On The Size-Dependent Electro-Mechanical Coupling Properties Of The Micro Components Incorporating Flexoelectric Effect

Flexoelectricity,characterizing the linear coupling relation between strain gradient and polarization or between electric field gradient and stress,may exist in all dielectrics.and it will be enhanced as structural characteristic size decreases.With rapid development of the micro-nano fabrication technologies,there emerges more and more researches on flexoelectricity-related theoretical modelling of the micro components and the experimental mearsurment.In microscale,strain gradient increases and the related strain gradient effect and polarization gradient effect will be highly enhanced.It is necessary to consider influences of the gradient-ralated effects on the flexoelectric response in micro components both theoretically and experimentally.In this thesis,taking the flexoelectric effect,strain gradient effect and polarization gradient effect into account,analytical models of the bilayered micro components,curved micro components and functionally graded micro components are established and the experimental validation of the increasement of the effective flexoelectric coefficient predicted by the functionally graded flexoelectric circular plate model is also carried out.The main contents are as followsBased on the displacement mode of the bilayered Euler-Bernoulli microbeam considering the strain gradient effect,the equations determining the zero-axial-displacement-axis is derived.Influence of the strain gradient effect on the zero-axial-displacement-axis is analyzed and an approximation of the actual displacement mode is proposed.Governing equations and associated boundary conditions of the bilayered Euler-Bernoulli microbeam and the bilayered Kirchhoff circular microplate are derived based on the energy variational principle.General solution of the high-order governing equations is given and the explicit solution for the direct/converse flexoelectric response is obtained.Then,flexoelectric response properties of the bilayered Euler-Bernoulli microbeam and the bilayered Kirchhoff circular microplate are studied and numerical results demonstrate that:When the total thickness is down to microscale,the flexoelectric effect will obviously decrease the bending rigidity of the bilayered structures,irrespective with the sing of the flexoelectric coefficient.When the total thickness is down to microscale,a larger converse flexoelectric response will be expected in the bilayer structure with smaller flexoelectric/elastic thickness ratio.When the total thickness tends to the material length scale parameters,the strain gradient effect will dramatically decrease the total charge induced in direct flexoelectric response and the defelction generated in converse flexoelectric response.Using the enthalpy variational principle,the flexoelectric repsosnse models of the curved microbeam and the axisymmetric spherical microshell based on the Euler-Bernoulli assumption and the Kirchhoff-Love assumption are proposed,respectively.General solution of the high-order governing equations is given and the explicit solution for the direct/converse flexoelectric response is obtained.Analysis of the flexoelectric response properties in curved microbeams and spherical microshells demonstrate that,for the curved microbeams:under the simply supported boundary,the direct and converse flexoelectric responses increase with the central angle increases;under the clamped boundary,the direct flexoelectric response decreases while the converse flexoelectric response increases with the central angle increases.For the spherical microshells:under the simply supported boundary,the direct and converse flexoelectric responses decrease with the central angle increases;under the clamped boundary,the direct flexoelectric response decreases while the converse flexoelectric response increases with the central angle increases.When the thickness reduces to the material length scale parameters,the strain gradient effect enhances the bending rigidity of the curved components and then suppresses the whole direct/converse flexoelectric responses while the strain gradient effect can be neglected when the thickness is far lager than the material length scale parameter.Considering the material constants gradient,the flexoelectric theory is extended to the isotropic functionally graded dielectrics.Flexoelectric responses model of the functionally graded flexoelectric Kirchhoff circular microplate is established.The effective direct/converse flexoelectric coefficients are derived.Theoretical solution of the direct flexoelectric response under uniform pressure and the converse flexoelectric response under applied voltage are obtained.Numerical results of the electro-mechanical coupling properties in functionally graded circular microplate demonstrate that the effective direct/converse flexoelectric coefficient in functionally graded flexoelectric circular plate may exceed that of its component materials when the ununiform flexocoupling coefficient are considered.To validate the increasement of the effective flexoelectric coefficients predicted by the functionally graded circular microplate model,the effective direct flexoelectric coefficients in both uniform Mn-doped Na0.5Ba0.5TiO3 and functionally graded Mn-doped Na0.5Ba0.5TiO3 circular microplate are measured.It is found that the effective direct flexoelectric coefficient in functionally graded circular microplate increases hundreds or even several thousand times of that of the uniform material.This provides a method to design materials or structures with large effective flexoelectric coefficient.The increasement of the effective flexoelectric coefficients can be explained and fitted by the derived expression of the effective direct flexoelectric coefficient.This phenomenon can be explained and fitted by the derived expression of the effective direct flexoelectric coefficient for the functionally graded circular plate.The established models of bilayered micro components,curved micro components and functionally graded micro components will provide a theoretical basis for the design and analysis of the relevant flexoelectric micro components.