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
When the size of a magneto-electro-elastic cylindrical shell (MEECS) is reduced to micro-/nano-scale, the size-dependent flexomagnetic effect (FME) and flexoelectric effect (FEE) significantly influence their multi-ph...When the size of a magneto-electro-elastic cylindrical shell (MEECS) is reduced to micro-/nano-scale, the size-dependent flexomagnetic effect (FME) and flexoelectric effect (FEE) significantly influence their multi-physical coupling behaviors. To investigate these effects on the post-buckling behaviors of an MEECS, a nonlinear post-buckling model is developed based on the higher-order shear deformation theory (HSDT) and magneto-electro-elastic (MEE) constitutive relations with the FME and FEE. The equilibrium path and the corresponding shell deformations are obtained with a set of newly developed generalized displacement functions within the framework of the Galerkin approach. These displacement functions are established based on the trigonometric series expansions, which accurately satisfy the clamped boundary conditions (BCs). The effects of geometry, flexomagnetic/flexoelectric coefficients, and external electromagnetic fields on the post-buckling behaviors of an MEECS with the FME and FEE are analyzed. Numerical results indicate that the FME decreases the upper critical load of an MEECS, whereas the FEE exhibits an opposite effect by increasing it.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
Based on the experimental phenomena of flexoelectric response at defect sites in nematic inversion walls conducted by Kumar et al., we gave the theoretical analysis using the Frank elastic theory. When a direct-curren...Based on the experimental phenomena of flexoelectric response at defect sites in nematic inversion walls conducted by Kumar et al., we gave the theoretical analysis using the Frank elastic theory. When a direct-current electric field normal to the plane of the substrate is applied to the parallel aligned nematic liquid crystal cell with weak anchoring, the rotation of 4-1 defects in the narrow inversion walls can be exhibited. The free energy of liquid crystal molecules around the ＋1 and - 1 defect sites in the nematic inversion walls under the electric field was formulated and the electric-field-driven structural changes at the defect site characterized by polar and azimuthal angles of the local director were simulated. The results reveal that the deviation of azimuthal angle induced by flexoelectric effect are consistent with the switching of extinction brushes at the - 1 and -1 defects obtained in the experiment conducted by Kumar et al.展开更多
Based on the new modified couple stress theory and considering the flexoelectric effect of the piezoelectric layers,the Euler Bernoulli nano-beam model of composite laminated materials driven by electrostatically fixe...Based on the new modified couple stress theory and considering the flexoelectric effect of the piezoelectric layers,the Euler Bernoulli nano-beam model of composite laminated materials driven by electrostatically fixed supports at both ends is established. The nonlinear differential governing equations and boundary conditions are derived by the Hamilton principle. The generalized differential quadrature method(GDQM) and the Newton Raphson method are used to numerically solve the differential governing equations. The influence of flexoelectric effect on the static and the dynamic pull-in characteristics of laminated nano-beams is analyzed. The results of the numerical calculation are in a good agreement with those in the literature when the model degenerated into a nanobeam model without flexoelectric effect. The stacking sequence,length scale parameter l and piezoelectric layer applied voltage V_(p) of the composite will affect the pull-in voltage,frequency and time-domain response of the structure. Given that the flexoelectric effect will reduce the pull-in voltage and dimensionless natural frequency of the structure,the maximum dimensionless displacement at the midpoint of the beam and the period of time-domain response should be increased.展开更多
Piezoelectric superlattice is a potential component for nanoelectromechanical systems. Due to the strong nonlocal effect such as flexoelectric effect at interfaces, classical piezoelectric theory is unable to accurate...Piezoelectric superlattice is a potential component for nanoelectromechanical systems. Due to the strong nonlocal effect such as flexoelectric effect at interfaces, classical piezoelectric theory is unable to accurately describe the electromechanical response of piezoelectric superlattice at nanoscale scale. Based on the previous nonlocal thermodynamics theory with flexoelectric effect Liu et al. （2016）, the size- dependent electromechanical properties of piezoelectric superlattices made of BaTiO3 （BTO） and PbTiO3 （PRO） layers are investigated systematically in the present work. Giant strain gradient is found near the interface between BTO and PTO layers, which leads to the significant enhancement of polarization in the superlattice due to the flexoelectric effect. For the piezoelectric BTO-PTO superlattices with different unit- cell sizes, the thickness of interface with nontrivial strain gradient is almost constant. The influence of strain gradient at the interface becomes significant when the size of superlattice decreases, As a result, a strong size dependence of electromechanical properties is predicted for the piezoelectric BTO-PTO superlattices, In particular, for the superlattices with a specific thickness ratio of BTO and PTO layers, the piezoelectric response can be several times larger than that of bulk structure. The present work demonstrates a practical wast to design the piezoelectric superlattices with high piezoelectric coefficient by using the nonlocal effect at nanoscale.展开更多
In addition to accounting for non-gradient nonlocal elastic stress,a nonlocal strain gradient theory(NSGT)also considers the nonlocality of higher-order strain gradients;thus,it is applicable to small-scale structures...In addition to accounting for non-gradient nonlocal elastic stress,a nonlocal strain gradient theory(NSGT)also considers the nonlocality of higher-order strain gradients;thus,it is applicable to small-scale structures and can account for both hardening and softening effects.An analytical model is constructed in this research endeavor to depict the free vibration characteristics of sandwich functionally graded porous(FGP)doubly-curved nanoshell integrated with piezoelectric surface layers consists of three distinct layers,taking into account flexoelectrici effect based on NSGT and novel refined high-order shear deformation hypothesis.The novelty of this study is that the two nonlocal coefficients and material length scale of the core layer are variable along thickness,like other material characteristics.The equilibrium equation of motion of the doubly-curved nanoshell is derived from Hamilton’s principle,then the Galerkin method is applied to derive the natural vibration frequency values of the doubly-curved nanoshell with different boundary conditions(BCs).The influence of parameters such as flexoelectric effect,nonlocal and length scale factors,elastic medium stiffness factor,porosity factor,and BCs on the free vibration esponse of the nanoshell is detected and comprehensively studied.This paper is claimed to provide a theoretical predicition on the impact of the size-small dependent and flexoelectric effect upon the oscillation of FGP nanoshell integrated with piezoelectric surface layers,thus sheding light on understanding the underlying physics of electromechanical coupling at the nanoshell to some extent.展开更多
The flexoelectric effect is very strong and coupled with large strain gradients for nanoscale dielectrics. At the nanoscale, the electrostatic force cannot be ignored. In this paper, we have established the electric e...The flexoelectric effect is very strong and coupled with large strain gradients for nanoscale dielectrics. At the nanoscale, the electrostatic force cannot be ignored. In this paper, we have established the electric enthalpy variational principle for nanosized dielectrics with the strain gradient and the polarization gradient effect, as well as the effect of the electrostatic force. The complete governing equations, which include the effect of the electrostatic force, are derived from this variational principle, and based on the principle the generalized electrostatic stress is obtained, the generalized electrostatic stress contains the Maxwell stress corresponding to the polarization and strain, and stress related to the polarization gradient and strain gradient. This work provides the basis for the analysis and computations for the electromechanical problems in nanosized dielectric materials.展开更多
Although forbidden band effect in perfectly periodic phononic crystals(PC)is very attractive,random disordered(i.e.detuning)phenomenon is inevitable in engineering processing,thus explor-ing the effect of detuning on ...Although forbidden band effect in perfectly periodic phononic crystals(PC)is very attractive,random disordered(i.e.detuning)phenomenon is inevitable in engineering processing,thus explor-ing the effect of detuning on the wave characteristics of PC becomes a necessity.In this study,fundamental governing equa-tions and boundary conditions are derived from the principle of virtual work.Wave characteristics and localization factor of one-dimensional(1D)detuned nano-PC are investigated based on the transfer matrix method,with flexoelectric effect duly accounted for.Subsequently,with BaTiO_(3)SrTiO_(3) nano-PC taken for illustration,forbidden band properties and localization factor of 1D elastic waves in harmonic and detuned states are systematically character-ized.It is demonstrated that localization factor can characterize the energy band structure of 1D PC perfectly.Flexoelectric effect tends to widen the width of forbidden band with increasing detuning,and detuning is linearly related to the bandwidth.The forbidden band is more sensitive to flexoelectric coefficient detuning than thickness detuning.The research results provide useful theoretical guidance for designing high-frequency nanoscaled devices with the function of filtering based on band gap effect of nano-PC.展开更多
In this work,a novel refined higher-order shear deformation plate theory is integrated with nonlocal elasticity theory for analyzing the free vibration,bending,and transient behaviors of fluid-infiltrated porous metal...In this work,a novel refined higher-order shear deformation plate theory is integrated with nonlocal elasticity theory for analyzing the free vibration,bending,and transient behaviors of fluid-infiltrated porous metal foam piezoelectric nanoplates resting on Pasternak elastic foundation with flexoelectric effects.Isogeometric analysis(IGA)and the Navier solution are applied to the problem.The innovation in the present study is that the influence of the in-plane variation of the nonlocal parameter on the free and forced vibration of the piezoelectric nanoplates is investigated for the first time.The nonlocal parameter and material characteristics are assumed to be material-dependent and vary gradually over the thickness of structures.Based on Hamilton’s principle,equations of motion are built,then the IGA approach combined with the Navier solution is used to analyze the static and dynamic response of the nanoplate.Lastly,we investigate the effects of the porosity coefficients,flexoelectric parameters,elastic stiffness,thickness,and variation of the nonlocal parameters on the mechanical behaviors of the rectangular and elliptical piezoelectric nanoplates.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
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
Coupled nanogenerators have been a research hotspot due to their ability to harvest a variety of forms of energy such as light,mechanical and thermal energy and achieve a stable direct current output.Ferroelectric fil...Coupled nanogenerators have been a research hotspot due to their ability to harvest a variety of forms of energy such as light,mechanical and thermal energy and achieve a stable direct current output.Ferroelectric films are frequently investigated for photovoltaic applications due to their unique photovoltaic properties and bandgap-independent photovoltage,while the flexoelectric effect is an electromechanical property commonly found in solid dielectrics.Here,we effectively construct a new form of coupled nanogenerator based on a flexible BiFeO_(3) ferroelectric film that combines both flexoelectric and photovoltaic effects to successfully harvest both light and vibration energies.This device converts an alternating current into a direct current and achieves a 6.2% charge enhancement and a 19.3%energy enhancement to achieve a multi-dimensional"1+1>2"coupling enhancement in terms of current,charge and energy.This work proposes a new approach to the coupling of multiple energy harvesting mechanisms in ferroelectric nanogenerators and provides a new strategy to enhance the transduction efficiency of flexible functional devices.展开更多
By engineering strain gradients in dielectrics,the flexoelectric effect can be created,which yields interesting physical properties via electromechanical coupling.Here,we report flexoelectric-induced photovoltaic effe...By engineering strain gradients in dielectrics,the flexoelectric effect can be created,which yields interesting physical properties via electromechanical coupling.Here,we report flexoelectric-induced photovoltaic effects in centrosymmetric LaFeO_(3) thin-film heterostructures grown on flexible mica sub-strates,in which partial relaxation of lattice-mismatch strain against LaAlO_(3) stretching layers results in giant strain gradients and pronounced electrical polarizations.The flexoelectric polarization modulates band alignment and leads to significant photovoltaic effects with a short-circuit current density of~0.4 mA/cm^(2) and an open circuit voltage of~-0.45 V in Pt/LaFeO_(3)/LaNiO_(3) devices.In addition,by con-cavely/convexly bending the mica substrate,mechanical strain gradients give rise to bi-directionally tunable photocurrents,in which continuously change of short-circuit current density with a magni-tude of~100% and good reproducibility in repetitive bending operations are observed in the Pt/LaFeO_(3)/LaNiO_(3) devices.The present work demonstrates an approach to design self-powered photoelectric de-vices with an electromechanical degree of freedom based on the flexoelectric effect in flexible thin-film heterostructures.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
Piezoelectric materials are widely utilized in sensors,actuators,and transducers for electro-mechanical conversion.Conventional materials have limited piezoelectric response(piezoelectric coefficient d 33<4000 pC N...Piezoelectric materials are widely utilized in sensors,actuators,and transducers for electro-mechanical conversion.Conventional materials have limited piezoelectric response(piezoelectric coefficient d 33<4000 pC N^(−1)),as well as a mutual restriction between properties and working temperature.Our research demonstrates that the limitation and restriction can be removed by designing piezoelectric metamaterials based on flexoelectricity.We enhance the flexoelectric response of BaTiO_(3)ceramics by 25 times compared with the highest reported results via reduction sintering.The BaTiO_(3)piezoelectric metamaterials exhibit a large effective d 33>20000 pC N^(−1)and no depoling above Curie temperature.The giantμeff is generated by spontaneously polarized surface layers and a negative capacitance amplification effect,caused by the defect inhomogeneity formed during sintering.These findings open up new possibilities for designing high-performance piezoelectric materials with extended working temperatures.展开更多
Two-dimensional(2D)molybdenum disulfide(MoS_(2))has shown considerable potential for photodetection,yet existing MoS_(2)-based photodetectors require either external voltage bias or complex heterojunctions.In this wor...Two-dimensional(2D)molybdenum disulfide(MoS_(2))has shown considerable potential for photodetection,yet existing MoS_(2)-based photodetectors require either external voltage bias or complex heterojunctions.In this work,we present a new device concept based on flexoelectric engineering of bulk photovoltaic effect(BPVE)of 2H-MoS_(2),simplifying the device configuration considerably while enhancing its self-powered photodetection performance.By introducing a strain gradient in the suspended 2H-MoS_(2),we break its inversion symmetry,resulting in BPVE in the otherwise centrosymmetric system.The significant flexoelectric polarization induced also facilitates efficient photocarrier separation,leading to a 41-fold enhancement in short-circuit photocurrent under a strain gradient of 0:95μm^(-1).Furthermore,the flexoelectric-engineered photodetector can be dynamically tuned via air pressure,enabling multilevel photoconductance and achieving a responsivity of 191 mA/W.This performance surpasses existing self-powered MoS_(2)-based photodetectors reported in literature,offering a strategy for enhanced photodetection.展开更多
Flexoelectric effect can be used to design actuators to control engi-neering structures including beams,plates,and shells.Multiple flexo-electric actuators method has the advantage of less stress concentration and bet...Flexoelectric effect can be used to design actuators to control engi-neering structures including beams,plates,and shells.Multiple flexo-electric actuators method has the advantage of less stress concentration and better control effect,but the mode-dependent optimal actuator locations could influence the flexoelectric actuation effect significantly.In this work,a neural network model is established to study the optimal combinations of multiple flexoelectric actuators on a rectangular plate.In the physical model,an atomic force micro-scope(AFM)probe was employed to generate an electric field gradient in the flexoelectric patch,so that flexoelectric control force and moment can be obtained.Multiple flexoelectric actuators on the plate was considered.Case studies showed that the flexoelectricity induced stress mainly concentrate near the probe,the size and shape of the flexoelectric patch have limited effect on the actuation,hence,only the actuator positions were choosing as the input of the ANN model.Using the prediction of the neural network model,the driving effect of a large number of actuators at different positions can be quickly obtained,and the optimal position of the actuator can be analyzed more accurately.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Project supported by the National Natural Science Foundation of China (No. 12472064)。
文摘When the size of a magneto-electro-elastic cylindrical shell (MEECS) is reduced to micro-/nano-scale, the size-dependent flexomagnetic effect (FME) and flexoelectric effect (FEE) significantly influence their multi-physical coupling behaviors. To investigate these effects on the post-buckling behaviors of an MEECS, a nonlinear post-buckling model is developed based on the higher-order shear deformation theory (HSDT) and magneto-electro-elastic (MEE) constitutive relations with the FME and FEE. The equilibrium path and the corresponding shell deformations are obtained with a set of newly developed generalized displacement functions within the framework of the Galerkin approach. These displacement functions are established based on the trigonometric series expansions, which accurately satisfy the clamped boundary conditions (BCs). The effects of geometry, flexomagnetic/flexoelectric coefficients, and external electromagnetic fields on the post-buckling behaviors of an MEECS with the FME and FEE are analyzed. Numerical results indicate that the FME decreases the upper critical load of an MEECS, whereas the FEE exhibits an opposite effect by increasing it.
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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11374087,11274088,and 11304074)the Natural Science Foundation of Hebei Province,China(Grant Nos.A2014202123 and A2016202282)+1 种基金the Research Project of Hebei Education Department,China(Grant Nos.QN2014130and QN2015260)the Key Subject Construction Project of Hebei Province University,China
文摘Based on the experimental phenomena of flexoelectric response at defect sites in nematic inversion walls conducted by Kumar et al., we gave the theoretical analysis using the Frank elastic theory. When a direct-current electric field normal to the plane of the substrate is applied to the parallel aligned nematic liquid crystal cell with weak anchoring, the rotation of 4-1 defects in the narrow inversion walls can be exhibited. The free energy of liquid crystal molecules around the ＋1 and - 1 defect sites in the nematic inversion walls under the electric field was formulated and the electric-field-driven structural changes at the defect site characterized by polar and azimuthal angles of the local director were simulated. The results reveal that the deviation of azimuthal angle induced by flexoelectric effect are consistent with the switching of extinction brushes at the - 1 and -1 defects obtained in the experiment conducted by Kumar et al.
文摘Based on the new modified couple stress theory and considering the flexoelectric effect of the piezoelectric layers,the Euler Bernoulli nano-beam model of composite laminated materials driven by electrostatically fixed supports at both ends is established. The nonlinear differential governing equations and boundary conditions are derived by the Hamilton principle. The generalized differential quadrature method(GDQM) and the Newton Raphson method are used to numerically solve the differential governing equations. The influence of flexoelectric effect on the static and the dynamic pull-in characteristics of laminated nano-beams is analyzed. The results of the numerical calculation are in a good agreement with those in the literature when the model degenerated into a nanobeam model without flexoelectric effect. The stacking sequence,length scale parameter l and piezoelectric layer applied voltage V_(p) of the composite will affect the pull-in voltage,frequency and time-domain response of the structure. Given that the flexoelectric effect will reduce the pull-in voltage and dimensionless natural frequency of the structure,the maximum dimensionless displacement at the midpoint of the beam and the period of time-domain response should be increased.
基金financial support from the National Natural Science Foundation of China(11472242,11672264,and 11621062)the Zhejiang Provincial Natural Science Foundation(LZ17A020001)the Fundamental Research Funds for the Central Universities
文摘Piezoelectric superlattice is a potential component for nanoelectromechanical systems. Due to the strong nonlocal effect such as flexoelectric effect at interfaces, classical piezoelectric theory is unable to accurately describe the electromechanical response of piezoelectric superlattice at nanoscale scale. Based on the previous nonlocal thermodynamics theory with flexoelectric effect Liu et al. （2016）, the size- dependent electromechanical properties of piezoelectric superlattices made of BaTiO3 （BTO） and PbTiO3 （PRO） layers are investigated systematically in the present work. Giant strain gradient is found near the interface between BTO and PTO layers, which leads to the significant enhancement of polarization in the superlattice due to the flexoelectric effect. For the piezoelectric BTO-PTO superlattices with different unit- cell sizes, the thickness of interface with nontrivial strain gradient is almost constant. The influence of strain gradient at the interface becomes significant when the size of superlattice decreases, As a result, a strong size dependence of electromechanical properties is predicted for the piezoelectric BTO-PTO superlattices, In particular, for the superlattices with a specific thickness ratio of BTO and PTO layers, the piezoelectric response can be several times larger than that of bulk structure. The present work demonstrates a practical wast to design the piezoelectric superlattices with high piezoelectric coefficient by using the nonlocal effect at nanoscale.
文摘In addition to accounting for non-gradient nonlocal elastic stress,a nonlocal strain gradient theory(NSGT)also considers the nonlocality of higher-order strain gradients;thus,it is applicable to small-scale structures and can account for both hardening and softening effects.An analytical model is constructed in this research endeavor to depict the free vibration characteristics of sandwich functionally graded porous(FGP)doubly-curved nanoshell integrated with piezoelectric surface layers consists of three distinct layers,taking into account flexoelectrici effect based on NSGT and novel refined high-order shear deformation hypothesis.The novelty of this study is that the two nonlocal coefficients and material length scale of the core layer are variable along thickness,like other material characteristics.The equilibrium equation of motion of the doubly-curved nanoshell is derived from Hamilton’s principle,then the Galerkin method is applied to derive the natural vibration frequency values of the doubly-curved nanoshell with different boundary conditions(BCs).The influence of parameters such as flexoelectric effect,nonlocal and length scale factors,elastic medium stiffness factor,porosity factor,and BCs on the free vibration esponse of the nanoshell is detected and comprehensively studied.This paper is claimed to provide a theoretical predicition on the impact of the size-small dependent and flexoelectric effect upon the oscillation of FGP nanoshell integrated with piezoelectric surface layers,thus sheding light on understanding the underlying physics of electromechanical coupling at the nanoshell to some extent.
基金supported by the National Basic Research Program of China (Grant No. 2007CB707702)the National Natural Science Founda-tion of China (Grant Nos. 10672130 and 10972173), and Ministry of Edu-cation of China
文摘The flexoelectric effect is very strong and coupled with large strain gradients for nanoscale dielectrics. At the nanoscale, the electrostatic force cannot be ignored. In this paper, we have established the electric enthalpy variational principle for nanosized dielectrics with the strain gradient and the polarization gradient effect, as well as the effect of the electrostatic force. The complete governing equations, which include the effect of the electrostatic force, are derived from this variational principle, and based on the principle the generalized electrostatic stress is obtained, the generalized electrostatic stress contains the Maxwell stress corresponding to the polarization and strain, and stress related to the polarization gradient and strain gradient. This work provides the basis for the analysis and computations for the electromechanical problems in nanosized dielectric materials.
基金This work is supported by the National Natural Science Foundation of China(11502110,11972185,and 12002156)the Open Fund of the State Key Laboratory for Strength and Vibration of Mechanical Structures,Xi’an Jiaotong University(No.SV2018-KF-01,No.SV2018-KF-22)the Open Project of Space Structure and Mechanism Technology Laboratory of China Aerospace Science and Technology Group Co.,Ltd.
文摘Although forbidden band effect in perfectly periodic phononic crystals(PC)is very attractive,random disordered(i.e.detuning)phenomenon is inevitable in engineering processing,thus explor-ing the effect of detuning on the wave characteristics of PC becomes a necessity.In this study,fundamental governing equa-tions and boundary conditions are derived from the principle of virtual work.Wave characteristics and localization factor of one-dimensional(1D)detuned nano-PC are investigated based on the transfer matrix method,with flexoelectric effect duly accounted for.Subsequently,with BaTiO_(3)SrTiO_(3) nano-PC taken for illustration,forbidden band properties and localization factor of 1D elastic waves in harmonic and detuned states are systematically character-ized.It is demonstrated that localization factor can characterize the energy band structure of 1D PC perfectly.Flexoelectric effect tends to widen the width of forbidden band with increasing detuning,and detuning is linearly related to the bandwidth.The forbidden band is more sensitive to flexoelectric coefficient detuning than thickness detuning.The research results provide useful theoretical guidance for designing high-frequency nanoscaled devices with the function of filtering based on band gap effect of nano-PC.
文摘In this work,a novel refined higher-order shear deformation plate theory is integrated with nonlocal elasticity theory for analyzing the free vibration,bending,and transient behaviors of fluid-infiltrated porous metal foam piezoelectric nanoplates resting on Pasternak elastic foundation with flexoelectric effects.Isogeometric analysis(IGA)and the Navier solution are applied to the problem.The innovation in the present study is that the influence of the in-plane variation of the nonlocal parameter on the free and forced vibration of the piezoelectric nanoplates is investigated for the first time.The nonlocal parameter and material characteristics are assumed to be material-dependent and vary gradually over the thickness of structures.Based on Hamilton’s principle,equations of motion are built,then the IGA approach combined with the Navier solution is used to analyze the static and dynamic response of the nanoplate.Lastly,we investigate the effects of the porosity coefficients,flexoelectric parameters,elastic stiffness,thickness,and variation of the nonlocal parameters on the mechanical behaviors of the rectangular and elliptical piezoelectric nanoplates.
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 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This work was supported by the National Natural Science Foundation of China(No.52072041)the Beijing Natural Science Foundation(No.JQ21007)the University of Chinese Academy of Sciences(No.Y8540XX2D2).
文摘Coupled nanogenerators have been a research hotspot due to their ability to harvest a variety of forms of energy such as light,mechanical and thermal energy and achieve a stable direct current output.Ferroelectric films are frequently investigated for photovoltaic applications due to their unique photovoltaic properties and bandgap-independent photovoltage,while the flexoelectric effect is an electromechanical property commonly found in solid dielectrics.Here,we effectively construct a new form of coupled nanogenerator based on a flexible BiFeO_(3) ferroelectric film that combines both flexoelectric and photovoltaic effects to successfully harvest both light and vibration energies.This device converts an alternating current into a direct current and achieves a 6.2% charge enhancement and a 19.3%energy enhancement to achieve a multi-dimensional"1+1>2"coupling enhancement in terms of current,charge and energy.This work proposes a new approach to the coupling of multiple energy harvesting mechanisms in ferroelectric nanogenerators and provides a new strategy to enhance the transduction efficiency of flexible functional devices.
基金This work was jointly sponsored by Natural Science Foundation of China(51872148)Natural Science Foundation of Shandong Province(ZR2020JQ03)+2 种基金D.W.acknowledges financial support from Natural Science Foundation of China(51725203 and U1932115)Z.W.acknowledges financial support from the Taishan Scholar Program of Shandong Province(tsqn201812045)the Youth Innovation Team Project of Shandong Provincial Education Department(2019KJJ012).
文摘By engineering strain gradients in dielectrics,the flexoelectric effect can be created,which yields interesting physical properties via electromechanical coupling.Here,we report flexoelectric-induced photovoltaic effects in centrosymmetric LaFeO_(3) thin-film heterostructures grown on flexible mica sub-strates,in which partial relaxation of lattice-mismatch strain against LaAlO_(3) stretching layers results in giant strain gradients and pronounced electrical polarizations.The flexoelectric polarization modulates band alignment and leads to significant photovoltaic effects with a short-circuit current density of~0.4 mA/cm^(2) and an open circuit voltage of~-0.45 V in Pt/LaFeO_(3)/LaNiO_(3) devices.In addition,by con-cavely/convexly bending the mica substrate,mechanical strain gradients give rise to bi-directionally tunable photocurrents,in which continuously change of short-circuit current density with a magni-tude of~100% and good reproducibility in repetitive bending operations are observed in the Pt/LaFeO_(3)/LaNiO_(3) devices.The present work demonstrates an approach to design self-powered photoelectric de-vices with an electromechanical degree of freedom based on the flexoelectric effect in flexible thin-film heterostructures.
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.
基金supported by the National Natural Science Foundation of China(51972297 and 12274389).
文摘Piezoelectric materials are widely utilized in sensors,actuators,and transducers for electro-mechanical conversion.Conventional materials have limited piezoelectric response(piezoelectric coefficient d 33<4000 pC N^(−1)),as well as a mutual restriction between properties and working temperature.Our research demonstrates that the limitation and restriction can be removed by designing piezoelectric metamaterials based on flexoelectricity.We enhance the flexoelectric response of BaTiO_(3)ceramics by 25 times compared with the highest reported results via reduction sintering.The BaTiO_(3)piezoelectric metamaterials exhibit a large effective d 33>20000 pC N^(−1)and no depoling above Curie temperature.The giantμeff is generated by spontaneously polarized surface layers and a negative capacitance amplification effect,caused by the defect inhomogeneity formed during sintering.These findings open up new possibilities for designing high-performance piezoelectric materials with extended working temperatures.
基金supported by National Key Research and Development Program of China(2022YFF0706100)the National Natural Science Foundation of China(12202079,12192213,12350002)+2 种基金the Guangdong Provincial Key Laboratory Program(2021B1212040001)from the Department of Science and Technology of Guangdong Province,the Shenzhen Science and Technology Program(JCYJ20220818100410022,RCBS20221008093246071)Guangdong Basic and Applied Basic Research Foundation(2023B1515130003)the Outstanding Talents Training Fund in Shenzhen.
文摘Two-dimensional(2D)molybdenum disulfide(MoS_(2))has shown considerable potential for photodetection,yet existing MoS_(2)-based photodetectors require either external voltage bias or complex heterojunctions.In this work,we present a new device concept based on flexoelectric engineering of bulk photovoltaic effect(BPVE)of 2H-MoS_(2),simplifying the device configuration considerably while enhancing its self-powered photodetection performance.By introducing a strain gradient in the suspended 2H-MoS_(2),we break its inversion symmetry,resulting in BPVE in the otherwise centrosymmetric system.The significant flexoelectric polarization induced also facilitates efficient photocarrier separation,leading to a 41-fold enhancement in short-circuit photocurrent under a strain gradient of 0:95μm^(-1).Furthermore,the flexoelectric-engineered photodetector can be dynamically tuned via air pressure,enabling multilevel photoconductance and achieving a responsivity of 191 mA/W.This performance surpasses existing self-powered MoS_(2)-based photodetectors reported in literature,offering a strategy for enhanced photodetection.
文摘Flexoelectric effect can be used to design actuators to control engi-neering structures including beams,plates,and shells.Multiple flexo-electric actuators method has the advantage of less stress concentration and better control effect,but the mode-dependent optimal actuator locations could influence the flexoelectric actuation effect significantly.In this work,a neural network model is established to study the optimal combinations of multiple flexoelectric actuators on a rectangular plate.In the physical model,an atomic force micro-scope(AFM)probe was employed to generate an electric field gradient in the flexoelectric patch,so that flexoelectric control force and moment can be obtained.Multiple flexoelectric actuators on the plate was considered.Case studies showed that the flexoelectricity induced stress mainly concentrate near the probe,the size and shape of the flexoelectric patch have limited effect on the actuation,hence,only the actuator positions were choosing as the input of the ANN model.Using the prediction of the neural network model,the driving effect of a large number of actuators at different positions can be quickly obtained,and the optimal position of the actuator can be analyzed more accurately.
