Effect of flexoelectricity on the electroelastic fields of a hollow piezoelectric nanocylinder

Flexoelectricity, referring to a spontaneous electric polarization in response to non-uniform strains (or strain gradients), is a universal electromechanical coupling in all dielectrics. In this work, the influence of the flexoelectricity on the electroelastic fields of a hollow piezoelectric nanocylinder under applied mechanical and electrical loads is investigated. Meanwhile, the associated pure non-local elastic effect in response to the strain gradients is also incorporated. The governing equations and the associated boundary conditions for the cylinder are derived from the variational principle. The analytical/approximate solutions of the problem with the consideration of diverse flexocoupling effects are obtained, respectively. It is found from the simulation results that the flexoelectricity has a momentous influence on the electroelastic fields of the cylinder. The influence of the flexoelectricity upon the size-dependent electromechanical coupling properties of the piezoelectric nanocylinder is also investigated and it is found that the size effects are more manifest for nanocylinders with smaller size. It is expected that the current work could provide increased understanding on the mechanisms of the flexoelectricity and its function in electromechanical coupling. (paper)