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 refers to the mechanical-electro coupling between strain gradient and electric polarization, and conversely, the electro-mechanical coupling between electric field gradient and mechanical stress. This...Flexoelectricity refers to the mechanical-electro coupling between strain gradient and electric polarization, and conversely, the electro-mechanical coupling between electric field gradient and mechanical stress. This unique effect shows a promising size effect which is usually large as the material dimension is shrunk down. Moreover, it could break the limitation of centrosymmetry, and has been found in numerous kinds of materials which cover insulators, liquid crystals, biological materials, and semiconductors. In this review, we will give a brief report about the recent discoveries in flexoelectricity, focusing on the flexoelectric materials and their applications. The theoretical developments in this field are also addressed. In the end, the perspective of flexoelectricity and some open questions which still remain unsolved are commented upon.展开更多
The separation of photogenerated electron–hole pairs is vitally important for photocatalysis,which can be effectively promoted by polarization field.However,it only manifests in piezoelectric/pyroelectric/ferroelectr...The separation of photogenerated electron–hole pairs is vitally important for photocatalysis,which can be effectively promoted by polarization field.However,it only manifests in piezoelectric/pyroelectric/ferroelectric materials that have a non-centrosymmetric structure.Here,we demonstrate that the polarization enhanced photocatalysis(with wide spectra from ultraviolet(UV)light to visible light)can be achieved in centrosymmetric semiconductors,such asδ-MnO_(2) and TiO_(2) nanosheets integrated nanoflowers,by using the strain-gradient-induced flexoelectric polarization that is always overlooked in polarization-enhanced catalysis.Under ultrasonic and illumination excitation,the organic pollutants(methylene blue(MB),etc.)can be effectively degraded within 30 min with excellent stability and repeatability.Compared with photocatalysis,the flexo-photocatalytic performance of above centrosymmetric semiconductors is substantially increased by 85%.Moreover,the factors related to flexo-photocatalysis such as material morphology,mechanical stimuli source,and adsorption are explored to deeply understand the mechanism of flexo-photocatalysis.This work opens up a way for high-performance photocatalysis in centrosymmetric semiconductors.展开更多
A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic （PAN） and hybri...A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic （PAN） and hybrid aligned nematic （HAN） cells, the dependences of the capacitance on the sum of flexoelectric coefficients and the applied voltage are obtained by numerical simulations, and the distributions of the director and the electric potential for different applied voltages and flexoelectric coefficients are also given. Based on this theoretical analysis, we propose an experimental design for measuring the capacitance of a liquid crystal cell using the improved precision LCR meter E4980A （Agilent）. Through comparing the experimental data with the simulated results, the sum of flexoeletric coefficients can be determined.展开更多
This paper presents isogeometric analysis(IGA)-based topology optimization for electrical performance of three-dimensional(3D)flexoelectric structures.IGA is employed to provide{C}^{1}continuity in shape function,whic...This paper presents isogeometric analysis(IGA)-based topology optimization for electrical performance of three-dimensional(3D)flexoelectric structures.IGA is employed to provide{C}^{1}continuity in shape function,which is required in treating high-order electromechanical coupling equations.To improve the computational efficiency in treating 3D problems,the redundant degrees of freedom removal technique is introduced.Regularization treatments are also implemented to avoid the numerical singularity induced by flexoelectricity.Both virtual loads and strain energy constraints are taken into consideration to prevent unexpected structural disconnection.Numerical examples and experiments on optimized structures demonstrate that the flexoelectric performance can be effectively improved using the proposed approach.展开更多
The flexoelectric effect describes the interplay between material polarization and strain gradient.While much research has focused on control strategies for flexoelectricity,the impact of ferroelectric domain structur...The flexoelectric effect describes the interplay between material polarization and strain gradient.While much research has focused on control strategies for flexoelectricity,the impact of ferroelectric domain structure on the flexoelectric effect remains elusive.Through phase field simulations,we conduct a comparative study on the flexoelectric response of two types of BaTiO_(3)–SrTiO_(3) binary films:BaTiO_(3)–SrTiO_(3) multilayers and(Ba,Sr)TiO_(3) solid solutions.Our findings reveal that the flexoelectric response of these two systems,at the same Ba/Sr ratio,differs not only in magnitude but also in other aspects like temperature dependence,linearity,and hysteresis,due to their different ferroelectric domain structures and evolution dynamics.Our study deepens our current understanding of flexoelectricity in ferroelectrics and suggests“domain engineering”as a potential way to tailor this effect.展开更多
Piezoelectric semiconductors(PSCs)find extensive applications in modern smart electronic devices because of their dual properties of being piezoelectric and semiconductive.With the increasing demand for miniaturizatio...Piezoelectric semiconductors(PSCs)find extensive applications in modern smart electronic devices because of their dual properties of being piezoelectric and semiconductive.With the increasing demand for miniaturization of these devices,the performance of their components needs to be carefully designed and optimized,especially when reduced to nanosize.It has been shown that surface elastic properties play a substantial role in the mechanical performance of nanoscale materials and structures.Building on this understanding,the surface elastic effects,encompassing surface residual stress,surface membrane stiffness,and surface bending stiffness,are comprehensively taken into account to explore the electromechanical responses of a PSC nanobeam.Additionally,the flexoelectric effect on their responses is also systematically studied.The results of this work reveal that surface elastic properties predominantly influence mechanical performance,while the flexoelectric effect plays a more dominant role in electric-related quantities at the nanoscale.Notably,the significance of surface bending rigidity,which was often underestimated in the earlier literature,is demonstrated.Furthermore,owing to the flexoelectric effect,the linear distribution of electric potential and charge carriers along the length transforms into a nonlinear pattern.The distributions of electric potential and charge carriers across the cross section are also evidently impacted.Moreover,the size-dependent responses are evaluated.Our findings may provide valuable insights for optimizing electronic devices based on nanoscale PSCs.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
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
Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity;...Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity;therefore, producing a large-scale flexoelectric effect is of great interest. In this paper, we explore a way to enhance the flexoelectric effect by utilizing the snap-through instability and a stiffness gradient present along the length of a curved dielectric plate. To analyze the effect of stiffness profiles on the plate, we employ numerical parameter continuation. Our analysis reveals a nonlinear relationship between the effective electromechanical coupling coefficient and the gradient of Young’s modulus. Moreover, we demonstrate that the quadratic profile is more advantageous than the linear profile. For a dielectric plate with a quadratic profile and a modulus gradient of − 0.9, the effective coefficient can reach as high as 15.74 pC/N, which is over three times the conventional coupling coefficient of piezoelectric material. This paper contributes to our understanding of the amplification of flexoelectric effects by harnessing snapping surfaces and stiffness gradient design.展开更多
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
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
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
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supported by the National Natural Science Foundation of China under Grant Nos. 11574126 and 11604135the Natural Science Foundation of Jiangxi Province (No. 20161BAB216110)+1 种基金China Postdoctoral Science Foundation (No. 2017M612162)Postdoctoral Science Foundation of Jiangxi Province (No. 2017KY02)
文摘Flexoelectricity refers to the mechanical-electro coupling between strain gradient and electric polarization, and conversely, the electro-mechanical coupling between electric field gradient and mechanical stress. This unique effect shows a promising size effect which is usually large as the material dimension is shrunk down. Moreover, it could break the limitation of centrosymmetry, and has been found in numerous kinds of materials which cover insulators, liquid crystals, biological materials, and semiconductors. In this review, we will give a brief report about the recent discoveries in flexoelectricity, focusing on the flexoelectric materials and their applications. The theoretical developments in this field are also addressed. In the end, the perspective of flexoelectricity and some open questions which still remain unsolved are commented upon.
基金supported by the National Natural Science Foundation of China(No.52202162).
文摘The separation of photogenerated electron–hole pairs is vitally important for photocatalysis,which can be effectively promoted by polarization field.However,it only manifests in piezoelectric/pyroelectric/ferroelectric materials that have a non-centrosymmetric structure.Here,we demonstrate that the polarization enhanced photocatalysis(with wide spectra from ultraviolet(UV)light to visible light)can be achieved in centrosymmetric semiconductors,such asδ-MnO_(2) and TiO_(2) nanosheets integrated nanoflowers,by using the strain-gradient-induced flexoelectric polarization that is always overlooked in polarization-enhanced catalysis.Under ultrasonic and illumination excitation,the organic pollutants(methylene blue(MB),etc.)can be effectively degraded within 30 min with excellent stability and repeatability.Compared with photocatalysis,the flexo-photocatalytic performance of above centrosymmetric semiconductors is substantially increased by 85%.Moreover,the factors related to flexo-photocatalysis such as material morphology,mechanical stimuli source,and adsorption are explored to deeply understand the mechanism of flexo-photocatalysis.This work opens up a way for high-performance photocatalysis in centrosymmetric semiconductors.
基金supported by the National Natural Science Foundation of China(Grant Nos.11274088,11374087,and 11304074)the Natural Science Foundation of Hebei Province,China(Grant No.A2014202123)+2 种基金the Research Project of Hebei Education Department,China(Grant Nos.Z2012061 and QN2014130)the Science and Technology Plan Project of Hebei Province,China(Grant No.134576260)the Key Subject Construction Project of Hebei Province University,China
文摘A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic （PAN） and hybrid aligned nematic （HAN） cells, the dependences of the capacitance on the sum of flexoelectric coefficients and the applied voltage are obtained by numerical simulations, and the distributions of the director and the electric potential for different applied voltages and flexoelectric coefficients are also given. Based on this theoretical analysis, we propose an experimental design for measuring the capacitance of a liquid crystal cell using the improved precision LCR meter E4980A （Agilent）. Through comparing the experimental data with the simulated results, the sum of flexoeletric coefficients can be determined.
基金support from the National Natural Science Foundation of China(12272075)Liao Ning Revitalization Talents Program(XLYC2001003,XLYC1907119)+1 种基金Fundamental Research Funds for the Central Universities(DUT22QN238)Program for Changjiang Scholars,Innovative Research Team in University(PCSIRT)and 111 Project(B14013)is gratefully acknowledged.
文摘This paper presents isogeometric analysis(IGA)-based topology optimization for electrical performance of three-dimensional(3D)flexoelectric structures.IGA is employed to provide{C}^{1}continuity in shape function,which is required in treating high-order electromechanical coupling equations.To improve the computational efficiency in treating 3D problems,the redundant degrees of freedom removal technique is introduced.Regularization treatments are also implemented to avoid the numerical singularity induced by flexoelectricity.Both virtual loads and strain energy constraints are taken into consideration to prevent unexpected structural disconnection.Numerical examples and experiments on optimized structures demonstrate that the flexoelectric performance can be effectively improved using the proposed approach.
基金support from the National Natural Science Foundation of China(Grant Nos.12222214,and 12132020)the Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices(No.2022B1212010008)+1 种基金the Shenzhen Science and Techonlogy Program(Grant Nos.202206193000001 and 20220818181805001)Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(SML2021SP405).
文摘The flexoelectric effect describes the interplay between material polarization and strain gradient.While much research has focused on control strategies for flexoelectricity,the impact of ferroelectric domain structure on the flexoelectric effect remains elusive.Through phase field simulations,we conduct a comparative study on the flexoelectric response of two types of BaTiO_(3)–SrTiO_(3) binary films:BaTiO_(3)–SrTiO_(3) multilayers and(Ba,Sr)TiO_(3) solid solutions.Our findings reveal that the flexoelectric response of these two systems,at the same Ba/Sr ratio,differs not only in magnitude but also in other aspects like temperature dependence,linearity,and hysteresis,due to their different ferroelectric domain structures and evolution dynamics.Our study deepens our current understanding of flexoelectricity in ferroelectrics and suggests“domain engineering”as a potential way to tailor this effect.
基金support of the National Natural Science Foundation of China[Grant number:11702076]the Natural Science Foundation of Anhui Province[Grant numbers:2208085MA17 and 2208085ME129].
文摘Piezoelectric semiconductors(PSCs)find extensive applications in modern smart electronic devices because of their dual properties of being piezoelectric and semiconductive.With the increasing demand for miniaturization of these devices,the performance of their components needs to be carefully designed and optimized,especially when reduced to nanosize.It has been shown that surface elastic properties play a substantial role in the mechanical performance of nanoscale materials and structures.Building on this understanding,the surface elastic effects,encompassing surface residual stress,surface membrane stiffness,and surface bending stiffness,are comprehensively taken into account to explore the electromechanical responses of a PSC nanobeam.Additionally,the flexoelectric effect on their responses is also systematically studied.The results of this work reveal that surface elastic properties predominantly influence mechanical performance,while the flexoelectric effect plays a more dominant role in electric-related quantities at the nanoscale.Notably,the significance of surface bending rigidity,which was often underestimated in the earlier literature,is demonstrated.Furthermore,owing to the flexoelectric effect,the linear distribution of electric potential and charge carriers along the length transforms into a nonlinear pattern.The distributions of electric potential and charge carriers across the cross section are also evidently impacted.Moreover,the size-dependent responses are evaluated.Our findings may provide valuable insights for optimizing electronic devices based on nanoscale PSCs.
基金supported by the National Natural Science Foundation of China(Nos.12172326,11972319,and 12302210)the Natural Science Foundation of Zhejiang province,China(No.LR21A020002)the specialized research projects of Huanjiang Laboratory.
文摘Based on the three-dimensional(3D)basic equations of piezoelectric semiconductors(PSs),we establish a two-dimensional(2D)deformation-polarization-carrier coupling bending model for PS structures,taking flexoelectricity into consideration.The analytical solutions to classical flexure of a clamped circular PS thin plate are derived.With the derived analytical model,we numerically investigate the distributions of electromechanical fields and the concentration of electrons in the circular PS thin plate under an upward concentrated force.The effect of flexoelectricity on the multi-field coupling responses of the circular PS plate is studied.The obtained results provide theoretical guidance for the design of novel PS devices.
基金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.
文摘Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity;therefore, producing a large-scale flexoelectric effect is of great interest. In this paper, we explore a way to enhance the flexoelectric effect by utilizing the snap-through instability and a stiffness gradient present along the length of a curved dielectric plate. To analyze the effect of stiffness profiles on the plate, we employ numerical parameter continuation. Our analysis reveals a nonlinear relationship between the effective electromechanical coupling coefficient and the gradient of Young’s modulus. Moreover, we demonstrate that the quadratic profile is more advantageous than the linear profile. For a dielectric plate with a quadratic profile and a modulus gradient of − 0.9, the effective coefficient can reach as high as 15.74 pC/N, which is over three times the conventional coupling coefficient of piezoelectric material. This paper contributes to our understanding of the amplification of flexoelectric effects by harnessing snapping surfaces and stiffness gradient design.
基金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.
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.
