Flexoelectric effect on the electroelastic responses of bending piezoelectric nanobeams

Abstract

Flexoelectricity, referring to a spontaneous electric polarization induced by strain gradient in dielectrics, presents a strong size dependency at the nanoscale. In the current work, the influence of the flexoelectric effect on the mechanical and electrical properties of bending piezoelectric nanobeams with different boundary conditions is investigated. Based on the extended linear piezoelectricity theory and the Euler beam model, analytical solutions of the electroelastic fields in the piezoelectric nanobeams subjected to both electrical and mechanical loads are obtained with the inclusion of the flexoelectric effect. Simulation results show that the flexoelectric effect on the elastic behavior of bending beams is sensitive to the beam boundary conditions and the applied electrical load. In addition, for a cantilever piezoelectric nanobeam, an axial relaxation strain is induced from the piezoelectric and flexoelectric effects, while these effects induce a resultant axial force in both the clamped-clamped and simply supported piezoelectric nanobeams. Results also indicate that the flexoelectric effect plays a significant role in the contact stiffness and electric polarization of piezoelectric beams when their thickness is at the nanoscale. It is found that the flexoelectric effect on the electroelastic responses of piezoelectric nanobeams is more pronounced for the beams with smaller thickness. These results are useful for understanding the fundamental mechanical and physical properties of bending piezoelectric nanobeams.