Research On The Strain Gradient Theory And Flexoelectric Response Of Micro-nano Intelligent Structures

The flexoelectricity is a special electromechanical coupling phenomenon induced by non-uniform deformation(strain gradient).In principle,it exists in all dielectric materials and has a size effect.In recent years,with the continuous development of the technical field towards the trend of miniaturization,flexoelectricity has attracted widespread attention,and related research work on the theoretical modeling and experimental measurement of micro-components have been increasing.In order to accurately describe this special electromechanical coupling effect,the flexoelectric theory has been created and improved by researchers.The higher-order strain tensor must be included in the theory.The higher-order strain tensor means that there are higher-order partial derivatives of displacements,which brings difficulties to the theoretical solution of the flexoelectric problem.Moreover,researchers have not yet reached a unified conclusion about which higher-order strain tensors should be considered in flexoelectric theory.Existing flexoelectric theories are either too complicated to consider because they consider too many higher-order strain tensors;or they are too simplified because they ignore too much,making it impossible to accurately describe the flexoelectric responses of micro-nano components.At the same time,the influence of the strain gradient elastic ity term on the flexoelectric response of the dielectric nanostructures is crucial,but in some studies,the role of this term has been underestimated or even neglected.Therefore,the flexoelectricity and the strain gradient elasticity term are comprehensively considered in this paper.Based on the general strain gradient elasticity theory with three independent material size parameters,the flex oelectric theory of micro-nano dielectric materials is established.The one-dimensional nano-Eulerian beam and the two-dimensional crumpled dielectric film are taken as examples to establish the corresponding flexoelectric theory,and their electromechanical coupling responses are studied,which provide a theoretical basis for the design of the energy harvesting based on flexoelectricity.The main research contents include:First,taking the one-dimensional nano-cantilever as an example,the corresponding flexoelectric theory is established.The mechanical and electrical governing equations of the cantilever beam are obtained from the Hamiltonian variation principle,and the deflection and polarization expressions are derived theoretically.Then,according to the finite element theory,a new nanobeam element with two nodes and six degrees of freedom which satisfies C2 weak continuity is created.The new nanobeam element contains the piezoelectric coefficient,flexoelectric coefficient and three independent material length scale parameters,which can describe the electromechanical coupling response and size effect.Using the new nanobeam element,the flexoelectric responses of the beam are obtained by the finite element method,and the numerical results are in good agreement with the theoretical results.The results show that on the one hand,the flexoelectric effect will reduce the equivalent bending stiffness ofthe nanobeam,and on the other hand,it will be coupled with the applied voltage as the equivalent bending moment acting on both ends of the beam.Moreover,when the characteristic size of the beam is equivalent to the material length scale parameters,flexoelectricity has the most significant influence on the results of the deflection,electric potential,and energy efficiency of the nanobeam.And as the size of the beam increases,both effects of the strain gradient elasticity term and the flexoelectricity will gradually decay,which illustrates the size dependence of them.Further,the one-dimensional problem is extended to the two-dimensional problem.Based on the flexoelectric theory model,the crumpling of both homogeneous and graded thin elastic sheets under an applied force are analyzed.There exists a rich of unusual nonlinear electromechanical behavior in a crumpled sheet.We establish a scaling law for the electromechanical behavior of a crumpled sheet to show that an infinitely sizeable flexoelectric response is obtained at the submicron length scale.This fantastic electromechanical coupling can be further enhanced by using a graded elastic sheet.Compared to a recent experiment on the crumpling of a polymer film,our theory shows that crumpling is a viable energy-harvesting route with potential applications in practical engineering,including wearable electronics,film energy harvesters and other related contexts.In this paper,the flexoelectric theory based on strain gradient theory lays a theoretical foundation for the analysis of flexoelectric response in micro-nano components.This theory once again verified the size dependence of the flex oelectrictiy,highlighting the importance of the strain gradient elastic ity term in the flexoelectric problem.In addition,a new finite element method considering flexoelectricity is proposed,which provides a theoretical basis for further numerical solution research of flexoelectricity.At the same time,the model of piezoelectric nanobeam and crumpl ed dielectric film established in this paper can provide the necessary theoretical basis and theoretical support for the design of micro/nano-components based on flexoelectric effects,such as micro-sensors,energy harvesters and so on.