Revisiting the Flexoelectricity in a Functionally Graded Dielectric Nanobeam

Flexoelectricity is a linear coupling between strain gradient (or non-uniform strain) and electric polarization. A bending dielectric nanobeam can induce giant flexoelectricity that can be used for energy harvesting; however, piezoelectricity is suppressed due to sign symmetry of strains. To break the symmetry of strains and incorporate both flexoelectricity and piezoelectricity, a functionally graded material (FGM) beam is studied. This paper reformulates the functionally graded dielectric nanobeam by incorporating the general strain gradient elasticity theory and the Euler-Bernoulli beam theorem. It shows that the non-uniformity not only evoke piezoelectricity but also enhances energy harvesting, comparing with the isotropic material beam. The optimal size of the FGM beam appears around one order of magnitude higher than that of the single material beam, which makes the beam size more justifiable on practical application. This work may be helpful in the analysis and design of smart piezoelectric nanostructures and could shed light on the flexoelectricity energy harvesting.