Size-dependent electromechanical coupling in functionally graded flexoelectric nanocylinders

Flexoelectricity is an electromechanical coupling between polarization and strain gradient, which not only exhibits strong size dependency but is structure associated (geometry or microstructure). By the definition of flexoelectric coefficients, the flexoelectricity-related strain gradients can be generated by tailoring mechanical structures, such as the traditional designed truncated pyramid. In this work, a novel asymmetric nanocylinder is composed of functionally graded materials presented with uniform pressures on the top surface to create a relatively large inhomogeneous strain field for the achievement of obvious flexoelectric polarization. Based on the power-law-distributed material property assumption, we investigate the flexoelectricity of the proposed functionally graded nanocylinder. Based on the extended linear theory of piezoelectricity, the closed-form solutions are obtained, which can specifically characterize the size-dependent flexoelectricity. The most common setups are applied to quantify the flexoelectric response. From the numerical results, we can conclude that the electromechanical properties can be significantly influenced by the given FG configuration with graded material parameters, which can be a guideline for the design of novel flexoelectric devices.