Mechanism Of Size-dependent And Flexoelectric Effects In Functionally Graded Dielectric Materials

Flexoelectricity,referring to the polarization induced by mechanical strain gradient or the deformation induced by electric field gradient.Unlike traditional piezoelectricity,flexoelectricity,as a new kind of electro-mechanical coupling effect,is free from the symmetry of dielectric materials,Curie temperature restriction and small size effect.Early studies of this subject mostly look at liquid crystals and biomembranes.Recently,the advent of nanotechnology revealed its importance also in solid structures,such as flexible electronics,thin films,energy harvesters,etc.Due to the limitations of traditional bulk dielectric materials that are difficult to obtain large strain gradients,many scholars use special shape structures(truncated-pyramid,truncated-cone)and composite structural materials(laminated plate,periodic layered structure)to explore the flexoelectric coupling property.However,the above material structure models have mechanical defects and are difficult to apply to practical engineering structures.Functionally graded materials(FGMs)are advanced functional composite materials,whose components present continuous and nonuniform distribution structure in space,and have excellent mechanical properties and engineering application value.Meanwhile,due to the nonuniform distribution,results in the symmetry breaking of the structure,and thus large nonuniform strain fields produced.In this paper,the mechanical properties,flexoelectric coupling properties,size effect and practical engineering application of FG dielectric materials are studied.The research contents of this paper mainly include:By using the method of Mori-Tanaka,the higher-order elastic modulus and flexoelectric coefficient can be predicted in the case of the spherical flexoelectric inclusion problem.Based on the Toupin-type theory of piezoelectricity and in the framework of flexoelectric theory,the general flexoelectric theory for isotropic materials including size-dependent and flexoelectric effects is reformulated.At the same time,on basis of the method of tensor analysis,the algebra operation of the sixth-order double symmetric tensor can be converted into simple matrix operation,and the high-order elastic tensors can be converted into the equivalent low-order elastic tensors.Then,the complex high order tensor problem which is difficult to be solved is transformed into the traditional problem.Static analysis.By solving the elastic theoretical solutions of FG nanocylinders and nanocolumns,it is found that FGMs can produce flexoelectric effect even if there is no bending deformation.On the basis of flexoelectric theory for isotropic materials,the mechanical and electrical responses of FG flexoelectric nanocylinders and columns are analyzed.Firstly,utilizing the efficient tensor algorithm operator and the axial symmetry relation,the elastic theoretical solution of the fourth order partial differential equation with variable coefficients for FG flexoelectric nanocylinder problem considering the inhomogeneity and the microstructure effect is given.Meaningwhile,the error of theoretical solution in the existing literature is pointed out.Secondly,the size effect and flexoelectric coupling of FG nanocylinders are discussed.Finally,a novel asymmetric nanocolumn is composed of FGMs presented with uniform compression to be evaluated the equivalent piezoelectric coefficients.Dynamic analysis.By analyzing the dynamic response of FG flexoelectric nanomaterials,the influences of the inhomogeneity and the size effect of FGMs on the flexoelectric effect are investigated.On the basis of applying the developed flexoelectric theory to the dynamic free vibration system,the mechanical and electrical responses of FG flexoelectric nanobeams are analyzed.Firstly,a more reasonable functional gradient structure is designed,which is different from the traditional FGMs,and the advantages of the FGMs over the traditional composites are compared.Secondly,the influences of gradient structures of FGMs on the flexoelectric effect and vibration frequencies is analyzed.Thirdly,the thermally induced nonlinear dynamics of FG flexoelectric nanobeams considering temperature-dependent is investigated.Finally,the effect of gradient index,size-dependent,flexoelectricity and temperature on the vibration amplitudes and frequencies of the structure are discussed.A new type of FG flexoelectric energy harvester is designed.Considering the influence of nonlinearity,the effects of different material composition ratio and gradient index on output voltage and output power are analyzed,and the electromechanical coupling performance of the energy harvester can be optimized by changing the composition and distribution structure of the model,adjusting the value of the external resistance load,selecting the appropriate model size.The results of this paper provide a meaningful theoretical guidance for the innovation and development of new devices.