Analysis Of Electromechanical Coupling Performance Of Functionally Graded Flexoelectric Materials

Flexoelectricity in solid dielectrics is an electromechanical mechanism induced by strain gradient or polarization(electric field)gradient.Different from the traditional piezoelectric effect,the flexoelectric effect exists in all-dielectric materials,whether it is centrosymmetric or non-centrosymmetric.The research of the flexoelectric effect originated from the research of liquid crystal and biofilm.However,with the development of nanotechnology,the influence of the flexoelectric effect has become increasingly apparent.Advanced manufacturing and production processes enable the structure to obtain a large strain gradient,which enables the researches of simple structures(blocks,cylinders,etc.),special structures(cones,pyramids),and composite structures(laminated plates,periodic layered structures)to have a new development.These studies have led to many applications of flexoelectric materials in flexible electronics,thin films,energy traps,nano electromechanics,etc.However,these material structure models still have mechanical defects and are difficult to apply in practical engineering.As an advanced functional composite material,the microstructure of functionally graded materials can change continuously and smoothly from one material to another in a specific gradient,which enables the material to have excellent mechanical properties and engineering applications.Due to the non-uniform structure of functionally graded materials,the structure exhibits obvious asymmetry,which in turn induces a large non-uniform strain field and a large strain gradient field.To analyze the mechanical and electrical coupling problems under these complex structures,a mixed finite element is developed based on the mixed variational principle.It is used as an analysis tool to study the mechanical properties,electromechanical effect,and scale effect of the functionally graded flexoelectric material.The effective material properties of particle flexoelectric composites are also be predicted.The main research contents of this paper are as follows:Based on the mixed variational principle,a complete mixed finite element program is developed on the MATLAB platform.By introducing displacement gradient and Lagrange multipliers as additional variables,mixed continuous equations containing only the first derivative are derived,and a nine-node square mixed element is developed.Using MATLAB as a development tool,a complete program of the mixed finite element was developed,including pre-processing,main program,and post-processing program.A uniformly flexoelectric cylinder is used as the verification model,and the results showed that the simulation results were consistent with the analytical solution.The program can be used to simulate flexoelectric materials.The electromechanical effects of axisymmetric load on a functionally graded flexoelectric micro-cylinder are studied.Based on the verification model,the concept of functionally graded material is introduced to make the material of the cylinder present gradient distribution along the radius.The results show that the electrical properties of the model are highly scale-dependent,and the appropriate material distribution will also greatly affect the electromechanical response of the cylinder.The maximum potential difference between the interior and the boundary can be 1.6 times that of a uniform material.The flexoelectric effects and related mechanical behaviors of two-dimensional functionally graded flexoelectric nanobeam are studied.By applying mechanical and electrical loads to two-dimensional functionally graded flexoelectric beams,the phenomenon of deflection platform is discovered.The influence of length scale,beam aspect ratio,size,and material distribution on the deflection platform is also studied.Results show that the length scale and aspect ratio of the beam will have a huge impact on the shape of the deflection platform.The size of the beam has an impact on the value of the deflection platform,but the impact on the dimensionless deflection platform is limited.The influence of material distribution on the deflection platform shows strong regularity.The effective mechanical and electrical properties of flexoelectric composites with inclusions are predicted.By establishing different types of inclusion models,the effective material properties of representative volume elements with a single spherical inclusion,square inclusion,regular octagonal inclusion,and multiple spherical inclusions are studied.The prediction results of the model considering only the strain gradient elasticity and the model considering both the strain gradient elasticity and flexoelectric effects are compared.The shape effects of the inclusion are also studied,it is found that the shape of the inclusions has a greater impact on the mechanical and electrical properties.