excellent jumping performance of the 147.1-g prototype, with a jump height of 8.55 times leg length and an energy-storing capacity of 35.39 J/kg.

Bistable soft jumper capable of fast response and high takeoff velocity.

In contrast with jumping robots made from rigid materials, soft jumpers composed of compliant and elastically deformable materials exhibit superior impact resistance and mechanically robust functionality. However, recent efforts to create stimuli-responsive jumpers from soft materials were limited in their response speed, takeoff velocity, and travel distance. Here, we report a magnetic-driven, ultrafast bistable soft jumper that exhibits good jumping capability (jumping more than 108 body heights with a takeoff velocity of more than 2 meters per second) and fast response time (less than 15 milliseconds) compared with previous soft jumping robots. The snap-through transitions between bistable states form a repeatable loop that harnesses the ultrafast release of stored elastic energy. On the basis of the dynamic analysis, the multimodal locomotion of the bistable soft jumper can be realized: the interwell mode of jumping and the intrawell mode of hopping. These modes are controlled by adjusting the duration and strength of the magnetic field, which endows the bistable soft jumper with robust locomotion capabilities. In addition, it is capable of jumping omnidirectionally with tunable heights and distances. To demonstrate its capability in complex environments, a realistic pipeline with amphibious terrain was established. The jumper successfully finished a simulative task of cleansing water through a pipeline. The design principle and actuating mechanism of the bistable soft jumper can be further extended for other flexible systems.

Increased force and elastic energy storage are not the mechanisms that improve jump performance with accentuated eccentric loading during a constrained vertical jump.

Accentuated eccentric loading (AEL) involves higher load applied during the eccentric phase of a stretch-shortening cycle movement, followed by a sudden removal of load before the concentric phase. Previous studies suggest that AEL enhances human countermovement jump performance, however the mechanism is not fully understood. Here we explore whether isolating additional load during the countermovement is sufficient to increase ground reaction force, and hence elastic energy stored, at the start of the upward movement and whether this leads to increased jump height or power generation. We conducted a trunk-constrained vertical jump test on a custom-built device to isolate the effect of additional load while controlling for effects of squat depth, arm swing, and coordination. Twelve healthy, recreationally active adults (7 males, 5 females) performed maximal jumps without AEL, followed by randomised AEL conditions prescribed as a percentage of body mass (10%, 20%, and 30%), before repeating jumps without AEL. No significant changes in vertical ground reaction force at the turning point were observed. High load AEL conditions (20% and 30% body weight) led to slight reductions in jump height, primarily due to decreased hip joint and centre of mass work. AEL conditions did not alter peak or integrated activation levels of the knee extensor muscles. The constrained movement task used here, which excluded potential contributions of trunk motion, arm swing, rate of descent, squat depth, and point of load application, allows the conclusion that increased elastic energy return is not the primary mechanism for potentiating effects of AEL on jump performance.

Research on the biomimetic quadruped jumping robot based on an efficient energy storage structure

AbstractThe ability of quadruped robots to overcome obstacles is a critical factor that limits their practical application. Here, a design concept and a control algorithm are presented that aim at enhancing the explosive force of quadruped robots during jumping by utilizing elastic energy storage components. The hind legs of the quadruped robot are designed as energy storage units. Tension springs are utilized as components for storing energy and are installed in a parallel structure on the hind leg. Energy is stored during the compression process of the robot’s torso and released during the jumping phase. The optimal foot force is calculated using a single rigid body model. The mapping relationship between the force applied to the foot and the resulting joint torque is established by developing a dynamic model of the hind legs. Simulation experiments were conducted using the Webots physics engine to compare the impact of varying spring stiffness on joint torque during the jumping process. This study determined the optimal spring stiffness under specific conditions. The hind legs’ torque saving ratio reaches 19%, and the energy-saving ratio reaches 13%, which validates the effectiveness and feasibility of integrating elastic energy storage components.

Effect of temperature on the nanoindentation behavior of monocrystalline silicon by molecular dynamics simulations

Monocrystalline silicon (Si) undergoes complex phase transformations under external loads, significantly affecting its performance and processing. In this study, molecular dynamics (MD) simulations are performed from 1 to 900 K to explore temperature effects on the mechanical properties and deformation behavior of monocrystalline silicon during nanoindentation. Results indicate that hardness and elastic modulus decrease with rising temperature. At lower temperature, the activation of plastic deformation is delayed. The suddenly release of stored elastic energy manifests as a pop-in event. The indentation creates a quadruple symmetric phase transformation zone, primarily consisting of Si-II at the core, flanked by Si-XIII and bct-5. Increasing temperature advances the plastic deformation of the sample. High temperatures facilitate the formation and subsequent phase transformation of Si-XIII, reduce the stability of bct-5 during unloading, and promote the amorphization of silicon. At high temperatures, the dislocation of silicon nucleates at the subsurface, resulting in the formation of a substable phase. The anisotropy of deformation is evident from the atomic perspective, based on the orientation dependence of the phase transformation. This research provides new insights into the deformation behavior and phase transformations of monocrystalline silicon, supporting manufacturing and application of silicon products.

Fracture-driven power amplification in a hydrogel launcher.

Robotic tasks that require robust propulsion abilities such as jumping, ejecting or catapulting require power-amplification strategies where kinetic energy is generated from pre-stored energy. Here we report an engineered accumulated strain energy-fracture power-amplification method that is inspired by the pressurized fluidic squirting mechanism of Ecballium elaterium (squirting cucumber plants). We realize a light-driven hydrogel launcher that harnesses fast liquid vapourization triggered by the photothermal response of an embedded graphene suspension. This vapourization leads to appreciable elastic energy storage within the surrounding hydrogel network, followed by rapid elastic energy release within 0.3 ms. These soft hydrogel robots achieve controlled launching at high velocity with a predictable trajectory. The accumulated strain energy-fracture method was used to create an artificial squirting cucumber that disperses artificial seeds over metres, which can further achieve smart seeding through an integrated radio-frequency identification chip. This power-amplification strategy provides a basis for propulsive motion to advance the capabilities of miniaturized soft robotic systems.

Definitive engineering strength and fracture toughness of graphene through on-chip nanomechanics

Fail-safe design of devices requires robust integrity assessment procedures which are still absent for 2D materials, hence affecting transfer to applications. Here, a combined on-chip tension and cracking method, and associated data reduction scheme have been developed to determine the fracture toughness and strength of monolayer-monodomain-freestanding graphene. Myriads of specimens are generated providing statistical data. The crack arrest tests provide a definitive fracture toughness of 4.4 MPam\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{{{{{{\\rm{m}}}}}}}$$\\end{document}. Tension on-chip provides Young’s modulus of 950 GPa, fracture strain of 11%, and tensile strength up to 110 GPa, reaching a record of stored elastic energy ~6 GJ m−3 as confirmed by thermodynamics and quantized fracture mechanics. A ~ 1.4 nm crack size is often found responsible for graphene failure, connected to 5-7 pair defects. Micron-sized graphene membranes and smaller can be produced defect-free, and design rules can be based on 110 GPa strength. For larger areas, a fail-safe design should be based on a maximum 57 GPa strength.