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
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
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
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
A finite element model is proposed permitting prediction of elastic wave bandgaps of periodic composite microplates incorporating flexoelectric effect.In this model,we applied curvature-based flexoelectricity and Mind...A finite element model is proposed permitting prediction of elastic wave bandgaps of periodic composite microplates incorporating flexoelectric effect.In this model,we applied curvature-based flexoelectricity and Mindlin plate theories and derived a finite element formulation that has been implemented for bandgap analysis.The finite element model utilizes a three-node triangle element with 30 degrees of freedom satisfying Mindlin kinematics assumptions.It is based on a non-conforming interpolation scheme which provides nodal C^(1) continuity and ensures compatibility with curvature-based flexoelectricity.The approach accounts for microstructure effects and,owing to the triangular element topology,can be used to assist the design of microplates with complex microstructures.Validation of the approach is performed through comparison with both analytical and numerical models,in which the effect of flexoelectricity on the bandgap is studied based on cases demonstrating size dependence.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
Flexoelectric effect, referring to the strain gradient induced polarization, widely exists in dielectric materials, but its molecular dynamics has not been studied so much so far. In this work, the radial distribution...Flexoelectric effect, referring to the strain gradient induced polarization, widely exists in dielectric materials, but its molecular dynamics has not been studied so much so far. In this work, the radial distribution function of BaTiO_(3) and the phase transition temperatures have been investigated, and the results show that the core-shell potential model is effective and the structure of BaTiO_(3) is stable in a temperature range of 10 K–150 K. Molecular dynamics simulated hysteresis loops of BaTiO_(3) show that anisotropy can play an important role in the coercive field. Based on the rational simulation process,the effects of cantilever beam bent angle and fixed length on the polarization are analyzed. It is found that the small bent angle of the curved cantilever beam can give a proportional relationship with a fixed end length and a non-linear relationship is presented when the bent angle is much larger. The prediction of flexoelectric coefficient in BaTiO_(3) is 18.5 nC/m. This work provides a computational framework for the study of flexoelectric effect by using molecular dynamics.展开更多
This paper presents a nonlinear thickness-shear vibration model for onedimensional infinite piezoelectric plate with flexoelectricity and geometric nonlinearity.The constitutive equations with flexoelectricity and gov...This paper presents a nonlinear thickness-shear vibration model for onedimensional infinite piezoelectric plate with flexoelectricity and geometric nonlinearity.The constitutive equations with flexoelectricity and governing equations are derived from the Gibbs energy density function and variational principle.The displacement adopted here is assumed to be antisymmetric through the thickness due to the thickness-shear vibration mode.Only the shear strain gradient through the thickness is considered in the present model.With geometric nonlinearity,the governing equations are converted into differential equations as the function of time by the Galerkin method.The method of multiple scales is employed to obtain the solution to the nonlinear governing equation with first order approximation.Numerical results show that the nonlinear thickness-shear vibration of piezoelectric plate is size dependent,and the flexoelectric effect has significant influence on the nonlinear thickness-shear vibration frequencies of micro-size thin plates.The geometric nonlinearity also affects the thickness-shear vibration frequencies greatly.The results show that flexoelectricity and geometric nonlinearity cannot be ignored in design of accurate high-frequency piezoelectric devices.展开更多
Coupling the effects of flexoelectricity with piezoelectricity has been proved to effectively harvest mechanical energy.In this study,a composition-graded core–shell structure(HAP@FAP)was prepared by surface-gradient...Coupling the effects of flexoelectricity with piezoelectricity has been proved to effectively harvest mechanical energy.In this study,a composition-graded core–shell structure(HAP@FAP)was prepared by surface-gradient F-doping in hydroxyapatite,which could introduce flexoelectricity by a built-in strain gradient.A flexoelectric-boosted piezoelectric response was demonstrated by piezoresponse force microscopy(PFM)characterization,showing that the piezoelectric constant of HAP@FAP was increased by 2.25 times via a lattice strain gradient induced by chemical heterogeneities derived from the unique composition-graded core-shell structure.Thus,the piezocatalytic activity of HAP@FAP for phenanthrene(PHE)degradation in soil was enhanced.This work provides a new strategy for the modification of piezoelectric catalysts for the remediation of organics-contaminated soils on industrial land.展开更多
Flexoelectric effect describes the electromechanical coupling between the strain gradient and its internal polarization in all dielectrics.Despite this universality,the resulting flexoelectric field remains small at t...Flexoelectric effect describes the electromechanical coupling between the strain gradient and its internal polarization in all dielectrics.Despite this universality,the resulting flexoelectric field remains small at the macroscopic level.However,in nanosystems,the size-dependent effect of flexoelectricity becomes increasingly significant,leading to a notable flexoelectric field that can strongly influence the material’s physical properties.This review aims to explore the flexoelectric effect specifically at the nanoscale.We achieve this by examining strain gradients generated through two distinct methods:internal inhomogeneous strain and external stimulation.In addition,advanced synthesis techniques are utilized to enhance the properties and functionalities associated with flexoelectricity.Furthermore,we delve into other coupled phenomena observed in thin films,including the coupling and utilization of flexomagnetic and flexophotovoltaic effects.This review presents the latest advancements in these areas and highlights their role in driving further breakthroughs in the field of flexoelectricity.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
Flexoelectricity in dielectrics suggests promising smart structures for sensors,actuators and transducers.In this review,dielectric materials,structures and the associated flexoelectric characterization methods are pr...Flexoelectricity in dielectrics suggests promising smart structures for sensors,actuators and transducers.In this review,dielectric materials,structures and the associated flexoelectric characterization methods are presented.First of all,we review structures and methods to measure different flexoelectric coefficients,includingμ1122;μ1111;μ1211;μ3121;μ2312;μ1123,etc.,via direct or converse flexoelectric effect.The flexoelectric materials in the form of bulk,thin films and 2D materials and the reported flexoelectric properties of these dielectrics will then be discussed.Semiconductor materials and the associated flexoelectric studies will also be reviewed.The progress of flexoelectric device study will next be presented,followed by the flexoelectricity research challenges and future trend.展开更多
Flexoelectricity is a symmetry independent electromechanical cou-pling phenomenon that outperforms piezoelectricity at micro and nanoscales due to its size-dependent behavior arising from gradi-ent terms in its consti...Flexoelectricity is a symmetry independent electromechanical cou-pling phenomenon that outperforms piezoelectricity at micro and nanoscales due to its size-dependent behavior arising from gradi-ent terms in its constitutive relations.However,due to this gradient term flexoelectricity,to exhibit itself,requires specially designed geometry or material composition of the dielectric material.First of its kind,the present study put forward a novel strategy of achieving electric field gradient and thereby converse flexoelectri-city,independent of geometry and material composition of the material.The spatial variation of the electric field is established inside the dielectric material,Ba_(0.67)Sr_(0.33)TiO_(3)(BST),by manipulating electrical boundary conditions.Three unique patterns of electrode placement are suggested to achieve this spatial variation.This varying direction of electric field gives rise to electric field gradient,the prerequisite of converse flexoelectricity.A multi-physics cou-pling based theoretical framework is established to solve the flexo-electric actuation by employing isogeometric analysis(IGA).Electromechanically coupled equations of flexoelectricity are solved to obtain the electric field distribution and the resulting displace-ments thereby.The maximum displacements of 0.2 nm and 2.36 nm are obtained with patterns I and II,respectively,while pattern III can yield up to 85 nm of maximum displacement.展开更多
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
Our extensive first-principles calculations reveal that the chemical activities of monolayer transition metal dichalcogenides(TMDs)MX_(2)(M=Mo or W,and X=Te,Se,or S)for water splitting and hydrogen evolution are modif...Our extensive first-principles calculations reveal that the chemical activities of monolayer transition metal dichalcogenides(TMDs)MX_(2)(M=Mo or W,and X=Te,Se,or S)for water splitting and hydrogen evolution are modified and promoted on their grain boundaries(GBs)when in-plane tensile loadings are applied.Compared with monolayer TMDs without GBs,the flexoelectricity induced by nonuniform deformation and strain gradient significantly enhances the charge polarizations of X and M atoms at the GB sites of monolayer TMDs,which facilitates the dissociation of water molecules on the GB sites and reduces the reaction barrier of hydrogen evolution reaction.The energy barriers of splitting water molecules and hydrogen adsorption free energies on the GB sites decrease with increasing the flexoelectric effect.These results highlight an attractive way of utilizing the flexoelectric effect of GB-containing TMDs to improve their surface catalytic capability for hydrogen generation.展开更多
In this work,we successfully prepared vertically aligned NaNbO_(3)nanotube(NN-NT)with trapezoidal shapes,in which the orthorhombic and monoclinic phases coexisted.According to the structure analysis,the NN-NT/epoxy co...In this work,we successfully prepared vertically aligned NaNbO_(3)nanotube(NN-NT)with trapezoidal shapes,in which the orthorhombic and monoclinic phases coexisted.According to the structure analysis,the NN-NT/epoxy composite film had excellent flexoelectric properties due to the lattice distortion caused by defects and irregular shape.The flexoelectric effect is the greatest in the vertical direction in the flexible NN-NT/epoxy composite film,and the flexoelectric coefficient()is 2.77×10^(−8)C·m^(−1),which is approximately 5-fold higher than that of the pure epoxy film.The photovoltaic current of the NN-NT/epoxy composite film increased from 39.9 to 71.8 nA·cm^(−2)in the direction of spontaneous polarization when the sample was bent upward due to the flexoelectricity-enhanced photovoltaic(FPV)effect.The flexoelectric effect of the NN-NT/epoxy composite film could modulate the photovoltaic response by increasing it by 80%or reducing it to 65%of the original value.This work provides a new idea for further exploration in efficient and lossless ferroelectric memory devices.展开更多
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.
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.
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.
文摘A finite element model is proposed permitting prediction of elastic wave bandgaps of periodic composite microplates incorporating flexoelectric effect.In this model,we applied curvature-based flexoelectricity and Mindlin plate theories and derived a finite element formulation that has been implemented for bandgap analysis.The finite element model utilizes a three-node triangle element with 30 degrees of freedom satisfying Mindlin kinematics assumptions.It is based on a non-conforming interpolation scheme which provides nodal C^(1) continuity and ensures compatibility with curvature-based flexoelectricity.The approach accounts for microstructure effects and,owing to the triangular element topology,can be used to assist the design of microplates with complex microstructures.Validation of the approach is performed through comparison with both analytical and numerical models,in which the effect of flexoelectricity on the bandgap is studied based on cases demonstrating size dependence.
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Project supported by the Natural Science Funds of Ningxia,China (Grant No.ZR1221)the National Natural Science Foundation of China (Grant No.11964027)。
文摘Flexoelectric effect, referring to the strain gradient induced polarization, widely exists in dielectric materials, but its molecular dynamics has not been studied so much so far. In this work, the radial distribution function of BaTiO_(3) and the phase transition temperatures have been investigated, and the results show that the core-shell potential model is effective and the structure of BaTiO_(3) is stable in a temperature range of 10 K–150 K. Molecular dynamics simulated hysteresis loops of BaTiO_(3) show that anisotropy can play an important role in the coercive field. Based on the rational simulation process,the effects of cantilever beam bent angle and fixed length on the polarization are analyzed. It is found that the small bent angle of the curved cantilever beam can give a proportional relationship with a fixed end length and a non-linear relationship is presented when the bent angle is much larger. The prediction of flexoelectric coefficient in BaTiO_(3) is 18.5 nC/m. This work provides a computational framework for the study of flexoelectric effect by using molecular dynamics.
基金Project supported by the National Natural Science Foundation of China(No.11702150)the Natural Science Foundation of Zhejiang Province of China(Nos.LY20A020002 and LY21A020003)+3 种基金the Natural Science Foundation of Ningbo(No.202003N4015)the Project of Key Laboratory of Impact and Safety Engineering(Ningbo University)the Ministry of Education(No.CJ202009)the Technology Innovation 2025 Program of Municipality of Ningbo(No.2019B10122)。
文摘This paper presents a nonlinear thickness-shear vibration model for onedimensional infinite piezoelectric plate with flexoelectricity and geometric nonlinearity.The constitutive equations with flexoelectricity and governing equations are derived from the Gibbs energy density function and variational principle.The displacement adopted here is assumed to be antisymmetric through the thickness due to the thickness-shear vibration mode.Only the shear strain gradient through the thickness is considered in the present model.With geometric nonlinearity,the governing equations are converted into differential equations as the function of time by the Galerkin method.The method of multiple scales is employed to obtain the solution to the nonlinear governing equation with first order approximation.Numerical results show that the nonlinear thickness-shear vibration of piezoelectric plate is size dependent,and the flexoelectric effect has significant influence on the nonlinear thickness-shear vibration frequencies of micro-size thin plates.The geometric nonlinearity also affects the thickness-shear vibration frequencies greatly.The results show that flexoelectricity and geometric nonlinearity cannot be ignored in design of accurate high-frequency piezoelectric devices.
基金the financial support provided by the National Natural Science Foundation of China(51973148 and 21938006)the National Key Technology R&D Program(2020YFC1818401)+1 种基金Basic Research Project of Leading Technology in Jiangsu Province(BK20202012)project supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD).
文摘Coupling the effects of flexoelectricity with piezoelectricity has been proved to effectively harvest mechanical energy.In this study,a composition-graded core–shell structure(HAP@FAP)was prepared by surface-gradient F-doping in hydroxyapatite,which could introduce flexoelectricity by a built-in strain gradient.A flexoelectric-boosted piezoelectric response was demonstrated by piezoresponse force microscopy(PFM)characterization,showing that the piezoelectric constant of HAP@FAP was increased by 2.25 times via a lattice strain gradient induced by chemical heterogeneities derived from the unique composition-graded core-shell structure.Thus,the piezocatalytic activity of HAP@FAP for phenanthrene(PHE)degradation in soil was enhanced.This work provides a new strategy for the modification of piezoelectric catalysts for the remediation of organics-contaminated soils on industrial land.
基金supported by the National Natural Science Foundation of China(Nos.51962020,12174174)Support from the Natural Science Foundation of Jiangxi Province(No.20212ACB214011)was also acknowledged.
文摘Flexoelectric effect describes the electromechanical coupling between the strain gradient and its internal polarization in all dielectrics.Despite this universality,the resulting flexoelectric field remains small at the macroscopic level.However,in nanosystems,the size-dependent effect of flexoelectricity becomes increasingly significant,leading to a notable flexoelectric field that can strongly influence the material’s physical properties.This review aims to explore the flexoelectric effect specifically at the nanoscale.We achieve this by examining strain gradients generated through two distinct methods:internal inhomogeneous strain and external stimulation.In addition,advanced synthesis techniques are utilized to enhance the properties and functionalities associated with flexoelectricity.Furthermore,we delve into other coupled phenomena observed in thin films,including the coupling and utilization of flexomagnetic and flexophotovoltaic effects.This review presents the latest advancements in these areas and highlights their role in driving further breakthroughs in the field of flexoelectricity.
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.
文摘Flexoelectricity in dielectrics suggests promising smart structures for sensors,actuators and transducers.In this review,dielectric materials,structures and the associated flexoelectric characterization methods are presented.First of all,we review structures and methods to measure different flexoelectric coefficients,includingμ1122;μ1111;μ1211;μ3121;μ2312;μ1123,etc.,via direct or converse flexoelectric effect.The flexoelectric materials in the form of bulk,thin films and 2D materials and the reported flexoelectric properties of these dielectrics will then be discussed.Semiconductor materials and the associated flexoelectric studies will also be reviewed.The progress of flexoelectric device study will next be presented,followed by the flexoelectricity research challenges and future trend.
文摘Flexoelectricity is a symmetry independent electromechanical cou-pling phenomenon that outperforms piezoelectricity at micro and nanoscales due to its size-dependent behavior arising from gradi-ent terms in its constitutive relations.However,due to this gradient term flexoelectricity,to exhibit itself,requires specially designed geometry or material composition of the dielectric material.First of its kind,the present study put forward a novel strategy of achieving electric field gradient and thereby converse flexoelectri-city,independent of geometry and material composition of the material.The spatial variation of the electric field is established inside the dielectric material,Ba_(0.67)Sr_(0.33)TiO_(3)(BST),by manipulating electrical boundary conditions.Three unique patterns of electrode placement are suggested to achieve this spatial variation.This varying direction of electric field gives rise to electric field gradient,the prerequisite of converse flexoelectricity.A multi-physics cou-pling based theoretical framework is established to solve the flexo-electric actuation by employing isogeometric analysis(IGA).Electromechanically coupled equations of flexoelectricity are solved to obtain the electric field distribution and the resulting displace-ments thereby.The maximum displacements of 0.2 nm and 2.36 nm are obtained with patterns I and II,respectively,while pattern III can yield up to 85 nm of maximum displacement.
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 the National Natural Science Foundation of China(Nos.11972186,11890674,and 51921003)the Fundamental Research Funds for the Central Universities(No.NE2019001)of Chinaa Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘Our extensive first-principles calculations reveal that the chemical activities of monolayer transition metal dichalcogenides(TMDs)MX_(2)(M=Mo or W,and X=Te,Se,or S)for water splitting and hydrogen evolution are modified and promoted on their grain boundaries(GBs)when in-plane tensile loadings are applied.Compared with monolayer TMDs without GBs,the flexoelectricity induced by nonuniform deformation and strain gradient significantly enhances the charge polarizations of X and M atoms at the GB sites of monolayer TMDs,which facilitates the dissociation of water molecules on the GB sites and reduces the reaction barrier of hydrogen evolution reaction.The energy barriers of splitting water molecules and hydrogen adsorption free energies on the GB sites decrease with increasing the flexoelectric effect.These results highlight an attractive way of utilizing the flexoelectric effect of GB-containing TMDs to improve their surface catalytic capability for hydrogen generation.
基金supported by the National Key Research&Development project from the Ministry of Science and Technology in China(No.2021YFB3200303)It was also partially supported by the National Natural Science Foundation of China(No.52172082).
文摘In this work,we successfully prepared vertically aligned NaNbO_(3)nanotube(NN-NT)with trapezoidal shapes,in which the orthorhombic and monoclinic phases coexisted.According to the structure analysis,the NN-NT/epoxy composite film had excellent flexoelectric properties due to the lattice distortion caused by defects and irregular shape.The flexoelectric effect is the greatest in the vertical direction in the flexible NN-NT/epoxy composite film,and the flexoelectric coefficient()is 2.77×10^(−8)C·m^(−1),which is approximately 5-fold higher than that of the pure epoxy film.The photovoltaic current of the NN-NT/epoxy composite film increased from 39.9 to 71.8 nA·cm^(−2)in the direction of spontaneous polarization when the sample was bent upward due to the flexoelectricity-enhanced photovoltaic(FPV)effect.The flexoelectric effect of the NN-NT/epoxy composite film could modulate the photovoltaic response by increasing it by 80%or reducing it to 65%of the original value.This work provides a new idea for further exploration in efficient and lossless ferroelectric memory devices.
