A Study of the Flexoelectric Effect on the Electroelastic Fields of a Cantilevered Piezoelectric Nanoplate

Abstract

Flexoelectricity, a spontaneous polarization in linear response to strain gradients or non-uniform deformation, is believed to contribute to the size-dependent electromechanical coupling of piezoelectric materials at the nanoscale. In the current work, the flexoelectric effect upon the static bending behaviors of a cantilevered piezoelectric nanoplate (PNP) is studied. Based on the Kirchhoff plate model and the extended linear piezoelectric theory, the non-conventional governing equations and the boundary conditions of the PNP under both mechanical and electrical loads are derived with the incorporation of the flexoelectric effect. Finite difference method (FDM) is performed to get the numerical solution for the electroelastic fields of the plate. Simulation results show that the flexoelectric effect is more prominent for the thinner plates with smaller thickness. It is also found that the flexoelectric effect upon the electroelastic responses of the clamped PNP is also sensitive to some other factors, including the boundary conditions, the plate geometric ratio, and the applied mechanical and electrical loads. This work aims to provide an increased understanding of the size-dependent electromechanical coupling properties of a piezoelectric plate structure.