New Insight into the Flexoelectricity in the View of Mechanics of Materials: Prismatic Beams Subjected to Bending

Flexoelectricity is a fascinating electromechanical phenomenon that occurs in non-homogeneously deformed dielectric materials. Unlike piezoelectricity, the flexoelectric effect is highly dependent on both the material scale and the deformation gradient. Although several theoretical models have been proposed to explain the mechanism of flexoelectricity, these models can be rather complicated for those who are interested in studying the topic. This paper aims to simplify the understanding of flexoelectricity by focusing on the bending behavior of a prismatic dielectric beam from a mechanics of material perspective. We avoid using complicated mathematical formulations based on continuum mechanics, including advanced tensor algebra and calculus of variations. Our formulation clearly explains how inhomogeneous deformations and material size affect the electromechanical coupling, changing the effective bending stiffness, deflection, and rotation angles of a bending beam. We hope this paper can help undergraduate students and researchers, who are unfamiliar with the electromechanical coupling in flexoelectricity, to develop an understanding of this phenomenon and encourage further research in this area.