Modeling the flexoelectric effect of an anisotropic dielectric nanoplate

Abstract

The static bending and the flexoelectric effect induced in an anisotropic dielectric nano-plate are studied in the frame of the simplified strain gradient elasticity theory (SSGT). The Kirchhoff plate theory is considered for a simply supported nano-plate loaded by a uniformly distributed constant forces at its upper surface. The displacement and the induced spontaneous polarization are formulated such that the dimensions of the problem reduce to two dimensions only. The variational concept of the internal energy and the virtual work exerted by the external forces are used to obtain the governing equations as well as the boundary conditions. The choose of the cubic materials avoid the ambiguity between piezoelectricity and flexoelectricity, where all odd tensors are vanished. The finite Fourier transform is employed to obtain the analytical solution. The numerical calculations of the problem are presented with the help of the commercial software Maple. Some selected significant results are introduced through sets of figures with physical explanations. The results reveal that the flexoelectric effect at the surface of the clamped nanoplate should be considered and cannot be neglected. Moreover, the nanoscale dimension enhances the flexoelectric effect more than macroscale.