On some basic aspects of flexoelectricity in the mechanics of materials

Abstract

Abstract Flexoelectricity is an interesting electromechanical coupling that exists in all dielectrics when the deformation is inhomogeneous. The intensity of flexoelectricity is highly related to the deformation gradient and the dimensions of dielectric structures. Although flexoelectricity plays a significant role in micro-/nano- devices behaviors, the complexity of electromechanical coupling impedes the utilization of flexoelectricity in engineering. In this paper, we revisit the strain gradient theory in three-dimensional spaces and decompose the strain gradient into four parts. Based on these decomposed strain gradients, we reformulate the general isotropic flexoelectric theory. To better illustrate the electromechanical coupling behaviors, we specialize the flexoelectric effects from three dimensional (3D) deformations to a few 1D deformations, including torsion, tension/compression and bending as buckling of columns in mechanics of materials. These deformations are commonly encountered in engineering, and we hope that this paper can help the design of micro-/nano- devices by harnessing flexoelectricity.