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The coupling between dielectric polarization and strain gradient, known as flexoelectricity, is a property of all dielectric materials. Flexoelectric coefficients are essential during applications. In order to increase the number of measurable flexoelectric coefficients, more experimental approaches are needed. In this work, circular terrace and column models are developed to generate shear strain gradients along radial and longitudinal directions to obtain the flexoelectric coefficients. Theoretical deduction, finite element method analyses, and experiments are applied to several polymeric specimens. The relationships between torque load and electric charge are then obtained, and the flexoelectric coefficients μφzρz and μφzzz are simultaneously obtained. This flexoelectric coefficient decoupling method is proved to be applicable to various polymeric materials. This work enhances the experimental methods of research on decoupled shear flexoelectric effects. [ABSTRACT FROM AUTHOR]

Over the past few years, several researchers have been increasingly attracted to flexoelectric transduction because of its potential application for sensing and actuation in NanoElectroMechanical Systems. The flexoelectric effect refers to coupling between polarization and strain gradient in centrosymmetric and non-centrosymmetric dielectrics. Consequently, not only piezoelectric dielectrics with an initial polarization are of interest, but also a larger range of dielectric materials. In contrast to piezoelectricity, the flexoelectric effect is scale-dependent and can exhibit large electromechanical coefficients only at small scales. This paper focuses on the effects of geometric nonlinearity, resulting from relatively large displacements and restrictive boundary conditions, on the static and dynamic responses of piezoelectric flexoelectric nanobeams. The derived equations of motion for the transverse displacement and variation of the internal electric potential are discretized using a Galerkin procedure. A closed-form solution for the nonlinear static response is proposed. The results are compared and validated with those found in the literature. For the dynamic response, a perturbation technique is used to solve analytically the nonlinear equations of motion for the primary and parametric resonances of the first mode. The analytical perturbation solution is validated using a numerical technique. The results show that a general hardening-type behavior is obtained and, therefore, several jumps are observed for the dynamic solution. High sensitivity of the solution to an applied AC voltage is also demonstrated for the principal resonance of the first mode. [ABSTRACT FROM AUTHOR]

Unlike the structure‐specific piezoelectric effect, flexoelectricity is a universal phenomenon that can offer a wide range of energy‐efficient, cost‐effective, mechano‐opto‐electro‐coupled applications. Even though the flexoelectric effect has been extensively studied at nanoscale, a fundamental, yet unresolved, the issue is how it can be exploited at larger scales for potential applications. Herein, the long‐range (>millimeter) stimulated and regulated impact of the localized inhomogeneous strain‐induced flexoelectric potential on centrosymmetric metal/titanium oxide heterojunction with nanoscale precision (≈5.8 nm) is demonstrated. The noticed phenomenon is attributed to the long‐range interaction between flexoelectric and build‐in potentials, which is further utilized to develop mechanically regulated (enhancement > 104%), self‐powered (i.e., 0 V), ultrafast (>10 million bits per second), and broadband (λ = 365–1720 nm) pyro‐photosensors having high responsivity (≈1.18 mA W−1). As prospective applications, proof‐of‐concept ultrafast night movement monitors (>720 km h−1), high‐performing stationery, and dynamic obstacle sensors with possible impact alerts are developed. These findings lay the groundwork for the micro‐to‐millimeter‐range flexo‐opto‐electrical coupling in centrosymmetric materials, which can have a wide variety of practical applications. [ABSTRACT FROM AUTHOR]

Taking into consideration the effects of micro-inertia, flexoelectricity, and non-uniform strain, the field equations of isotropic dielectrics with centrosymmetric microstructures are specialized for a plane. Plane-wave solutions of these two-dimensional (2D) governing equations suggest the possibility of two plane waves propagating in a flexoelectric medium. Reflection phenomenon of the plane harmonic waves from the stress-free boundary of a dielectric half space is explored. The expressions for the coefficients of reflection and energy shares of reflected waves are obtained for the cases of both incident plane waves. The relevant physical constants of strontium titanate are chosen for numerical computations of the speeds, coefficients of reflection and energy shares of reflected waves. These wave characteristics are illustrated graphically to show the influences of incident angle, wavenumber, length parameter, and flexocoupling coefficient. [ABSTRACT FROM AUTHOR]

A numerical procedure based on isogeometric analysis (IGA) is developed to analyze the dynamic response of flexoelectric systems in the frequency domain. In materials or composites with an effective flexoelectric response, a polarization can be induced by local strain gradients. In general, these effects are small in the static regime. However, larger effects may be induced by dynamic loads, and can be used in energy harvesters converting mechanical vibrations into electrical energy. In this work, the equations describing frequency response of flexoelectric systems under dynamic loads are first described. Then, an IGA discretization procedure is employed to handle the C 1 continuity of the displacement fields. The conditions of both open and close-circuits are formulated. The numerical methodology is used to evaluate the sensitivity of different parameters such as load resistors, dynamic scale parameter, and the use of flexoelectric or non-flexoelectric materials on the frequency response of output voltage, power and displacements of beam-like structures, possibly incorporating structural geometrical features. The potential of IGA with respect to mesh refinement (h-refinement) and higher order approximation (p-refinement) for modeling complex geometries within the present framework is invetigated. [ABSTRACT FROM AUTHOR]

Nanoscale beams and rods are extensively used in several nano-electro-mechanical systems (NEMS) and their applications such as sensors and actuators. The surface and flexoelectricity phenomena have an extensive effect on nanosized structures and are related to their scale-dependent characteristics. This article presents the effect of different surface parameters and flexoelectricity on the electrostatic response of graphene-reinforced hybrid composite (GRHC) nanorods (NRs) using the theory of linear piezoelectricity, Euler-Bernoulli (EB), and Galerkin residual method. Based on these theories, the theoretical and finite element (FE) model is produced to investigate the static bending deflection of GRHC NRs when subjected to point and uniformly distributed load (UDL) considering different boundary conditions: cantilever (FC), fixed-fixed (FF), and simply supported (SS). This proposed FE model provides a useful tool for analyzing and investigating the outcomes of analytical models, which are found to be in good agreement. Our results presented in this article reveal that the effect of surface and flexoelectricity on the static bending response of GRHC NRs is noteworthy. These effects diminish with increased thickness/diameter of NR, and hence, these effects can be neglected for large-sized structures. The results presented here would help to identify the desired electrostatic response of GRHC NRs in terms of static bending response for a range of NEMS using different loading and boundary conditions as well as graphene volume fraction. This current study offers pathways for developing new proficient novel GRHC materials with enhanced control authority and present models can be exploited for numerous other materials as well as line-type structural systems such as beams, wires, rods, column/piers, and piles to study their global response. [ABSTRACT FROM AUTHOR]

Some people, entirely untrained in music, can listen to a song and replicate it on a piano with unnerving accuracy. What enables some to “hear” music so much better than others? Long-standing research confirms that part of the answer is undoubtedly neurological and can be improved with training. However, are there structural, physical, or engineering attributes of the human hearing mechanism apparatus (i.e., the hair cells of the internal ear) that render one human innately superior to another in terms of propensity to listen to music? In this work, we investigate a physics-based model of the electromechanics of the hair cells in the inner ear to understand why a person might be physiologically better poised to distinguish musical sounds. A key feature of the model is that we avoid a “black-box” systems-type approach. All parameters are well-defined physical quantities, including membrane thickness, bending modulus, electromechanical properties, and geometrical features, among others. Using the two-tone interference problem as a proxy for musical perception, our model allows us to establish the basis for exploring the effect of external factors such as medicine or environment. As an example of the insights we obtain, we conclude that the reduction in bending modulus of the cell membranes (which for instance may be caused by the usage of a certain class of analgesic drugs) or an increase in the flexoelectricity of the hair cell membrane can interfere with the perception of two-tone excitation. [ABSTRACT FROM AUTHOR]

A graphene–silicon Schottky junction (GSJ), which has potentials of large-scale manufacturing and integration, can bring new opportunities to Schottky solar cells for photovoltaic (PV) power conversion. However, the essential power conversion limitation for these devices lies in a small open-circuit voltage ( V o c ), which depends on the Schottky barrier height. In this study, we introduce an electromechanical method based on a flexoelectric effect to enhance the PV efficiency in GSJ. By atomic force microscope (AFM) tip-based indentation and in situ current measurement, the current–voltage (I–V) responses under a flexoelectric strain gradient are obtained. The V o c is observed to increase for up to 20%, leading to an evident improvement of the power conversion efficiency. Our studies suggest that the strain gradient may offer unprecedented opportunities for the development of GSJ-based flexo-photovoltaic applications. [ABSTRACT FROM AUTHOR]

This study investigates the size-dependent dynamic pull-in instability of piezoelectrically and electrostatically actuated micro/nanobeams considering the Euler–Bernoulli theory and von-Kármán hypothesis based on the nonlocal strain gradient theory. In this respect, the impacts of flexoelectricity and piezoelectricity are considered using electrical Gibbs-free energy density and the governing equation is acquired with the help of Hamilton's principle for a sandwich beam with elastic core and two piezoelectric layers. In the present model, different nonlinear forces, such as the fringing field, electrostatic, and intermolecular forces are taken into account. Then, the governing equation is converted from partial differential equation into ordinary one by the Galerkin method considering various boundary conditions, subsequently, the homotopy analysis method is applied as an analytical procedure. The results are validated by comparing the linear frequency, nonlinear frequency, and dynamic pull-in voltage with those in the literature. Consequently, the impacts of different parameters including piezoelectric voltage, nonlocal parameter, length scale parameter, initial amplitude, electrostatic force, flexoelectric, and gap to thickness ratio are discussed in detail. [ABSTRACT FROM AUTHOR]

A new model for electro-elastic Bernoulli–Euler beams of centrosymmetric cubic materials is proposed, which incorporates microstructure and flexoelectric effects. The wave equations and boundary conditions are derived simultaneously through a variational approach based on Hamilton's principle. The new beam model is then applied to predict elastic wave band gaps in a periodic electro-elastic composite beam structure. Bloch's theorem and the transfer matrix method for periodic structures are used to solve the wave equations and determine band gaps. The current model reduces to its flexoelectric and classical elastic counterparts as special cases. To illustrate the new model, the effects of microstructure, flexoelectricity, beam thickness, unit cell length and volume fraction on band gaps are investigated through a parametric study. The numerical results show that the microstructure and flexoelectric effects lead to increased band gap frequencies, and these two effects are important when the beam thickness is at the submicron and micron scales. In addition, it is found that the unit cell length and volume fraction can significantly affect the band gap size at all length scales. These findings indicate that band gap frequencies and size can be tailored by adjusting the microstructural and material parameters. [ABSTRACT FROM AUTHOR]

Dielectric spectrum of polymer-dispersed antiferroelectric liquid crystals (PDAFLC) was studied theoretically by considering the influence of flexoelectric polarization. Such flexoelectric polarization arose due to mechanical distortion as a whole and contributed a direct dependence on the bulk free energy with the free volume interactions, bulk anchoring strength of the in-layer molecular director and polymeric cross-link. The behaviour of both the low-frequency in-phase mode and the high-frequency anti-phase mode depending on the variation of flexoelectric polarization in PDAFLC was studied in detail theoretically. The dielectric permittivity and the dielectric strength were affected strongly because of the co-operative motion of the molecules and the polymeric cross-links for both occasions. The variation of relaxation times and unwinding critical field of both phases with the variation of flexoelectric polarization and interlayer interaction strength was studied in detail. [ABSTRACT FROM AUTHOR]

Beams, plates, and shells, as the fundamental mechanical structures, are widely used in microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) as sensors, actuators, energy harvesters, and among others. Deeply understand the electromechanical coupling of these dielectric structures is of crucial for designing, fabricating, and optimizing practice devices in these systems. Herein we demonstrate the electromechanical coupling in flexoelectric circular plate, in which higher-order strain gradients were considered to extend the classical electromechanical properties to isotropic materials, in which the non-uniform distribution of the electric potential along the radial direction was considered. Analytical solutions for the vibration modes of the flexoelectric circular plates showed that the dynamic modes were totally different from the piezoelectric circular plates owing to the inversion symmetry breaking by the strain gradient. The electromechanical coupling dynamic modes are sensitive to bending, twisting modes owing to the sensitivity of the flexoelectric effect to bending. This work provides a fundamental understanding of the electromechanical coupling in flexoelectric circular plate, which is helpful in designing novel flexoelectric circular plate-based devices, such as flexoelectric mirrors. [ABSTRACT FROM AUTHOR]

Flexoelectric polarisation in liquid crystalline elastomers with wedge-shaped mesogens was investigated. Flexoelectric polarisation was fixed in the elastomers that were cross-linked under uniaxial deformation with splay distortion. X-ray diffractometry revealed that the orientational order partially remained at about S = 0.2 even in the temperature region of the isotropic phase designated tentatively as the pseudo-isotropic phase. The electric charge caused by polarisation due to the flexoelectric effect was estimated to be −809 pC/mm2 in the splay distorted liquid crystalline elastomers, whereas almost no electric charge was detected in the uniaxially and uniformly aligned elastomers. We tentatively conclude that the macroscopic polarisation due to flexoelectric effect emerged and was fixed in the liquid crystalline elastomers by cross-linking under splay distortion. [ABSTRACT FROM AUTHOR]

Present study elucidates shear surface wave dispersion and attenuation in a piezoelectric-flexoelectric micro layer bedded over a heterogeneous initially stressed fiber-reinforced host structure with or with out a thin mass loading layer (ZnO layer) at the top surface of the micro-layer. Mechanical imperfection between host structure and electrically active layer is modelled with the help of Shear-lag model. Dual electromechanical coupled (flexoelectric and piezoelectric) field equations are solved by means of analytical technique and dispersion relations are obtained for electroded and non-electroded surface, separately when the infinitesimal mass loading layer is associated or not associated with piezo-flexo layer. With the help of suitable numerical example phase velocity curves and dissipation curves are plotted to illuminate the parametric responses of flexoelectricity, piezoelectricity, dielectricity, imperfection, reinforcement anisotropy and initial tensile stress. Detailed discussions about electromechanical coupling are done for different cases. Influence of piezoelectricity, dielectricity and flexoelectricity on mass loading sensitivity are also expatiated. The study may provide theoretical guidelines in investigations about mass loading sensitivity of SAW sensors with piezo-flexo coupling. [ABSTRACT FROM AUTHOR]

In this manuscript, a functionally graded beam model considering both flexoelectric and dynamic flexoelectric effects was established. Based on the modified strain gradient theory, the governing equation was reformulated, which included the effects of the dynamic flexoelectric coefficient and the material length scale parameters. Using the electrical open circuit condition, a analytical solutions of the lateral displacement and axial displacement under static bending were obtained. In order to further analyze the influence of dynamic flexoelectric effect on the natural frequency of free vibration, the frequency equation was obtained from Navier method. Numerical results show that the electric potential, polarization, and energy efficiency of functionally graded beam can be controlled by adjusting the gradient index and material length scale parameters. In addition, the simulation results also show that the dynamic flexoelectric effect coefficient has a more significant effect on the natural frequency at small span ratios. This work can provide helpful guidance for designing energy harvesting devices in functionally graded materials. [ABSTRACT FROM AUTHOR]

The flexoelectric effect implies a wide application potential in micro- and nanoscale electromechanical systems, where cylinders are widely used due to their wide range of applications. At the same time, functionally graded materials combine the advantages of different materials to achieve optimized material properties. Motivated by these considerations, we use the generalized power series method for the first time to derive exact solutions to functionally graded flexoelectric cylinder problems, including pressure and shear scenarios. This research systematically investigates the effects of material gradation, characteristic length parameters, and flexoelectric coefficients on the intricate electromechanical coupling behavior of functionally graded flexoelectric micro-cylinders. In addition, a comparative analysis between the exact and mixed finite element solutions demonstrates remarkable agreement. In particular, this investigation pioneers the extension of the Lamé problem, a cornerstone of classical elasticity, into the advanced realm of higher-order electroelasticity in inhomogeneous materials. This advance holds great promise for the design and optimization of micro- and nanoscale electromechanical systems based on the principles of flexoelectricity. • Exact solutions for functionally graded flexoelectric micro-cylinders are derived. • The material gradation regulates mechanical and electrical variable distributions. • Effects of material characteristic length and flexoelectric coefficients are studied. • A mixed finite element method is employed to compare with the exact solutions. [ABSTRACT FROM AUTHOR]

Materials with different combinations of piezoelectric and flexoelectric properties offer multifunctionality and versatility in terms of modes of operation in sensing, actuation, and energy harvesting. We explore a microscopic mechanism for tailoring the macroscopic quasi-static mechanoelectrical output of polymer-particle composites by taking advantage of heterogeneity-induced enhancement of the stress fields and strain gradient fields. The idea focuses on using microscopic inclusions, such as embedded particles and voids, to manipulate the activation and relative contributions of the piezoelectric and flexoelectric effects under different modes of mechanical excitation, such as uniaxial compression and flexural bending. The material system studied is a composite of poly(vinylidene fluoride-co-trifluoroethylene [P(VDF-TrFE)] polymer and nanoaluminum (nAl) particles, or P(VDF-TrFE)/nAl. This system is interesting because P(VDF-TrFE) exhibits both piezoelectric and flexoelectric behaviors and nAl particles have significantly higher elastic stiffness than the polymer. A range of piezoelectric and flexoelectric properties of P(VDF-TrFE) and the stiffness of the particles are considered. Significant microstructural effects are found to enable tailoring of the mechanoelectrical response through microstructure variation. The responses of the composite are quantified using the effective piezoelectric constant (d 33 , eff o) and the effective flexoelectric coefficient (μ TR , eff o). It is found that the effective macroscopic piezoelectric and flexoelectric behaviors can be changed either independently or simultaneously through different combinations of microstructure attribute changes. The mechanism revealed points out avenues for developing materials with tunable mechanoelectrical behaviors and multifunctionality. [ABSTRACT FROM AUTHOR]

This paper presents a variational modeling framework for investigating the flexoelectricity-driven evolution of remanent polarization in piezoceramics. In small-scale electromechanical systems, strain gradients can exhibit polarization in dielectric materials via the direct flexoelectric effect. In ferroelectrics, it is reasonable to expect that a sufficiently large magnitude of the flexoelectricity leads to a switching of the domain structure and thus the material becomes remanently polarized. It is interesting to note that this means that poling would be able to occur in the absence of any external electrical source. This provides the motivation to gain a better understanding of this effect for a possible technical use in e.g. sensor applications. For this purpose, a macroscopic model is presented that couples flexoelectricity and ferroelectric domain switching processes. By embedding the model in the variational framework of the generalized standard materials (GSM), a minimum-type potential structure and thus a stable and efficient numerical treatment is obtained. A mixed finite element formulation based on the Helmholtz free energy is introduced to solve the higher-order flexoelectric boundary value problem. In order to realistically predict the flexoelectric material behavior, the model response is adapted to experimental results in literature obtained for a piezoceramic in a bending test. By simulations based on the adapted model the evolution of the flexoelectricity-driven remanent polarization in the vicinity of a notch is shown. • A variational modeling framework for flexoelectric problems is introduced. • A mixed finite element formulation based on Helmholtz free energy is used. • The model response is adapted to experimental results on the flexoelectric effect. • The flexoelectricity-driven remanent polarization in piezoceramics is investigated. [ABSTRACT FROM AUTHOR]

In this study, n-type stannic sulfide (SnS 2) nanosheets and p-type bismuth oxychloride (BiOCl) nanosheets prepared by hydrothermal method are utilized to construct the heterostructure SnS 2 -BiOCl composite through ultrasonication and grinding procedures. The piezoelectric SnS 2 -BiOCl heterojunction nanosheets are incorporated into the ferroelectric polyvinylidene fluoride (PVDF) membrane to fabricate the PVDF-based SnS 2 -BiOCl (PVDF-SnS 2 -BiOCl) flexoelectric strain sensor. The optimal amount of SnS 2 -BiOCl heterojunction in the PVDF-SnS 2 -BiOCl membrane is determined. A thorough analysis is conducted on the impact of bending curvature, frequency of bending, the size and thickness of the membrane, water flapping, underwater bending, resistance to fatigue from repeated bending, and resistance to corrosions from acid and alkali on the membrane's output current and voltage. The experimental and density functional theory (DFT) calculation results indicate that the PVDF-SnS 2 -BiOCl(2:1)-10 % membrane, functioning as a smart strain sensor, has the ability to monitor human joint movements and water fluctuations in different situations. Additionally, it can be used as a coating for polyester and linen fabrics and can be connected in series or in parallel. The experimental findings align closely with the results obtained from DFT calculations. The outcomes demonstrate that the PVDF-SnS 2 -BiOCl membrane strain sensor, which is highly flexible, sensitive, and attachable, is well-suited for smart wearable electronic materials. [Display omitted] • 2D SnS 2 -BiOCl heterojunction can improve the electrical field of PVDF film. • 2D SnS 2 -BiOCl heterojunction can enhance the polarization value of PVDF. • The polarizability of PVDF-SnS 2 -BiOCl membrane increases upon bending stress. • The increased polarization value of PVDF-SnS 2 -BiOCl is due to the charged ions. • PVDF-SnS 2 -BiOCl strain sensor can detect body motion and water fluctuation. [ABSTRACT FROM AUTHOR]

Living tissues experience various external forces on cells, influencing their behaviour, physiology, shape, gene expression, and destiny through interactions with their environment. Despite much research done in this area, challenges remain in our better understanding of the behaviour of the cell in response to external stimuli, including the arrangement, quantity, and shape of organelles within the cell. This study explores the electromechanical behaviour of biological cells, including organelles like microtubules, mitochondria, nuclei, and cell membranes. A two-dimensional bio-electromechanical model for two distinct cell structures has been developed to analyze the behavior of the biological cell to the external electrical and mechanical responses. The piezoelectric and flexoelectric effects have been included via multiphysics coupling for the biological cell. All the governing equations have been discretized and solved by the finite element method. It is found that the longitudinal stress is absent and only the transverse stress plays a crucial role when the mechanical load is imposed on the top side of the cell through compressive displacement. The impact of flexoelectricity is elucidated by introducing a new parameter called the maximum electric potential ratio (VR,max\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$V_{R,{\text {max}}}$$\end{document}). It has been found that VR,max\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$V_{R,{\text {max}}}$$\end{document} depends upon the orientation angle and shape of the microtubules. The magnitude of VR,max\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$V_{R,{\text {max}}}$$\end{document} exhibit huge change when we change the shape and orientation of the organelles, which in some cases (boundary condition (BC)-3) can reach to three times of regular shape organelles. Further, the study reveals that the number of microtubules significantly impacts effective elastic and piezoelectric coefficients, affecting cell behavior based on structure, microtubule orientation, and mechanical stress direction. The insight obtained from the current study can assist in advancements in medical therapies such as tissue engineering and regenerative medicine. [ABSTRACT FROM AUTHOR]

The nonlinear bending and vibration behaviors of a variable-width piezoelectric nanoplate considering flexoelectric effect are investigated in this paper. The nonlinear Mindlin plate theory and finite element method are applied to derive the governing equations of variable-width piezoelectric nanoplate with flexoelectricity. The influences of geometric nonlinearity, flexoelectricity, and varying width on the bending deflection and natural frequency of the piezoelectric nanoplate with flexoelectricity under four kinds of boundary conditions are explored in detail. The numerical results show that the flexoelectric effect can strongly influence the maximum deflection, the morphology of deformation, and the natural frequency of the variable-width piezoelectric nanoplate. The consideration of geometric nonlinearity becomes necessary for nanoplate exhibiting strong flexoelectricity or subject to significant voltage loads. The boundary conditions not only affect the morphology of deformation but also influence the variation trend of natural frequency with the variable-width ratio of the piezoelectric nanoplate. While the variation trend of maximum deflection is jointly affected by the boundary conditions and flexoelectricity. The closer the shape of the piezoelectric nanoplate is to a triangle, the greater the combined effect of boundary conditions and flexoelectricity on the variation trend of maximum deflection. The results of this study can contribute to the optimization of piezoelectric nanostructures, and they are helpful in enhancing our comprehension of the mechanical behavior of piezoelectric nanostructures. [ABSTRACT FROM AUTHOR]

Dielectric Functionally Graded Materials (FGMs) exhibit superior flexoelectric properties. Gradual changes in material properties lead to large strain gradients and excellent flexoelectric responses. Cracks behave in a complex manner inside piezoelectric-flexoelectric FGMs subjected to electromechanical loading. An extended isogeometric analysis (XIGA)-based formulation is developed for flexoelectric FGMs with crack discontinuities. Ceramic-polymer FGMs of barium titanate (BTO) and polyvinylidene fluoride (PVDF) are selected for analysis since this material combination has shown better flexoelectric response solely due to gradation. A higher-order electromechanical J-integral is used to study the behavior of cracks. The fracture behavior of different crack geometries at various grading indices and levels of flexoelectricity is investigated. A crack interaction study is conducted with varying crack parameters. The length-scale effect on the energy release rate is also shown. A significant reduction in the energy release rate is observed in FGMs due to the flexoelectric effect. [ABSTRACT FROM AUTHOR]

With the rapid advancement of 5 G technology, the demand for surface acoustic wave (SAW) devices is experiencing exponential growth. Precisely forecasting the speed at which Rayleigh waves propagate, taking into account size effects and flexoelectric properties, is vital for enhancing SAW device design. To address this need, the study explores Rayleigh wave propagation in a stratified system consisting of a nanoscale piezoelectric guiding layer atop an isotropic elastic substrate. The governing equations, boundary conditions, and interface continuity conditions between the guiding layer and substrate are established through the Hamiltonian principle. Following this, the dispersion equations for Rayleigh waves under electric open-circuit and electric short-circuit conditions are derived and solved numerically. Additionally, the effects of flexoelectricity, inertial gradients, strain gradients, electric field gradients, and the piezoelectric guiding layer thickness on the phase velocity of Rayleigh waves are extensively explored. Our findings indicate that flexoelectricity and strain gradients elevate the phase velocity, while inertial gradients and electric field gradients result in a decrease in the phase velocity. As the frequency of Rayleigh waves increases, the impact of these factors becomes more prominent. In addition, it is observed that electric field gradients play a less significant role compared to inertial gradients and strain gradients. The findings of this study could offer valuable insights for the advancement of miniaturized SAW devices designed for high-frequency service. • Investigation of piezoelectric layer guided in-plane surface waves. • Consideration of size effects in nanoscale piezoelectric thin film. • Study of both electrically open- and short-circuit cases. • Findings show that flexoelectricity and strain gradients increase the phase velocity. • Discovery that inertial and electric field gradients decrease the phase velocity. [ABSTRACT FROM AUTHOR]

Flexoelectricity is the coupling between strain gradients and electric fields. This phenomenon can significantly enhance piezocomposite response in addition to linear piezoelectricity. This enhancement is especially important for lead-free piezocomposites, which generally underperform compared to lead-based counterparts. Flexoelectric enhancement is facilitated by structural anisotropy in piezocomposites. However, challenges in modeling flexoelectric effects arise from several unknowns. Firstly, the shear flexoelectric coefficient is not well-characterized experimentally. Secondly, significant discrepancies exist between theoretical predictions and experimental measurements of flexoelectric coefficients. Thirdly, the influence of matrix mechanical properties on flexoelectric behavior is poorly understood. To address these issues, we construct a parametric flexoelectric model of a lead-free piezocomposite with graded inclusion concentration. We then systematically analyze the impact of each parameter to identify which significantly influence flexoelectric behavior. This study is intended to provide direction to further experimental studies towards understanding and tailoring this subset of parameters. [ABSTRACT FROM AUTHOR]

• An accurate nonlinear buckling model is proposed for the flexoelectric cylindrical nanoshell. • The pre-buckling nonlinear deformation is employed to improve the accuracy of critical buckling stresses and buckling mode shapes. • The effects of key influencing parameters on buckling characteristics of the flexoelectric cylindrical nanoshell is investigated and reveal. In this paper, a buckling analysis for flexoelectric cylindrical nanoshells under axial compression is performed by considering the higher-order shear deformation theory and non-uniform pre-buckling deformation. Size-dependent critical buckling stresses and buckling mode shapes are obtained by the Galerkin's method with newly proposed displacement functions. Numerical results are compared with existing solutions and excellent agreements are observed. Furthermore, a comprehensive parametric study of boundary conditions, geometrical parameters and applied electric voltage is carried out to reveal the influence of flexoelectric effect on the size-dependent buckling characteristics of flexoelectric cylindrical nanoshells. [ABSTRACT FROM AUTHOR]

The flexoelectric effect of polymers is normally much weaker than that of ferroelectric oxides. In order to improve the flexoelectric response of the poly(vinylidene fluoride) (PVDF) ferroelectric polymer, PVDF/Ba0.67Si0.33TiO3 (BST) nanocomposites were fabricated. BST nanofibers were prepared by the electrospinning method, and the fibers were further surface modified with H2O2 to achieve a stronger interfacial interaction between the fibers and polymer matrix. Due to the high dielectric properties and strong flexoelectric effect of the BST, both dielectric constant and flexoelectric response of the composite with 25 vol. % surface modified BST are 3-4 times higher than those of PVDF. The dependence of the dielectric constant and the flexoelectric coefficient on the composition of the nanocomposites can be fitted by the empirical Yamada model, and the dielectric constant and the flexoelectric coefficient are correlated by a linear relationship. This study provides an approach to enhance the flexoelectric response of PVDF-based polymers. [ABSTRACT FROM AUTHOR]

Recently, flexoelectric effect has attracted considerable attention owing to ubiquitous existence in all dielectrics, regardless of the symmetry. It promises intriguingly physical phenomena, such as strain gradient-induced electric polarizations, photocurrents, and interfacial transports, as well as their electromechanical coupling with external force loading, in diverse materials for multifunctional applications in electronics. In this work, we report the flexoelectric-modulation on surface potential of LaFeO3 (LFO) thin-film heterostructures. The LFO thin film with or without the flexoelectric effect has been achieved by controlling epitaxial misfit against a substrate. Lattice structures and strain behaviors are observed by atomic-resolution high-angle annular dark-field imaging. Grown on a LaAlO3 substrate, a giant strain gradient of ∼3 × 106 m−1 is generated in the LFO thin film due to the gradual relaxation of large misfit strain with increasing thickness, yielding a robust flexoelectric polarization pointing to the heterostructure surface. In contrast, the LFO is almost fully strained on a SrTiO3 substrate due to the small lattice mismatch. The flexoelectric polarization results in an increase in surface potential in the LFO heterostructure due to the incomplete screening of positive polarization bound charges, as observed by scanning kelvin probe microscopy. Furthermore, x-ray photoelectron spectroscopy reveals that the flexoelectric polarization can downward bend the band alignment of the LFO layer and modulate the interfacial potential barriers. These results provide the way for experimental observations of the flexoelectric effect and deliver physical insight into deep understanding of interfacial electronic structures of flexoelectric-based devices. [ABSTRACT FROM AUTHOR]

Flexoelectricity of semiconductors usually exhibits large flexoelectric coefficients due to their significantly enhanced surface piezoelectricity caused by surface symmetry breaking. In this Letter, we reported a general paradigm to tune the semiconductor flexoelectricity through interface engineering. We selected Nb-SrTiO3 (Nb-STO) single crystals as the targets and tuned their surface piezoelectricity through depositing TiO2-terminated and SrO-terminated ultra-thin BaTiO3 (BTO) films. The results suggested that the deposition of TiO2-terminated and SrO-terminated ultra-thin BaTiO3 films to Nb-STO can induce a downward and upward out-of-plane surface polarization, respectively, thereby significantly increasing/decreasing the apparent flexoelectric coefficients of Nb-STO single crystals. Our work proves the feasibility of interface engineering in the application of flexoelectricity and also provides a possible route to achieve the large apparent flexoelectricity of semiconductor materials. [ABSTRACT FROM AUTHOR]

• New triple-layer phononic crystal composite beams are proposed based on flexoelectricity theory. • The bandgap of elastic waves of new composite beams is analytically solved using transfer matrix method. • The predictions by the current model agree well with those by a 3-D Finite element model at large scale. • The microstructure and flexoelectric effects elevate the bandgap frequency at the nanoscale. • Tunable bandgaps can be relaized by adjusting the external magnetic potential field at all scales. A new triple-layer phononic crystal (PC) composite beam model is proposed, which binds two piezomagnetic layers to conventional PCs coupling the microstructure and flexoelectric effects. A variational approach is employed to derive the relevant equations of motion and boundary conditions (BCs), followed by using the Bloch theory and transfer matrix method (TMM) to accurately calculate the bandgap of elastic waves. Numerical results show that the microstructure and flexoelectric effects elevate the bandgap frequency at the micro-and nano-scales, respectively, but both can be neglected at the macroscale. The thickness of the piezomagnetic layers and the volume fraction of the PC play an important role in the generation of the bandgap. With the help of the piezomagnetic layers, tunable bandgaps can be obtained by adjusting the external magnetic potential field at all scales. This paper provides an innovative idea for flexoelectric-based PC devices designing when magnetic fields are involved. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the internal viscosity model developed by Professor Williams to semiflexible polymers, biofilaments, and worm‐like micelles, where molecular dissipation is generated by bending. Current models for viscoelasticity with internal viscosity in semiflexible polymers and filaments are based on generalizations of the worm‐like model, but they neglect potential electromechanical couplings such as flexoelectricity. In this paper, inspired by the early work of Professor Williams, we develop a model for worm‐like viscoelastic flexoelectric filaments based on the "line liquid crystal model". The electroelastic free energy and entropy production are formulated and used to derive the shape equation for these filaments undergoing thermal fluctuations. The resulting time relaxation spectrum is a useful tool to characterize experimentally viscoelastic material parameters. We show that flexoelectricity or polarization‐induced bending softens the filaments. The predicted time relaxation spectrum shows that at longer wavelength modes, the filament behaves like a rigid rod in a viscous solvent, but at shorter wavelengths, it reaches a plateau defined by the bending time scale. The key effect of flexoelectricity is to shift the entire spectrum to higher values, slowing down the response. The model itself is validated using the worm‐like chain and the viscoelasticity of liquid crystals, and the predictions are shown to be in qualitative consistency with the data. Since filament flexoelectricity is associated with 1D sensor‐actuator functionalities, the presented model has many potential novel applications in reduced geometries. [ABSTRACT FROM AUTHOR]

Until now, conventional nanogenerators could only produce electric pulses with relatively low-power densities. Herein, we invent a novel controllable growth technique for two-dimensional (2-D) cuprous oxide (p-Cu2O) single-crystal films, and on this basis, a new concept of 2-D single-crystal film flexoelectric nanogenerators (FENGs) are rationally designed and constructed for the first time, which has the characteristics of long-range order lattice, few grain boundaries and defects. More importantly, the accumulated built-in polarization potential in the bent 2-D p-Cu2O single-crystal film FENGs is in the same orientation as the output electricity, resulting in the first nanogenerator that can output continuous and stable electric signals with high voltage (Voc of 2.8 V), current (Jsc of 11.5 μA·cm−2) and power density (14.4 μW·cm−2), exhibiting great practical application potential for power generation and motion capture. This research breaks new ground and establishes a precedent for high-performance and continuous-output nanogenerators, as well as smart wearable sensors. [ABSTRACT FROM AUTHOR]

High-performance, wearable, and self-powered mechanical sensors for human health monitoring, motion detection systems, and human–machine interfaces are attracting attention owing to the increased interest in green energy. Piezoelectric and triboelectric effects are being exploited to develop various types of self-powered mechanical sensors; however, unresolved issues such as complicated processes and limitations in material selection and practical applications remain. A type of effective self-powered mechanical sensor based on the hybrid triboelectric–flexoelectric effect of multilayered MoS2 hollow spheres is reported herein. This triboelectric–flexoelectric mechanical sensor (TFMS) exhibits superior sensing characteristics, including wide-range pressure detection and superior stability, owing to the remarkable hybrid triboelectric–flexoelectric effect of optimized MoS2 hollow spheres under stress. In addition, the operating mechanism of the fabricated TFMS is discussed based on the size and number of the multilayered MoS2 spheres using finite element method (FEM) simulations of the effective stress under pressure changes. Furthermore, the effective operation of the sensor in detecting various human physiological motions from the wrist pulse to walking/running is demonstrated. These results are expected to promote the development of advanced mechanical sensors for applications such as next-generation prostheses and human–machine interfaces. [ABSTRACT FROM AUTHOR]

This work presents the development of a unified gradient electromechanical theory for thin flexoelectric beams considering both direct and converse flexoelectric effects. The two-way coupled electromechanical theory is developed starting from 3D variationals formulation by considering an electric field-strain-based free energy function. The formulation incorporates mechanical as well as electrical size effects. The coupled 3D theory is specialized to isotropic materials, and a 1D beam theory for composite flexoelectric curved beams is derived using the classical Kirchhoff assumptions. The beam theory is solved using a novel C 2 continuous finite element framework for different loading and boundary conditions. Our finite element results are verified with analytical solutions for a simply supported flexoelectric beam operating in both actuator and sensor modes. The results are also compared with existing literature for the special case of a passive micro-beam. Our computational framework is subsequently used to perform various parametric studies to analyze the effect of electrical and mechanical length scale parameters, geometric parameters like the radius of curvature, flexoelectric layer thickness etc., on the response of the beam. Also, contribution of converse flexoelectricity in the overall response of the flexoelectric beam is compared with that of the direct effect. Our simulation results predict that the converse effect is significant (≈ 10–25% of the direct effect) for a wide range of thickness and length scale parameter values. It is also observed that the effective electromechanical coupling coefficient, calculated in terms of the voltage developed across the flexoelectric layer thickness, is higher in flexoelectric materials compared to piezoelectric materials at smaller length scales (thickness of the order of a few microns). Our simulation results also agree well with the trends observed in recent experiments [1]. [ABSTRACT FROM AUTHOR]

Flexoelectricity has trigged emergent phenomena and functionalities, such as flexo‐resistance, flexo‐photovoltaic, photo‐flexoelectric, flexo‐electronics and so on. Analogous to piezocatalysis, the flexoelectric effect can provide a novel mechanism to enhance the sonochemical redox reactions. Here, by extending flexoelectricity to electrochemical functionality, an unprecedented phenomenon is demonstrated of flexo‐catalysis effect in centrosymmetric nanoparticles to degrade organic dyes. Simulations have been performed to elucidate the bubble cavitation induced strain gradients and polarization variation, and in turn the flexoelectricity induced reactive species have been verified by trapping experiment. The flexo‐catalytic results show that more than 92.2% of Rhodamine B can be degraded at a rate of ≈k = 0.6 h−1. This finding not only suggests a new strategy to generate the flexoelectric effect, but also opens up the possibility to extend existing catalytic techniques. [ABSTRACT FROM AUTHOR]

The flexoelectric effect, a type of electromechanical property, is proposed to generate thermal-electrical like response in ferroelectric ceramics; however, presently, the electric current output achieved is small. Here, we show that changing the composition of the Na 0.5 Bi 0.5 TiO 3 -based ceramics to improve their conductivity can enhance their thermal-electrical like response to several orders of magnitude larger than that reported earlier. We also found that the measured thermal-electrical like response mainly originates from the spontaneously polarised surface existing in ferroelectrics, which generates a flexoelectric-like response under inhomogeneous deformation. The coupling of the flexoelectric-like response and high conductivity leads to a large thermal-electrical like response. [ABSTRACT FROM AUTHOR]

Flexoelectricity in multilayer graphene (MLG) buckling can stimulate kink-shaped crinkle formation. In the process, the bifurcation becomes subcritical and the suspended-MLG's crinkle curvature is localized to a narrow band of ∼ 2 n m width. We extend the study to flexoelectric layers bonded to a soft elastic substrate. Elastic substrates can guide the morphology of MLG and produce periodic patterns. We show that MLG's flexoelectricity together with substrate elasticity can produce periodic crinkles, which qualitatively explains the grade-dependent mosaic spreading in highly oriented pyrolytic graphite (HOPG). Experimental measurements of HOPG's surface-slope variations indeed confirm curvature localization at the crinkle valleys and ridges. [ABSTRACT FROM AUTHOR]

We study magnetically‐induced electromechanical fields in a sandwich plate of a flexoelectric semiconductor layer between two piezomagnetic dielectric layers under a transverse magnetic field. A set of two‐dimensional equations for the bending of the plate is derived from the three‐dimensional macroscopic theory of piezomagnetics and flexoelectric semiconductors. A few solutions from the plate equations are obtained for static and time‐harmonic magnetic loadings. Results show that various distributions of mobile charges and electric fields can be created by different magnetic fields, which is the foundation for flexotronics when magnetic fields are involved. In the case of pure bending under a uniform magnetic field, a combination of physical and geometric parameters is identified as a coefficient characterizing the strength of the interaction between the applied magnetic field and the mobile charges. The coefficient assumes a maximum for a particular thickness ratio between the two types of material layers. The frequency dependence of the coupling coefficient in time‐harmonic motions is also obtained. [ABSTRACT FROM AUTHOR]

Deliberate manipulation of topological defects is of particular interest for liquid crystal applications. For example, surface bistability occurs in the grating aligned Zenithal Bistable Device due to the stabilisation of ±½ defects at the points of high surface curvature. Conventional latching between continuous and defect states has previously been simulated satisfactorily using Q-tensor models that include the effect of weak-anchoring and flexoelectricity. However, experimental studies show that some arrangements lead to anomalous latching regimes. The Q-tensor model is used to show that such effects occur when the defects become detached from the surface and have more complex paths in the bulk of the sample. [ABSTRACT FROM AUTHOR]

The flexoelectric effect is the coupling between strain, polarization, and their gradients, which are prominent at the nanoscale. Although this effect is important to understand nanostructures, such as domain walls in ferroelectrics, its electronic mechanism is not clear. In this work, we combined phase-field simulations and first-principles calculations to study the 180° domain walls in tetragonal ferroelectric PbTiO3 and found that the source of Néel components is the gradient of the square of spontaneous polarization. Electronic structural analysis reveals that there is a redistribution of electronic charge density and potential around domain walls, which produces the electric field and N°eel components. This work thus sheds light on the electronic mechanism of the flexoelectric effect around 180° domain walls in tetragonal ferroelectrics. [ABSTRACT FROM AUTHOR]

The flexoelectric effect is the coupling between strain, polarization, and their gradients, which are prominent at the nanoscale. Although this effect is important to understand nanostructures, such as domain walls in ferroelectrics, its electronic mechanism is not clear. In this work, we combined phase-field simulations and first-principles calculations to study the 180° domain walls in tetragonal ferroelectric PbTiO3 and found that the source of Néel components is the gradient of the square of spontaneous polarization. Electronic structural analysis reveals that there is a redistribution of electronic charge density and potential around domain walls, which produces the electric field and N°eel components. This work thus sheds light on the electronic mechanism of the flexoelectric effect around 180° domain walls in tetragonal ferroelectrics. [ABSTRACT FROM AUTHOR]

Flexoelectricity, an intrinsic property observed in materials under nonuniform deformation, entails a coupling between polarization and strain gradients. Recent catalyst advancements have reignited interest in flexoelectricity, particularly at the nanoscale, where pronounced strain gradients promote robust flexoelectric effects. This paper comprehensively examines flexoelectricity, encompassing methodologies for precise measurement, elucidating its distinctions from related phenomena, and exploring its potential applications in augmenting catalytic properties. So far, the greatest potentials are based on lead strontium titanate (PST) and other metallic titanates such as titania (TiO 2 ), strontium titanate (STO), barium strontium titanate (BST) sulfates (MoS 2 , ZnS) and halide perovskites (with archetype XPbI 3 ). This review explores the promise of flexoelectric properties in addressing material and photocatalytic challenges, such as charge carrier recombination and ineffective surface charge separation. Additionally, it sheds light on the synergy with emerging paradigms like photo-flexo catalysis and synergistic flexo-piezo catalysis, specifically focusing on selective chemical transformations like green hydrogen production. Current limitations related to the usage of photoflexoelectricity for photocatalysis are mostly the stability of the used substance (susceptibility to photodegradation) or the voltage values, which represent the inferior potential for specific practical applications. This work underscores the indispensable role of flexoelectricity in catalysis and its capacity to steer future research and technological advancement., (© 2024 The Author(s). Small published by Wiley‐VCH GmbH.)

The mechanical properties at small length scales are not only significant for understanding the intriguing size-dependent behaviors but also critical for device applications. Nanoindentation via atomic force microscopy is widely used for small-scale mechanical testing, yet determining the Young's modulus of quasi-2D films from freestanding force-displacement curve of nanoindentation remains challenging, complicated by both bending and stretching that are highly nonlinear. To overcome these difficulties, a machine learning model is developed based on the back propagation (BP) neural network and finite element training to accurately determine the Young's modulus, pretension, and thickness of freestanding films from nanoindentation force-displacement curves simultaneously, improving the computational efficiency by two orders of magnitude over conventional brute force curve fitting. Using this technique, anomalously high apparent Young's modulus is discovered of 2.8 nm thick PbZr 0.2 Ti 0.8 O 3 (PZT) film as large as 229.4 ± 12.1 GPa, much higher than the bulk value. The enhancement can be attributed to the strain gradient-induced flexoelectric effect, and the corresponding flexoelectric coefficient is estimated to be ≈200 nC m -1 . The method is developed to enable an artificial intelligence (AI) system to study the mechanical properties of a wide range of low-dimensional materials., (© 2024 Wiley‐VCH GmbH.)

The isolation and concentration of electrical charges at ionic-electronic interfaces are prevalent phenomena that impede effective communication between ionic and electronic systems. Detecting these concentrated charges at the interface is crucial for applications, such as signal transmission and ion detection. Current electrical detection approaches introduce additional ionic-electronic interfaces via metallic electrodes with an external stimulating voltage, which alters the initial ion distributions at the interfaces. In this work, we introduce the flexoelectricity of liquids to examine the electrical charge aggregation at ionic-electronic interfaces under cyclic mechanical loads. The measured electrical responses reflect the coupling phenomena between the flexoelectricity and the electric double layer. This proposed approach demonstrates the capability to quantify ion types and concentrations at interfaces. Furthermore, it can identify ion types in mixed solutions and offers high sensitivity at ultralow concentrations. This work promotes a nonchemical, general mechanical method for charge detection at ionic-electronic interfaces.

Since the recent discovery of polar topologies, a recurrent question has been how to remotely tune them. Many efforts have focused on the pumping of polar optical phonons from optical methods, but with limited success, as only switching between specific phases has been achieved so far. Additionally, the correlation between optical pulse characteristics and the resulting phase is poorly understood. Here, we propose an alternative approach and demonstrate the deterministic and dynamical tailoring of polar topologies using acoustic phonon excitations. Our second-principles simulations reveal that by pumping specific longitudinal and transverse acoustic phonons, various topological textures can be induced in materials like BaTiO 3 or PbTiO 3 . This method leverages the strong coupling between polarization and strain in these materials, enabling predictable and dynamic control of polar patterns. Our findings open up an alternative possibility for the manipulation of polar textures, suggesting a promising research direction.

An enduring question in science has been why sliding plays a major role in the triboelectric generation of static electricity-the "tribo" in triboelectricity. We provide here a general explanation which is rooted in established science. When sliding is taking place, there is symmetry breaking due to elastic shear, so the front of the sliding body experiences different elastic strains from the back. Consequently the polarization and associated charges at the front and back are not the same, and the difference between the two leads to current flow similar to the difference in air pressure above and below a plane's wing leading to lift. Specific calculations are provided which show good agreement with prior experimental measurements of size and shape dependencies, and reasonable quantitative agreement with experimental current measurements.

Nearly four decades have passed since IBM scientists pioneered atomic force microscopy (AFM) by merging the principles of a scanning tunneling microscope with the features of a stylus profilometer. Today, electrical AFM modes are an indispensable asset within the semiconductor and nanotechnology industries, enabling the characterization and manipulation of electrical properties at the nanoscale. However, electrical AFM measurements suffer from reproducibility issues caused, for example, by surface contaminations, Joule heating, and hard-to-minimize tip drift and tilt. Using as experimental system nanoscale Schottky diodes assembled on oxide-free silicon crystals of precisely defined surface chemistry, it is revealed that voltage-dependent adhesion forces lead to significant rotation of the AFM platinum tip. The electrostatics-driven tip rotation causes a strain gradient on the silicon surface, which induces a flexoelectric reverse bias term. This directional flexoelectric internal-bias term adds to the external (instrumental) bias, causing both an increased diode leakage as well as a shift of the diode knee voltage to larger forward biases. These findings will aid the design and characterization of silicon-based devices, especially those that are deliberately operated under large strain or shear, such as in emerging energy harvesting technologies including Schottky-based triboelectric nanogenerators (TENGs)., (© 2024 The Author(s). Advanced Science published by Wiley‐VCH GmbH.)

In a flexoelectric sensing element using bending mode, estimation of the flexoelectric coefficient was investigated using 3-D stress/strain analysis and experiments. The proposed method uses the results (deformation and strain) from the finite element analysis (FEA). The estimated flexoelectric coefficients were compared with those obtained via the conventional method (Euler’s beam theory) under the assumption of the quasi 1-D stress field. The results show that the RMS value and standard deviation of the estimated flexoelectric coefficient for the 3-D stress field case of the sensing element are 31.51 µC/m and 0.24%, respectively. In addition, we found that the flexoelectric coefficient obtained from the results of the 3-D stress analysis is 1.8% smaller than that of the quasi-1-D stress analysis. Therefore, in order to obtain a more reliable flexoelectric coefficient in the sensing element, the results of the 3-D numerical stress analysis should be used for accurate estimation of the flexoelectric coefficient.

The low flexoelectric coefficients of polymers are the key problem that limit their application. In this paper, electret-like PDMS/metal conductive layer/PDMS laminated structures have been prepared, an internal electric field are applied on the metal conductive layer aimed at improving electromechanical response. Experiments on the flexoelectric responses of polymer laminated structures under impact are performed based on SHPB, in-layer voltage supply system and polarization voltage measuring system. Numerical simulations are also conducted to investigate the dynamic stress-strain relationship and polarization characteristics of polymer laminated structure under different in-layer voltages. The results show that maximum stress increases with decreasing in-layer voltage; the maximum polarization voltage increases first and then decreases with absolute value of in-layer voltage; the minimum polarization voltage decreases with absolute value of in-layer voltage. Specimen with negative voltage has advantage of conversing electric energy and transferring charges. The impact induced strain gradients have been investigated based on numerical simulation and the related flexoelectricity coefficients are obtained. Addition of metal conductive layer and application of in-layer voltage are effective ways to enhance flexoelectricity.