Flexoelectric Energy Harvester Research Articles

Analysis of the electromechanical responses of sandwich circular nano-plate based on flexoelectric nano-ultrasonic transducer

Flexoelectric nano-ultrasonic transducer is an important development direction of ultra-high frequency ultrasonic transducers. The key to its development lies in addressing the electromechanical coupling dynamics of a flexoelectric nano-element, that is, sandwich circular nano-plate. In this paper, a novel dynamic theoretical model of sandwich circular nano-plate is developed based on the transversely isotropic flexoelectricity couple stress and Kirchhoff plate theories. Based on the novel model, this study demonstrates the influence of flexoelectricity effect and size effect on its electromechanical responses of the core component in the nano-ultrasonic transducer. Simultaneously, using finite element software, the paper presents the first six mode shapes of the structure and reveals the mode shape most conducive to the energy conversion of the transducer. The main objective of this study is to provide a theoretical foundation for the development of nano-ultrasonic transducers based on flexoelectric materials. The novel model can also be applied in various energy conversion devices, including flexoelectric actuator and flexoelectric energy harvesters.

Y2O3-doped BST flexoelectric ceramic energy harvester

The study employed the water-based casting technique to prepare BST sheets, which were then combined with PDMS to BST composite sheets for wind energy harvesting. By adding 0.3–1.2 mol% Y2O3 as an additive, the dielectric constant and the flexoelectric coefficient of the BST sheets were significantly enhanced. The Y2O3 and BST powders were mixed to form a casting slurry with the appropriate viscosity, which was then cast into a sheet. After the sintering process, silver electrodes were coated on both surfaces of the sheet. To enhance the flexibility of the sheet, PDMS was applied to the silver-coated surfaces, creating a "sandwich structure" composite sheet. The flexoelectric properties of the composite sheets are characterized utilized the micro cantilever beam method. The energy harvesting experiments, conducted in a simulated wind tunnel environment, demonstrate that the composite sheets exhibit varying flexoelectric properties and energy conversion efficiencies, depending on their thickness. When the doping amount of Y2O3 is 0.6mol%, the composite sheets with a BST layer thickness of 200 μm exhibit the highest flexoelectric coefficient of 1.1 μC/m; the composite sheets with a BST layer thickness of 100 μm exhibit the strongest current output capability of 4.2 nA. These findings indicate that the developed composite sheets could be promising for applications in renewable energy harvesting, particularly for capturing and converting wind energy into useable electrical power.

Nonlinear analysis of flexoelectric acoustic energy harvesters with Helmholtz resonator

This paper presents a Helmholtz Resonator-type Flexoelectric Acoustic Energy Harvester (HR-FAEH), composed of a Helmholtz Resonator (HR) and a double-sided Flexoelectric Disk Oscillator (FDO). The electromechanical governing equations, incorporating geometric nonlinearity, are derived using Hamilton's principle. Utilizing the multiscale method, we obtain the cavity sound pressure, oscillator displacement, and voltage output response, with validation through simulations in COMSOL. The study's innovation lies in the concurrent consideration of piezoelectric and flexoelectric effects, enhancing the system's performance. The inclusion of geometric nonlinearity, accounting for large deformations, enhances the model's accuracy under high sound pressure excitations. Our research unveils performance degradation in the Helmholtz Resonator-type acoustic energy harvester under elevated environmental sound pressure. The combination of nonlinear analysis and structural optimization effectively mitigates this degradation. In comparison to the non-optimized harvester, the maximum voltage output increases by 39.1 %, and expressions for the optimized model parameters are provided. Additionally, we conduct parameter analyses for the HR and the FDO, elucidating the impact and optimal values of parameters such as film coverage radius and load resistance on system performance.

Surface tension effect on flexoelectric energy harvesting based on extended isogeometric analysis

This study presents a numerical framework to model the effect of surface tension on a flexoelectric energy harvesting system with liquid inclusions. The equivalent Young’s modulus and Poisson’s ratio of the liquid inclusions embedded in flexoelectric composites considering the surface tension are derived for the first time. An extended isogeometric analysis (XIGA) based on non-uniform rational B-splines (NURBS) is developed to model and solve the electromechanical response of weak discontinuities in flexoelectric composites. The interface between liquid and solid materials is implicitly represented by the level set method. Several numerical examples are presented as linear dielectric solids embedded with liquid inclusions under mechanical compression and different electric circuit configurations, including square matrixes and truncated pyramids. The simulation results indicate that a significant enhancement in the electromechanical coupling coefficient can be obtained by considering the effect of surface tension in open- and closed-circuit configurations. The maximum electric potential and energy conversion are higher in the open-circuit configuration. In addition, the XIGA simulation shows that the energy conversion of the flexoelectric devices increases as the size of the structural system and Young’s modulus of the flexoelectric material decrease. The maximum energy conversion capability of the flexoelectric composite, including the effect of surface tension, is enhanced by 32.4% with a central inclusion and 57% or higher with random inclusions. Finally, the influence of the length scale on the flexoelectricity is analyzed.

On comprehensive nonlinear size-dependent analysis of nano-scale flexoelectric energy harvesters considering strain gradient, surface elasticity and thickness size effect

On comprehensive nonlinear size-dependent analysis of nano-scale flexoelectric energy harvesters considering strain gradient, surface elasticity and thickness size effect

An electro-mechanical dynamic model for flexoelectric energy harvesters

Flexoelectricity is a universal electro-mechanical coupling effect that occurs in dielectrics of all symmetric groups and becomes dominant at the micro- and nano-scales. It plays an important role in evaluating micro-electro-mechanical systems (MEMS) such as energy harvesters which convert vibrational energy to electric energy. At finer length scales, micro-inertia effects significantly contribute to the behavior of flexoelectric materials due to the mechanical dispersion. Hence, to properly characterize the vibrational behavior of MEMS, a reliable theoretical approach is required accounting for all possible phenomena that affect the output of the system such as voltage or power density. In this work, we present a consistent (dynamic) model and associated computational framework for flexoelectric structures to study the characteristics of the vibrational behavior of energy harvesters showing the dominance of the flexoelectric effect at micro- and nano-scales. In this context, we quantify the impact of the micro-inertia length scale and the flexoelectric dynamic parameter on both frequency and time responses of energy harvesters.

Anaerobe Syntrophic Co-culture-Mediated Green Synthesis of Ultrathin Niobium Carbide (NbC) Sheets for Flexoelectricity Generation

Niobium carbide (NbCx)-based materials have garnered significant attention in energy- and power-based applications. The physiochemistry-mediated preparation of two-dimensional (2D) NbC structures is often limited by extremely high-temperature and -pressure reaction conditions conjugated with toxic chemicals. In the present study, a unique biobased strategy, utilizing a solid–gas reaction, is developed, which involves the carburization of niobium salt (NbCl5)-based oxides using methane (CH4) and other metabolic gases produced by methanogen syntrophic culture. Thermodynamic calculations were performed to comprehend the reaction conditions of the biosystem during NbC formation. The bioprepared NbC sheets were found to be ∼10 nm thin and were studied for their potential in energy harvesting applications. The strain-induced charge generation was evaluated by fabricating a flexoelectric energy harvester with NbC sheets as a flexoelectric material. The maximum power output was ∼2.64 mW/m2 for 8.8 N applied force. We obtained clear evidence of flexoelectricity in NbC using Raman analysis. Finally, external pressure-, magnetic force-, and temperature-dependent responses were recorded to visualize the practical applications of NbC-based flexible flexoelectric nanogenerators in wearable electronics and sensing.

A computational framework for topology optimisation of flexoelectricity at finite strains considering a multi-field micromorphic approach

This paper presents a novel in-silico framework for the design of flexoelectric energy harvesters at finite strains using topology optimisation. The main ingredients of this work can be summarised as follows: (i) a micromorphic continuum approach is exploited to account for size dependent effects in the context of finite strains, thus permitting the modelling and simulation of flexoelectric effects in highly deformable materials such as dielectric elastomers. A key feature of the multi-field (mixed) formulation pursued is its flexibility as it permits, upon suitable selection of material parameters, to degenerate into other families of high order gradient theories such as flexoelectric gradient elasticity. (ii) A novel energy interpolation scheme is put forward, whereby different interpolation strategies are proposed for the various contributions that the free energy density function is decomposed into. This has enabled to circumvent numerical artifacts associated with fictitious high flexoelectric effects observed in the vicinity of low and intermediate density regions, where extremely high strain gradients tend to develop. (iii) A weighted combination of efficiency-based measures and aggregation functions of the stress is proposed to remedy the shortcomings of state-of-the-art efficiency-based functionals, which promotes the development of hinges with unpractical highly localised large strain gradients. Finally, a series of numerical examples are analysed, studying the development of direct flexoelectricity induced by bending, compression and torsional deformations.

Bending and Vibration Analysis of Flexoelectric Beam Structure on Linear Elastic Substrates.

With the development of micro-nanotechnology, smart electronic devices are being updated and developed, and more and more flexoelectric sensors, actuators, and energy harvesters attached to elastic substrates have attracted a surge of interest due to unique features at the nano-scale. In this paper, the static bending behavior and vibration characteristics of a flexoelectric beam structure based on a linear elastic substrate under a magnetic field environment are investigated. Based on the electrical Gibbs free energy density, the governing equations and boundary conditions of structures are derived by using the Euler–Bernoulli beam theory and the Hamilton’s variational principle. The expressions of the deflection and the induced electric potential of the beam structure are expressed analytically. The natural frequency of the beam under the open-circuit electrical conditions with surface electrodes (OCI) are obtained after further extending the solution. The results show that the flexoelectric effect, the linear elastic substrate, and the magnetic field have significant effects on the static bending and vibration behaviors of the flexoelectric beam which are beneficial for designing and developing flexoelectric devices with elastic substrates.

A finite element approach for flexoelectric nonuniform nanobeam energy harvesters

In this work, we present a finite element (FE) approach for analyzing flexoelectric beam energy harvesters with nonuniform cross-section. A two nodes finite element model with 10 degrees of freedom is proposed and Hermite polynomials are adopted to satisfy the higher order continuity requirement of the electric potential and displacement due to flexoelectricity. The proposed model can also be simplified to investigate a flexoelectric actuator, for which analytical solutions are obtained and thus can be used to validate the proposed FE method. Results indicate the performance of flexoelectric energy harvesters with nonuniform cross-section can exceed that of rectangular ones.

Comprehensive Review on Flexoelectric Energy Harvesting Technology: Mechanisms, Device Configurations, and Potential Applications

Comprehensive Review on Flexoelectric Energy Harvesting Technology: Mechanisms, Device Configurations, and Potential Applications

Flexoelectric energy harvesters utilizing controllably wrinkled micro-dielectric film

Self-powered electronic devices require energy harvesting systems to support their energy needs, but their energy harvesting efficiency seems still insufficient. In this paper, a flexoelectric energy harvester based on controllable wrinkling mechanism is theoretically proposed to enhance the energy harvesting efficiency. The dielectric film, partly bonded to a pre-stretched substrate, wrinkles after release to achieve controllable wavy shapes. A harmonic cyclic post-stretch is employed to stimulate the generation of electric charges. Meanwhile, an electrode-regrouping technique is resorted to optimize the energy harvesting efficiency. Formulation toward this problem includes both the flexoelectricity and piezoelectricity of dielectrics. Theoretical prediction indicates that electrode-regrouping technique can effectively act to relieve neutralization of the charges induced mainly by flexoelectricity and thus improve the energy harvesting efficiency of FEHs. A larger loading frequency and a lower resistance are preferred to optimize the effective power. The power density of the present FEHs is at least 1 orders of magnitude higher than that of vibrational FEHs under micro-scale. Meanwhile, with the scale shrinking below 100 nm, the energy density of the present FEHs may exceed 104W/m3 which is generally 2–4 orders of magnitude higher than that of most vibrational energy harvesters (including electrostatic, electromagnetic, piezoelectric types).

A wideband flexoelectric energy harvester based on graphene substrate

High efficiency and wide bandwidth are the main optimization directions for energy harvester. Based on flexoelectric theory, this paper presents a micro cantilever vibration energy harvester (VEH) with a broad bandwidth which achieved by collisions of two beams. The nanocrystalline graphene (NCG) is selected as base layer because its quality factor (Q factor) is highest compared with common materials, which means its energy loss in progress of power conversion is lowest and device has a high sensitivity to external excitation. Considering flexoelectric effect, based on Hamilton’s principle and Hertz contact force model, the electromechanical coupling equations are obtained. Numerical simulations are conducted. Output voltages of upper and lower beam are calculated respectively and the frequency response curve of the power density is obtained. It has been found that the maximum output voltage of flexoelectric energy harvester is almost 5 times that of piezoelectric energy harvester when the thickness of substrate layer is 400 nm. The effects of some parameters, such as resistance, gap distance between two beams, and tip mass, on the performance of harvester are studied. It indicates that the working bandwidth of the VEH has increased approximately fourfold, and the output power density is improved in some case due to collision of two beams, which has been verified by experiment. This work designs a novel efficient micro VEH and provides a theoretical basis for structure optimization.

Flexoelectric Energy Harvesting Using Circular Thin Membranes

Abstract In this work, we propose a circular membrane-based flexoelectric energy harvester. Different from previously reported nanobeams based flexoelectric energy harvesters, for the flexoelectric membrane, the polarization direction around its center is opposite in sign to that far away from the center. To avoid the cancelation of the electric output, electrodes coated to upper and lower surfaces of the flexoelectric membrane are respectively divided into two parts according to the sign of bending curvatures. Based on Hamilton’s principle and Ohm’s law, we obtain governing equations for the circular membrane-based flexoelectric energy harvester. A generalized assumed-modes method is employed for solving the system, so that the performance of the flexoelectric energy harvester can be studied in detail. We analyze the effects of the thickness h, radius r0, and their ratio on the energy harvesting performance. Specifically, we show that, by selecting appropriate h and r0, it is possible to design an energy harvester with both high energy conversion efficiency and low working frequency. At last, through numerical simulations, we further study the optimization ratio for which the electrodes should be divided.

Surface integrity and size dependent modeling and performance of non-uniform flexoelectric energy harvesters

Piezoelectric energy harvesters have recently been the focus of several researchers over several years due to their effectiveness at submicron scales by including the flexoelectric effect. Though the size-dependency of the flexoelectric effect had been examined at nanoscales, the size dependent effects of the material structure had been neglected; these nanoscale models do not accurately represent models at the nanoscale. A robust reduced-order model is introduced in this study that incorporates material structure size-dependency through the couple stress theory, the effects of the surface profile by examining the average roughness and slope of roughness and the impacts of the surface stress through the Gurtin–Murdoch surface elasticity theory on a non-uniform cantilever beam energy harvester. Couple stress considerations greatly impact all examined systems, harden the system, and increase the power bandwidth whereas surface roughness influences the expected harvestable power and optimal loading of the system, by reducing expected power output. This analysis shows the importance of considering the size dependent effects on the performance of flexoelectric energy harvesters in nanoscale.

The surface tension effect on flexoelectric energy harvesting based on isogeometric analysis

Surface tension can cause important deformations in fluids but is usually overlooked in solids. Recent work has shown that surface tension can become significant in the deformations of soft solids. Here, we present an isogeometric-analysis-based numerical example of cantilever beams under a point load for modeling the influences of surface tension on the flexoelectric energy harvesting system. The interface of the fluid/solid is implicitly represented using level set method. These results show that the maximum electric potential decreases when the number of liquid inclusions increases. However, the electric potential near the solid/liquid interface increases when considering the surface tension effect.

Electromechanical model of layered flexoelectric energy harvesters with strain gradient effect

Small size wireless devices entirely self-sufficient through energy harvesting from their local surroundings have wide applications. In this paper, an analytical model incorporating the effect of strain gradient for nanoscale flexoelectric energy harvesters is developed. The approximate closed-form solution of voltage output, which can provide a quick assessment of the efficiency of nanoscale flexoelectric energy harvesters, is provided. It is found that the optimal load resistance is not sensitive to the effects transverse shearing and strain gradient. For example, the optimal load resistances are 6.6 MΩ, 6.5 MΩ and 6.3 MΩ for the characteristic length scales are choses as 0 nm, 25 nm and 50 nm, respectively. The effect of transverse shearing on power output is more significant for a nanoscale flexoelectric energy harvester with smaller length to thickness ratio and larger proof mass. For example, power outputs predicted by Euler beam model are 17.6%, 3.8% and 0.06% higher than these predicted by Timoshenko beam model for the length to thickness ratios are 5, 10 and 20, respectively. In addition, the effect of strain gradient enhances the frequency therefore reduces the power output of the beam. The present model may be helpful for mechanical engineers and materials scientists for designing high-performance nanoscale flexoelectric energy harvesters.

Nonlinear analysis of functionally graded flexoelectric nanoscale energy harvesters

Due to the strong size-dependent property, flexoelectricity is one of the most advantageous applications of piezoelectricity on the micro/nano scale energy harvesting. However, rare researches have been conducted on energy harvesters composed by functionally graded flexoelectric materials (FGFMs). In this paper, the nonlinear vibration of a FGFMs energy harvesting nanobeam with a concentrated mass located at free end is analyzed theoretically while considering the electromechanical coupling effect induced by strain gradients. By referring to the Galerkin's method, the corresponding equations of the coupled system and the approximated closed-form solutions of the electric and the power output are obtained. In numerical part, the influences of the volume ratio of the material components, the gradient index and the loading resistance on the voltage output and power density are studied in detail. It is found that, for FGFMs energy harvester, the effective voltage output and the power density depend enormously on the material constituents, the gradient index, the scaled size and the loading resistance. And the rationality of our proposed model is verified by the numerical results. Thus, we can conclude that, for the energy harvesting triggered by flexoelectricity, the FGFMs may be a good way for device design owing to its easy generation of large strain gradients.

Modeling of functionally graded circular energy harvesters due to flexoelectricity

Flexoelectric effect can be enhanced in micro/nano scale due to its size-dependency, making it particularly suitable for energy harvesting. In this work, a theoretical model is built to characterize the functionally graded circular flexoelectric energy harvesters based on the Kirchhoff thin plate hypothesis. Using Hamilton's principle, both the force balance equation and current balance equation are obtained. Approximated closed-form solutions of the energy harvesting performances are achieved through the assumed-mode method. Numerical analysis results demonstrate that the clamped circular energy harvesters with the ratio of the electrode radius to the plate radius be 0.64 will generate the maximum electrical output. The volume fraction coefficient has a significant impact on the resonant frequency, electrical output as well as the optimal load resistance. Meanwhile, shrinking the thickness of the circular energy harvester from 10µm to 0.1µm will lead to a remarkable increase of the optimal energy conversion efficiency from 10−6 to 10−2. Furthermore, the strain gradient effect is examined to result in a higher resonant frequency while suppress the electrical output particularly if the length scale parameter is relatively large.

Analytical Electromechanical Modeling of Nanoscale Flexoelectric Energy Harvesting

With the attention focused on harvesting energy from the ambient environment for nanoscale electronic devices, electromechanical coupling effects in materials have been studied for many potential applications. Flexoelectricity can be observed in all dielectric materials, coupling the strain gradients and polarization, and may lead to strong size-dependent effects at the nanoscale. This paper investigates the flexoelectric energy harvesting under the harmonic mechanical excitation, based on a model similar to the classical Euler–Bernoulli beam theory. The electric Gibbs free energy and the generalized Hamilton’s variational principle for a flexoelectric body are used to derive the coupled governing equations for flexoelectric beams. The closed-form electromechanical expressions are obtained for the steady-state response to the harmonic mechanical excitation in the flexoelectric cantilever beams. The results show that the voltage output, power density, and mechanical vibration response exhibit significant scale effects at the nanoscale. Especially, the output power density for energy harvesting has an optimal value at an intrinsic length scale. This intrinsic length is proportional to the material flexoelectric coefficient. Moreover, it is found that the optimal load resistance for peak power density depends on the beam thickness at the small scale with a critical thickness. Our research indicates that flexoelectric energy harvesting could be a valid alternative to piezoelectric energy harvesting at micro- or nanoscales.