The flexoelectric effect refers to the electromechanical coupling between electric polarization and mechanical strain gradient.It universally exists in a variety of materials in any space group,such as liquid crystals...The flexoelectric effect refers to the electromechanical coupling between electric polarization and mechanical strain gradient.It universally exists in a variety of materials in any space group,such as liquid crystals,dielectrics,biological materials,and semiconductors.Because of its unique size effect,nanoscale flexoelectricity has shown novel phenomena and promising applications in electronics,optronics,mechatronics,and photovoltaics.In this review,we provide a succinct report on the discovery and development of the flexoelectric effect,focusing on flexoelectric materials and related applications.Finally,we discuss recent flexoelectric research progress and still‐unsolved problems.展开更多
Flexoelectricity refers to the link between electrical polarization and strain gradient fields in piezoelectric materials,particularly at the nano-scale.The present investigation aims to comprehensively focus on the s...Flexoelectricity refers to the link between electrical polarization and strain gradient fields in piezoelectric materials,particularly at the nano-scale.The present investigation aims to comprehensively focus on the static bending analysis of a piezoelectric sandwich functionally graded porous(FGP)double-curved shallow nanoshell based on the flexoelectric effect and nonlocal strain gradient theory.Two coefficients that reduce or increase the stiffness of the nanoshell,including nonlocal and length-scale parameters,are considered to change along the nanoshell thickness direction,and three different porosity rules are novel points in this study.The nanoshell structure is placed on a Pasternak elastic foundation and is made up of three separate layers of material.The outermost layers consist of piezoelectric smart material with flexoelectric effects,while the core layer is composed of FGP material.Hamilton’s principle was used in conjunction with a unique refined higher-order shear deformation theory to derive general equilibrium equations that provide more precise outcomes.The Navier and Galerkin-Vlasov methodology is used to get the static bending characteristics of nanoshells that have various boundary conditions.The program’s correctness is assessed by comparison with published dependable findings in specific instances of the model described in the article.In addition,the influence of parameters such as flexoelectric effect,nonlocal and length scale parameters,elastic foundation stiffness coefficient,porosity coefficient,and boundary conditions on the static bending response of the nanoshell is detected and comprehensively studied.The findings of this study have practical implications for the efficient design and control of comparable systems,such as micro-electromechanical and nano-electromechanical devices.展开更多
Balancing high display performance with energy efficiency is crucial for global sustainability.Lowering operating frequencies—such as enabling 1 Hz operation in fringe-field switching(FFS)liquid crystal displays—red...Balancing high display performance with energy efficiency is crucial for global sustainability.Lowering operating frequencies—such as enabling 1 Hz operation in fringe-field switching(FFS)liquid crystal displays—reduces power consumption but is hindered by image flicker.While negative dielectric anisotropy liquid crystals(nLCs)mitigate flicker,their high driving voltages and production costs limit adoption.Positive dielectric anisotropy liquid crystals(pLCs)offer lower operating voltages,faster response times,and broader applicability,making them a more viable alternative.This study introduces a novel approach to minimizing flexoelectric effects in pLCs by investigating how single components influence flexoelectric behavior in mixtures through an effective experimental methodology.Two innovative measurement techniques—(1)flexoelectric coefficient difference analysis and(2)displacement-current measurement(DCM)—are presented,marking the first application of DCM for verifying flexoelectric effects.The proposed system eliminates uncertainties associated with previous methods,providing a reliable framework for selecting liquid crystal components with minimal flexoelectric effects while preserving key electro-optic properties.Given pLCs'higher reliability,lower production costs,and broader material selection,these advancements hold significant potential for low-power displays.We believe this work enhances flexoelectric analysis in nematic liquid crystals and contributes to sustainable innovation in the display industry,aligning with global energy-saving goals.展开更多
Traditional impact protection structures(IPSs)dissipate impact energy according to the plastic dissipation mechanism,which is only effective for single impacts due to the irreversible deformation of structures.To achi...Traditional impact protection structures(IPSs)dissipate impact energy according to the plastic dissipation mechanism,which is only effective for single impacts due to the irreversible deformation of structures.To achieve multi-impact protection,this paper proposes a novel chiral periodic structure with the deformation self-recovery function and the high energy conversion efficiency based on the flexoelectric mechanism.A theoretical model is formulated on the electromechanical responses of a flexoelectric beam under rotational boundaries.The equivalent stiffness and damping characteristics are subsequently derived to construct the electromechanical responses of the structure under constant velocity and mass impacts.Discussions are addressed for the influence of the structural scale effect and resistance on the electromechanical responses.The results show that the energy conversion efficiency increases by 2 to 3 orders of magnitude,reaching as high as 85.3%,which can match well with those of structures reported in the literature based on the plastic energy dissipating mechanism.展开更多
To address the urgent demand for the miniaturization and multifunctional integration of high-frequency Rayleigh surface wave devices in 5G communication technology,the propagation characteristics of Rayleigh surface w...To address the urgent demand for the miniaturization and multifunctional integration of high-frequency Rayleigh surface wave devices in 5G communication technology,the propagation characteristics of Rayleigh surface waves in an elastic half-space attached by a nanoscale piezoelectric semiconductor(PSC)thin layer with flexoelectricity and size-effects are systematically investigated.Based on the Hamiltonian principle,the elastic dynamic equations and Gauss's theorem of electrostatics are obtained.The eigenvalue problem is numerically solved with a genetic algorithm in MATLAB,and the dispersion properties are obtained.The effects of various key factors,including the flexoelectricity,inertia gradients,strain gradients,electric field gradients,PSC layer thickness,steady-state carrier concentration,and bias electric fields,on the propagation and attenuation characteristics of Rayleigh surface waves are analyzed.The results demonstrate that the increases in the flexoelectric coefficient and strain gradient characteristic length lead to an increase in the real part of the complex phase velocity,while the increases in the inertia gradient characteristic length,electric field gradient characteristic length,PSC layer thickness,and steady-state carrier concentration result in a decrease.Additionally,the bias electric fields significantly influence the Rayleigh surface wave attenuation.The present findings are crucial for the accurate property evaluation of miniaturized highfrequency Rayleigh wave devices,and provide valuable theoretical support for their design and optimization.展开更多
Flexoelectricity is a two-way coupling effect between the strain gradient and electric field that exists in all dielectrics,regardless of point group symmetry.However,the high-order derivatives of displacements involv...Flexoelectricity is a two-way coupling effect between the strain gradient and electric field that exists in all dielectrics,regardless of point group symmetry.However,the high-order derivatives of displacements involved in the strain gradient pose challenges in solving electromechanical coupling problems incorporating the flexoelectric effect.In this study,we formulate a phase-field model for ferroelectric materials considering the flexoelectric effect.A four-node quadrilateral element with 20 degrees of freedom is constructed without introducing high-order shape functions.The microstructure evolution of domains is described by an independent order parameter,namely the spontaneous polarization governed by the time-dependent Ginzburg–Landau theory.The model is developed based on a thermodynamic framework,in which a set of microforces is introduced to construct the constitutive relation and evolution equation.For the flexoelectric part of electric enthalpy,the strain gradient is determined by interpolating the mechanical strain at the node via the values of Gaussian integration points in the isoparametric space.The model is shown to be capable of reproducing the classic analytical solution of dielectric materials incorporating the flexoelectric contribution.The model is verified by duplicating some typical phenomena in flexoelectricity in cylindrical tubes and truncated pyramids.A comparison is made between the polarization distribution in dielectrics and ferroelectrics.The model can reproduce the solution to the boundary value problem of the cylindrical flexoelectric tube,and demonstrate domain twisting at domain walls in ferroelectrics considering the flexoelectric effect.展开更多
Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity;...Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity;therefore, producing a large-scale flexoelectric effect is of great interest. In this paper, we explore a way to enhance the flexoelectric effect by utilizing the snap-through instability and a stiffness gradient present along the length of a curved dielectric plate. To analyze the effect of stiffness profiles on the plate, we employ numerical parameter continuation. Our analysis reveals a nonlinear relationship between the effective electromechanical coupling coefficient and the gradient of Young’s modulus. Moreover, we demonstrate that the quadratic profile is more advantageous than the linear profile. For a dielectric plate with a quadratic profile and a modulus gradient of − 0.9, the effective coefficient can reach as high as 15.74 pC/N, which is over three times the conventional coupling coefficient of piezoelectric material. This paper contributes to our understanding of the amplification of flexoelectric effects by harnessing snapping surfaces and stiffness gradient design.展开更多
The flexoelectric effect describes the interplay between material polarization and strain gradient.While much research has focused on control strategies for flexoelectricity,the impact of ferroelectric domain structur...The flexoelectric effect describes the interplay between material polarization and strain gradient.While much research has focused on control strategies for flexoelectricity,the impact of ferroelectric domain structure on the flexoelectric effect remains elusive.Through phase field simulations,we conduct a comparative study on the flexoelectric response of two types of BaTiO_(3)–SrTiO_(3) binary films:BaTiO_(3)–SrTiO_(3) multilayers and(Ba,Sr)TiO_(3) solid solutions.Our findings reveal that the flexoelectric response of these two systems,at the same Ba/Sr ratio,differs not only in magnitude but also in other aspects like temperature dependence,linearity,and hysteresis,due to their different ferroelectric domain structures and evolution dynamics.Our study deepens our current understanding of flexoelectricity in ferroelectrics and suggests“domain engineering”as a potential way to tailor this effect.展开更多
Biopolymers,the potential flexoelectric materials,are environment-friendly,degradable,lightweight,cost-effective,and possess remarkable processing properties catering to the requirements of advanced devices.However,th...Biopolymers,the potential flexoelectric materials,are environment-friendly,degradable,lightweight,cost-effective,and possess remarkable processing properties catering to the requirements of advanced devices.However,the flexoelectric coefficient of biopolymers is normally much weaker than that of ceramic materials,limiting their potential applications for designing high-performance green electromechanical coupling devices.To improve the flexoelectric response in biopolymers,we composited barium titanate(BTO)with 2,2,6,6-tetramethylpiperidine-1-oxyl-oxidized cellulose nanofibrils(TOCNF)to enhance the flexoelectric response of TOCNF.Owing to the high permittivity and flexoelectric effect of BTO,the relative dielectric constant and flexoelectric coefficient of 33.3 wt%BTO-TOCNF films reached 30.94@1 kHz and 50.05±1.88 nC/m@1 Hz,which were almost 172 times and 27 times higher than those of TOCNF,respectively.The composite thin film contains high dielectric constant and flexoelectric coefficient,as well as excellent flexibility.Our study provided a straightforward and efficient method for improving the flexoelectric effect of biopolymers,and demonstrated its great potential applications in flexoelectric-based devices.展开更多
Based on the three-dimensional(3D)basic equations of piezoelectric semiconductors(PSs),we establish a two-dimensional(2D)deformation-polarization-carrier coupling bending model for PS structures,taking flexoelectricit...Based on the three-dimensional(3D)basic equations of piezoelectric semiconductors(PSs),we establish a two-dimensional(2D)deformation-polarization-carrier coupling bending model for PS structures,taking flexoelectricity into consideration.The analytical solutions to classical flexure of a clamped circular PS thin plate are derived.With the derived analytical model,we numerically investigate the distributions of electromechanical fields and the concentration of electrons in the circular PS thin plate under an upward concentrated force.The effect of flexoelectricity on the multi-field coupling responses of the circular PS plate is studied.The obtained results provide theoretical guidance for the design of novel PS devices.展开更多
This paper presents isogeometric analysis(IGA)-based topology optimization for electrical performance of three-dimensional(3D)flexoelectric structures.IGA is employed to provide{C}^{1}continuity in shape function,whic...This paper presents isogeometric analysis(IGA)-based topology optimization for electrical performance of three-dimensional(3D)flexoelectric structures.IGA is employed to provide{C}^{1}continuity in shape function,which is required in treating high-order electromechanical coupling equations.To improve the computational efficiency in treating 3D problems,the redundant degrees of freedom removal technique is introduced.Regularization treatments are also implemented to avoid the numerical singularity induced by flexoelectricity.Both virtual loads and strain energy constraints are taken into consideration to prevent unexpected structural disconnection.Numerical examples and experiments on optimized structures demonstrate that the flexoelectric performance can be effectively improved using the proposed approach.展开更多
A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization...A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.展开更多
In this study,machine learning representation is introduced to evaluate the flexoelectricity effect in truncated pyramid nanostructure under compression.A Non-Uniform Rational B-spline(NURBS)based IGA formulation is e...In this study,machine learning representation is introduced to evaluate the flexoelectricity effect in truncated pyramid nanostructure under compression.A Non-Uniform Rational B-spline(NURBS)based IGA formulation is employed to model the flexoelectricity.We investigate 2D system with an isotropic linear elastic material under plane strain conditions discretized by 45×30 grid of B-spline elements.Six input parameters are selected to construct a deep neural network(DNN)model.They are the Young's modulus,two dielectric permittivity constants,the longitudinal and transversal flexoelectric coefficients and the order of the shape function.The outputs of interest are the strain in the stress direction and the electric potential due flexoelectricity.The dataset are generated from the forward analysis of the flexoelectric model.80%of the dataset is used for training purpose while the remaining is used for validation by checking the mean squared error.In addition to the input and output layers,the developed DNN model is composed of four hidden layers.The results showed high predictions capabilities of the proposed method with much lower computational time in comparison to the numerical model.展开更多
A nonlocal strain gradient theory(NSGT) accounts for not only the nongradient nonlocal elastic stress but also the nonlocality of higher-order strain gradients,which makes it benefit from both hardening and softening ...A nonlocal strain gradient theory(NSGT) accounts for not only the nongradient nonlocal elastic stress but also the nonlocality of higher-order strain gradients,which makes it benefit from both hardening and softening effects in small-scale structures.In this study, based on the NSGT, an analytical model for the vibration behavior of a piezoelectric sandwich nanobeam is developed with consideration of flexoelectricity. The sandwich nanobeam consists of two piezoelectric sheets and a non-piezoelectric core. The governing equation of vibration of the sandwich beam is obtained by the Hamiltonian principle. The natural vibration frequency of the nanobeam is calculated for the simply supported(SS) boundary, the clamped-clamped(CC) boundary, the clamped-free(CF)boundary, and the clamped-simply supported(CS) boundary. The effects of geometric dimensions, length scale parameters, nonlocal parameters, piezoelectric constants, as well as the flexoelectric constants are discussed. The results demonstrate that both the flexoelectric and piezoelectric constants enhance the vibration frequency of the nanobeam.The nonlocal stress decreases the natural vibration frequency, while the strain gradient increases the natural vibration frequency. The natural vibration frequency based on the NSGT can be increased or decreased, depending on the value of the nonlocal parameter to length scale parameter ratio.展开更多
We study electromechanical responses of a flexoelectric semiconductor plate in bending under mechanical loads.A two-dimensional theory for classical bending without shear deformation is derived from the three-dimensio...We study electromechanical responses of a flexoelectric semiconductor plate in bending under mechanical loads.A two-dimensional theory for classical bending without shear deformation is derived from the three-dimensional macroscopic theory of flexoelectric semiconductors.A simple solution is obtained for pure bending.A combination of physical and geometric parameters is introduced as a measure of the strength of the coupling between the mechanical load and the redistribution of charge carriers.A trigonometric series solution is obtained for a simply supported rectangular plate under a local normal mechanical load,which shows concentration of mobile charges and the formation of electric potential barriers near the loading area.The results are fundamental to the mechanical manipulation of charge carriers in these plates.We also analyze the buckling of a simply supported rectangular plate under in-plane compressive forces.A series of buckling loads and modes are obtained.Numerical results show that flexoelectric coupling exhibits a stiffening effect and increases the buckling load,while semiconduction weakens the flexoelectric stiffening.The distributions of mobile charges in the first few buckling modes are presented.展开更多
Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa.The truncated pyramid compression test is amo...Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa.The truncated pyramid compression test is among the most common setups to estimate the flexoelectric effect.We present a three-dimensional isogeometric formulation of flexoelectricity with its MATLAB implementation for a truncated pyramid setup.Besides educational purposes,this paper presents a precise computational model to illustrate how the localization of strain gradients around pyramidal boundary shapes contributes in generation of electrical energy.The MATLAB code is supposed to help learners in the Isogeometric Analysis and Finite Elements Methods community to learn how to solve a fully coupled problem,which requires higher order approximations,numerically.The complete MATLAB code which is available as source code distributed under a BSD-style license,is provided in the part of Supplementary Materials of the paper.展开更多
In this work,the static and dynamic response of a piezoelectric semiconductor cantilever under the transverse end force with consideration of flexoelectricity and strain gradient elasticity is systematically investiga...In this work,the static and dynamic response of a piezoelectric semiconductor cantilever under the transverse end force with consideration of flexoelectricity and strain gradient elasticity is systematically investigated.The one-dimensional governing equations and the corresponding boundary conditions are derived based on Hamilton’s principle.After that,combining with the linearized equations for the conservation of charge,the effects of characteristic length and flexoelectric coefficient on the working performance of a ZnO nanowire are demonstrated as a numerical case,including the static mechanical and electric fields,natural frequencies,and the frequency–response characteristics at resonances.The results indicate that the flexoelectric effect has a great influence on the electric properties of the nanowire,while the strain gradient effect directly contributes to its mechanical properties.To some extent,the increase in characteristic length is equivalent to the stiffness strengthening.The qualitative results and quantitative data are beneficial for revealing the underlying physical mechanism and provide guidance for the design of piezoelectric semiconductor devices.展开更多
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.De...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.展开更多
A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic （PAN） and hybri...A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic （PAN） and hybrid aligned nematic （HAN） cells, the dependences of the capacitance on the sum of flexoelectric coefficients and the applied voltage are obtained by numerical simulations, and the distributions of the director and the electric potential for different applied voltages and flexoelectric coefficients are also given. Based on this theoretical analysis, we propose an experimental design for measuring the capacitance of a liquid crystal cell using the improved precision LCR meter E4980A （Agilent）. Through comparing the experimental data with the simulated results, the sum of flexoeletric coefficients can be determined.展开更多
A new model of a first-order composite beam with flexoelectric and piezomagnetic layers is developed.The new model is under a transverse magnetic field and can capture the couple stress and its flexoelectric effects.T...A new model of a first-order composite beam with flexoelectric and piezomagnetic layers is developed.The new model is under a transverse magnetic field and can capture the couple stress and its flexoelectric effects.The governing equations are obtained through a variational approach.To illustrate the new model,the static bending problem is analytically solved based on a Navier’s technique.The numerical results reveal that the extension,deflection,and shear deformation of the current or couple stress relevant flexoelectric model are always smaller than those of classical models at very small scale.It is also found that the electric potentials only appear with the presence of the flexoelectric effect for this non-piezoelectric composite beam model.Furthermore,various electric potential distributions can be manipulated by the particular magnetic fields,and remote/non-contact control at micro-and nano-scales can be realized by current functional composite beams.展开更多
基金support of the National Natural Science Foundation of China(Grant Nos.52192611,51872031,61904013,and 62405157)China Postdoctoral Science Foundation(Nos.2023M741890 and GZC20231215)the Fundamental Research Funds for the Central Universities.
文摘The flexoelectric effect refers to the electromechanical coupling between electric polarization and mechanical strain gradient.It universally exists in a variety of materials in any space group,such as liquid crystals,dielectrics,biological materials,and semiconductors.Because of its unique size effect,nanoscale flexoelectricity has shown novel phenomena and promising applications in electronics,optronics,mechatronics,and photovoltaics.In this review,we provide a succinct report on the discovery and development of the flexoelectric effect,focusing on flexoelectric materials and related applications.Finally,we discuss recent flexoelectric research progress and still‐unsolved problems.
基金This work was supported by the Le Quy Don Technical University Research Fund(Grant No.23.1.11).
文摘Flexoelectricity refers to the link between electrical polarization and strain gradient fields in piezoelectric materials,particularly at the nano-scale.The present investigation aims to comprehensively focus on the static bending analysis of a piezoelectric sandwich functionally graded porous(FGP)double-curved shallow nanoshell based on the flexoelectric effect and nonlocal strain gradient theory.Two coefficients that reduce or increase the stiffness of the nanoshell,including nonlocal and length-scale parameters,are considered to change along the nanoshell thickness direction,and three different porosity rules are novel points in this study.The nanoshell structure is placed on a Pasternak elastic foundation and is made up of three separate layers of material.The outermost layers consist of piezoelectric smart material with flexoelectric effects,while the core layer is composed of FGP material.Hamilton’s principle was used in conjunction with a unique refined higher-order shear deformation theory to derive general equilibrium equations that provide more precise outcomes.The Navier and Galerkin-Vlasov methodology is used to get the static bending characteristics of nanoshells that have various boundary conditions.The program’s correctness is assessed by comparison with published dependable findings in specific instances of the model described in the article.In addition,the influence of parameters such as flexoelectric effect,nonlocal and length scale parameters,elastic foundation stiffness coefficient,porosity coefficient,and boundary conditions on the static bending response of the nanoshell is detected and comprehensively studied.The findings of this study have practical implications for the efficient design and control of comparable systems,such as micro-electromechanical and nano-electromechanical devices.
基金supported by Basic Science Research Program through the National Research Foundation(NRF)of Korea,funded by the Ministry of Science and ICT(MSIT),Korea[2022R1A2C2091671]by ITECH R&D Program of MOTIE/KEIT(Ministry of Trade,Industry&Energy/Korea Evaluation Institute of Industrial Technology)[20016808].
文摘Balancing high display performance with energy efficiency is crucial for global sustainability.Lowering operating frequencies—such as enabling 1 Hz operation in fringe-field switching(FFS)liquid crystal displays—reduces power consumption but is hindered by image flicker.While negative dielectric anisotropy liquid crystals(nLCs)mitigate flicker,their high driving voltages and production costs limit adoption.Positive dielectric anisotropy liquid crystals(pLCs)offer lower operating voltages,faster response times,and broader applicability,making them a more viable alternative.This study introduces a novel approach to minimizing flexoelectric effects in pLCs by investigating how single components influence flexoelectric behavior in mixtures through an effective experimental methodology.Two innovative measurement techniques—(1)flexoelectric coefficient difference analysis and(2)displacement-current measurement(DCM)—are presented,marking the first application of DCM for verifying flexoelectric effects.The proposed system eliminates uncertainties associated with previous methods,providing a reliable framework for selecting liquid crystal components with minimal flexoelectric effects while preserving key electro-optic properties.Given pLCs'higher reliability,lower production costs,and broader material selection,these advancements hold significant potential for low-power displays.We believe this work enhances flexoelectric analysis in nematic liquid crystals and contributes to sustainable innovation in the display industry,aligning with global energy-saving goals.
基金Project supported by the National Natural Science Foundation of China(No.12272138)。
文摘Traditional impact protection structures(IPSs)dissipate impact energy according to the plastic dissipation mechanism,which is only effective for single impacts due to the irreversible deformation of structures.To achieve multi-impact protection,this paper proposes a novel chiral periodic structure with the deformation self-recovery function and the high energy conversion efficiency based on the flexoelectric mechanism.A theoretical model is formulated on the electromechanical responses of a flexoelectric beam under rotational boundaries.The equivalent stiffness and damping characteristics are subsequently derived to construct the electromechanical responses of the structure under constant velocity and mass impacts.Discussions are addressed for the influence of the structural scale effect and resistance on the electromechanical responses.The results show that the energy conversion efficiency increases by 2 to 3 orders of magnitude,reaching as high as 85.3%,which can match well with those of structures reported in the literature based on the plastic energy dissipating mechanism.
基金supported by the Singapore Ministry of Education(MOE)Academic Research Fund(AcRF)Tier 1(Nos.RG145/23 and RG78/24)the National Natural Science Foundation of China(No.U24A2005)Ningbo Natural Science Foundation(No.2024J183)。
文摘To address the urgent demand for the miniaturization and multifunctional integration of high-frequency Rayleigh surface wave devices in 5G communication technology,the propagation characteristics of Rayleigh surface waves in an elastic half-space attached by a nanoscale piezoelectric semiconductor(PSC)thin layer with flexoelectricity and size-effects are systematically investigated.Based on the Hamiltonian principle,the elastic dynamic equations and Gauss's theorem of electrostatics are obtained.The eigenvalue problem is numerically solved with a genetic algorithm in MATLAB,and the dispersion properties are obtained.The effects of various key factors,including the flexoelectricity,inertia gradients,strain gradients,electric field gradients,PSC layer thickness,steady-state carrier concentration,and bias electric fields,on the propagation and attenuation characteristics of Rayleigh surface waves are analyzed.The results demonstrate that the increases in the flexoelectric coefficient and strain gradient characteristic length lead to an increase in the real part of the complex phase velocity,while the increases in the inertia gradient characteristic length,electric field gradient characteristic length,PSC layer thickness,and steady-state carrier concentration result in a decrease.Additionally,the bias electric fields significantly influence the Rayleigh surface wave attenuation.The present findings are crucial for the accurate property evaluation of miniaturized highfrequency Rayleigh wave devices,and provide valuable theoretical support for their design and optimization.
基金funded by the National Natural Science Foundation of China(Grant No.12272020)Beijing Natural Science Foundation(Grant No.JQ21001)+1 种基金S.W.acknowledges support from the Fundamental Research Funds for the Central Universities(Grant No.YWF-23-SDHK-L-019)M.Y.acknowledges support from the National Natural Science Foundation of China(Grant Nos.12302134,12272173,and 11902150).
文摘Flexoelectricity is a two-way coupling effect between the strain gradient and electric field that exists in all dielectrics,regardless of point group symmetry.However,the high-order derivatives of displacements involved in the strain gradient pose challenges in solving electromechanical coupling problems incorporating the flexoelectric effect.In this study,we formulate a phase-field model for ferroelectric materials considering the flexoelectric effect.A four-node quadrilateral element with 20 degrees of freedom is constructed without introducing high-order shape functions.The microstructure evolution of domains is described by an independent order parameter,namely the spontaneous polarization governed by the time-dependent Ginzburg–Landau theory.The model is developed based on a thermodynamic framework,in which a set of microforces is introduced to construct the constitutive relation and evolution equation.For the flexoelectric part of electric enthalpy,the strain gradient is determined by interpolating the mechanical strain at the node via the values of Gaussian integration points in the isoparametric space.The model is shown to be capable of reproducing the classic analytical solution of dielectric materials incorporating the flexoelectric contribution.The model is verified by duplicating some typical phenomena in flexoelectricity in cylindrical tubes and truncated pyramids.A comparison is made between the polarization distribution in dielectrics and ferroelectrics.The model can reproduce the solution to the boundary value problem of the cylindrical flexoelectric tube,and demonstrate domain twisting at domain walls in ferroelectrics considering the flexoelectric effect.
文摘Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity;therefore, producing a large-scale flexoelectric effect is of great interest. In this paper, we explore a way to enhance the flexoelectric effect by utilizing the snap-through instability and a stiffness gradient present along the length of a curved dielectric plate. To analyze the effect of stiffness profiles on the plate, we employ numerical parameter continuation. Our analysis reveals a nonlinear relationship between the effective electromechanical coupling coefficient and the gradient of Young’s modulus. Moreover, we demonstrate that the quadratic profile is more advantageous than the linear profile. For a dielectric plate with a quadratic profile and a modulus gradient of − 0.9, the effective coefficient can reach as high as 15.74 pC/N, which is over three times the conventional coupling coefficient of piezoelectric material. This paper contributes to our understanding of the amplification of flexoelectric effects by harnessing snapping surfaces and stiffness gradient design.
基金support from the National Natural Science Foundation of China(Grant Nos.12222214,and 12132020)the Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices(No.2022B1212010008)+1 种基金the Shenzhen Science and Techonlogy Program(Grant Nos.202206193000001 and 20220818181805001)Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(SML2021SP405).
文摘The flexoelectric effect describes the interplay between material polarization and strain gradient.While much research has focused on control strategies for flexoelectricity,the impact of ferroelectric domain structure on the flexoelectric effect remains elusive.Through phase field simulations,we conduct a comparative study on the flexoelectric response of two types of BaTiO_(3)–SrTiO_(3) binary films:BaTiO_(3)–SrTiO_(3) multilayers and(Ba,Sr)TiO_(3) solid solutions.Our findings reveal that the flexoelectric response of these two systems,at the same Ba/Sr ratio,differs not only in magnitude but also in other aspects like temperature dependence,linearity,and hysteresis,due to their different ferroelectric domain structures and evolution dynamics.Our study deepens our current understanding of flexoelectricity in ferroelectrics and suggests“domain engineering”as a potential way to tailor this effect.
基金supported by the National Natural Science Foundation of China(Grant Nos.12272285,12322205,and 12122209)the Young Elite Scientist Sponsorship Program by CAST(Grant No.2019QNRC001)+1 种基金the 1000-Plan Program of Shaanxi Provincethe Young Talent Support Plan of Xi’an Jiaotong University.
文摘Biopolymers,the potential flexoelectric materials,are environment-friendly,degradable,lightweight,cost-effective,and possess remarkable processing properties catering to the requirements of advanced devices.However,the flexoelectric coefficient of biopolymers is normally much weaker than that of ceramic materials,limiting their potential applications for designing high-performance green electromechanical coupling devices.To improve the flexoelectric response in biopolymers,we composited barium titanate(BTO)with 2,2,6,6-tetramethylpiperidine-1-oxyl-oxidized cellulose nanofibrils(TOCNF)to enhance the flexoelectric response of TOCNF.Owing to the high permittivity and flexoelectric effect of BTO,the relative dielectric constant and flexoelectric coefficient of 33.3 wt%BTO-TOCNF films reached 30.94@1 kHz and 50.05±1.88 nC/m@1 Hz,which were almost 172 times and 27 times higher than those of TOCNF,respectively.The composite thin film contains high dielectric constant and flexoelectric coefficient,as well as excellent flexibility.Our study provided a straightforward and efficient method for improving the flexoelectric effect of biopolymers,and demonstrated its great potential applications in flexoelectric-based devices.
基金supported by the National Natural Science Foundation of China(Nos.12172326,11972319,and 12302210)the Natural Science Foundation of Zhejiang province,China(No.LR21A020002)the specialized research projects of Huanjiang Laboratory.
文摘Based on the three-dimensional(3D)basic equations of piezoelectric semiconductors(PSs),we establish a two-dimensional(2D)deformation-polarization-carrier coupling bending model for PS structures,taking flexoelectricity into consideration.The analytical solutions to classical flexure of a clamped circular PS thin plate are derived.With the derived analytical model,we numerically investigate the distributions of electromechanical fields and the concentration of electrons in the circular PS thin plate under an upward concentrated force.The effect of flexoelectricity on the multi-field coupling responses of the circular PS plate is studied.The obtained results provide theoretical guidance for the design of novel PS devices.
基金support from the National Natural Science Foundation of China(12272075)Liao Ning Revitalization Talents Program(XLYC2001003,XLYC1907119)+1 种基金Fundamental Research Funds for the Central Universities(DUT22QN238)Program for Changjiang Scholars,Innovative Research Team in University(PCSIRT)and 111 Project(B14013)is gratefully acknowledged.
文摘This paper presents isogeometric analysis(IGA)-based topology optimization for electrical performance of three-dimensional(3D)flexoelectric structures.IGA is employed to provide{C}^{1}continuity in shape function,which is required in treating high-order electromechanical coupling equations.To improve the computational efficiency in treating 3D problems,the redundant degrees of freedom removal technique is introduced.Regularization treatments are also implemented to avoid the numerical singularity induced by flexoelectricity.Both virtual loads and strain energy constraints are taken into consideration to prevent unexpected structural disconnection.Numerical examples and experiments on optimized structures demonstrate that the flexoelectric performance can be effectively improved using the proposed approach.
基金supported by a Major Research Project in Higher Education Institutions in Henan Province,with Project Number 23A560015.
文摘A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.
文摘In this study,machine learning representation is introduced to evaluate the flexoelectricity effect in truncated pyramid nanostructure under compression.A Non-Uniform Rational B-spline(NURBS)based IGA formulation is employed to model the flexoelectricity.We investigate 2D system with an isotropic linear elastic material under plane strain conditions discretized by 45×30 grid of B-spline elements.Six input parameters are selected to construct a deep neural network(DNN)model.They are the Young's modulus,two dielectric permittivity constants,the longitudinal and transversal flexoelectric coefficients and the order of the shape function.The outputs of interest are the strain in the stress direction and the electric potential due flexoelectricity.The dataset are generated from the forward analysis of the flexoelectric model.80%of the dataset is used for training purpose while the remaining is used for validation by checking the mean squared error.In addition to the input and output layers,the developed DNN model is composed of four hidden layers.The results showed high predictions capabilities of the proposed method with much lower computational time in comparison to the numerical model.
基金Project supported by the National Natural Science Foundation of China(Nos.51965041,1197237,11602072)。
文摘A nonlocal strain gradient theory(NSGT) accounts for not only the nongradient nonlocal elastic stress but also the nonlocality of higher-order strain gradients,which makes it benefit from both hardening and softening effects in small-scale structures.In this study, based on the NSGT, an analytical model for the vibration behavior of a piezoelectric sandwich nanobeam is developed with consideration of flexoelectricity. The sandwich nanobeam consists of two piezoelectric sheets and a non-piezoelectric core. The governing equation of vibration of the sandwich beam is obtained by the Hamiltonian principle. The natural vibration frequency of the nanobeam is calculated for the simply supported(SS) boundary, the clamped-clamped(CC) boundary, the clamped-free(CF)boundary, and the clamped-simply supported(CS) boundary. The effects of geometric dimensions, length scale parameters, nonlocal parameters, piezoelectric constants, as well as the flexoelectric constants are discussed. The results demonstrate that both the flexoelectric and piezoelectric constants enhance the vibration frequency of the nanobeam.The nonlocal stress decreases the natural vibration frequency, while the strain gradient increases the natural vibration frequency. The natural vibration frequency based on the NSGT can be increased or decreased, depending on the value of the nonlocal parameter to length scale parameter ratio.
基金This work was supported by the National Natural Science Foundation of China(No.12072253)111 Project version 2.0,and the Fundamental Research Funds for the Central Universities(xzy022020016).
文摘We study electromechanical responses of a flexoelectric semiconductor plate in bending under mechanical loads.A two-dimensional theory for classical bending without shear deformation is derived from the three-dimensional macroscopic theory of flexoelectric semiconductors.A simple solution is obtained for pure bending.A combination of physical and geometric parameters is introduced as a measure of the strength of the coupling between the mechanical load and the redistribution of charge carriers.A trigonometric series solution is obtained for a simply supported rectangular plate under a local normal mechanical load,which shows concentration of mobile charges and the formation of electric potential barriers near the loading area.The results are fundamental to the mechanical manipulation of charge carriers in these plates.We also analyze the buckling of a simply supported rectangular plate under in-plane compressive forces.A series of buckling loads and modes are obtained.Numerical results show that flexoelectric coupling exhibits a stiffening effect and increases the buckling load,while semiconduction weakens the flexoelectric stiffening.The distributions of mobile charges in the first few buckling modes are presented.
基金Hamid Ghasemi acknowledge the support of the Mechanical Engineering department at Arak University of Technology.Xiaoying Zhuang gratefully acknowledge the financial support by European Research Council for COTOFLEXI project(802205)Harold Park acknowledges the support of the Mechanical Engineering department at Boston University.Timon Rabczuk gratefully acknowledge financial support by the 2019 Foreign Experts Plan of Hebei Province.
文摘Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa.The truncated pyramid compression test is among the most common setups to estimate the flexoelectric effect.We present a three-dimensional isogeometric formulation of flexoelectricity with its MATLAB implementation for a truncated pyramid setup.Besides educational purposes,this paper presents a precise computational model to illustrate how the localization of strain gradients around pyramidal boundary shapes contributes in generation of electrical energy.The MATLAB code is supposed to help learners in the Isogeometric Analysis and Finite Elements Methods community to learn how to solve a fully coupled problem,which requires higher order approximations,numerically.The complete MATLAB code which is available as source code distributed under a BSD-style license,is provided in the part of Supplementary Materials of the paper.
基金This work was supported by the National Natural Science Foundation of China(12061131013 and 11972276)the State Key Laboratory of Mechanics and Control of Mechanical Structures at NUAA(No.MCMS-E-0520K02)+1 种基金the Fundamental Research Funds for the Central Universities(NE2020002 and NS2019007)the start-up fund supported by NUAA,and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD).
文摘In this work,the static and dynamic response of a piezoelectric semiconductor cantilever under the transverse end force with consideration of flexoelectricity and strain gradient elasticity is systematically investigated.The one-dimensional governing equations and the corresponding boundary conditions are derived based on Hamilton’s principle.After that,combining with the linearized equations for the conservation of charge,the effects of characteristic length and flexoelectric coefficient on the working performance of a ZnO nanowire are demonstrated as a numerical case,including the static mechanical and electric fields,natural frequencies,and the frequency–response characteristics at resonances.The results indicate that the flexoelectric effect has a great influence on the electric properties of the nanowire,while the strain gradient effect directly contributes to its mechanical properties.To some extent,the increase in characteristic length is equivalent to the stiffness strengthening.The qualitative results and quantitative data are beneficial for revealing the underlying physical mechanism and provide guidance for the design of piezoelectric semiconductor devices.
基金supported by the National Natural Science Foundation of China(Grant Nos.12122209,12072251,and 12102153)the Project B18040.
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11274088,11374087,and 11304074)the Natural Science Foundation of Hebei Province,China(Grant No.A2014202123)+2 种基金the Research Project of Hebei Education Department,China(Grant Nos.Z2012061 and QN2014130)the Science and Technology Plan Project of Hebei Province,China(Grant No.134576260)the Key Subject Construction Project of Hebei Province University,China
文摘A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic （PAN） and hybrid aligned nematic （HAN） cells, the dependences of the capacitance on the sum of flexoelectric coefficients and the applied voltage are obtained by numerical simulations, and the distributions of the director and the electric potential for different applied voltages and flexoelectric coefficients are also given. Based on this theoretical analysis, we propose an experimental design for measuring the capacitance of a liquid crystal cell using the improved precision LCR meter E4980A （Agilent）. Through comparing the experimental data with the simulated results, the sum of flexoeletric coefficients can be determined.
基金This work was supported by the National Natural Science Foundation of China(Grants 12002086 and 12072253).
文摘A new model of a first-order composite beam with flexoelectric and piezomagnetic layers is developed.The new model is under a transverse magnetic field and can capture the couple stress and its flexoelectric effects.The governing equations are obtained through a variational approach.To illustrate the new model,the static bending problem is analytically solved based on a Navier’s technique.The numerical results reveal that the extension,deflection,and shear deformation of the current or couple stress relevant flexoelectric model are always smaller than those of classical models at very small scale.It is also found that the electric potentials only appear with the presence of the flexoelectric effect for this non-piezoelectric composite beam model.Furthermore,various electric potential distributions can be manipulated by the particular magnetic fields,and remote/non-contact control at micro-and nano-scales can be realized by current functional composite beams.
