BENDING PERFORMANCE ANALYSIS OF FLEXOELECTRIC NANOPLATE CONSIDERING ELECTRIC FIELD GRADIENTS

The size-dependent flexoelectric effect plays an increasingly critical role in the design of smart devices. Researchers have done much work in multi-physics field analysis at the micro- or nano-scale. The electromechanical coupling behavior of nanoplate in the bending problem is analyzed based on the non-classical theory of elastic dielectric materials considering the flexoelectric effect and electric field gradient effect, using two-dimensional nanoplate as an example. The Mindlin assumption is used to obtain the first-order truncation of the displacement field and electric potential field of the Mindlin plate, the material of plate is assumed to be a cubic crystal in m3m class, the two-dimensional constitutive equations are obtained by substituting the three-dimensional constitutive equations into the expressions of higher-order stress, higher-order couple stress, higher-order electric displacement and higher-order quadrupole, the governing equations of the plate and the line integral equation on the boundary are simultaneously derived through the elastic dielectric variational principle, hence the higher-order bending equations, the higher-order electric potential equation, and the corresponding simply-supported boundary conditions of the rectangular plate are obtained by substituting the two-dimensional constitutive equations and the directional cosine on the boundary into the governing equations of the plate and the line integral equation on the boundary, respectively. According to the higher-order bending equations, higher-order electric potential equation, the corresponding simply-supported boundary conditions of rectangular plate, and the Navier solution theory, the electric potential field of nanoplate are analytically solved, with a focus on the influence of electric field gradient effect on the electric potential in the plate. The numerical results show that the electric field gradient weakens the first-order electric potential generated by the flexoelectric effect in the nanoplate, and the greater the material parameter g₁₁, the greater the weakening of the first-order electric potential. In addition, the existence of the electric field gradient eliminates the singularities of the first-order electric potential of nanoplate under transverse concentrated loading. Present work can be seen as an extension of the structural analysis theory of nanoplate with flexoelectric effect and electric field gradient effect, which provides a reference for the structural design of micro- or nano-scale devices.