Influence of Flexoelectricity on Electromechanical Properties of Functionally Graded Piezoelectric Nanobeams Based on Modified Couple Stress Theory

Flexoelectricity refers to the linear coupling between the strain gradient and electric polarization at micro/nanometer scale and exists in all dielectrics. Flexoelectricity exhibits strong size-dependence, which can be remarkably enhanced by size reduction. Flexoelectricity is also shape-associated and the strain gradients induced electric polarization in nonpiezoelectric dielectrics with irregular shapes (i.e., truncated pyramids) depend on shape geometry, dimension and aspect ratio of the structures. In this work, a novel asymmetric piezoelectric nanobeam based on functionally graded (FG) nanomaterial is modeled and the flexoelectricity in such a designed structure is theoretically examined. Since the material properties of FG nanomaterial vary along a certain direction, it is expected that such an inhomogeneity will result in large strain gradients in the nanobeam and a large flexoelectric response will occur. By assuming that the material properties of FG nanomaterial obey a power volume fraction distribution, we derive a six-order governing equation based on modified couple stress elasticity theory, and closed-form solutions are obtained. Results indicate that the fiexoelectricity has a significant influence on the electromechanical responses in FG piezoelectric nanobeams. The results obtained from the current work may help explain the extremely large flexoelectric coefficients observed in some classes of materials with irregular shapes.