Exact solutions for the electromechanical responses of a dielectric nano-ring

Based on an extended linear theory for dielectrics, this work presents exact solutions for the electromechanical responses of a dielectric nano-ring subjected to mechanical and electrical loads. By incorporating terms involving the strain gradient and the electric field gradient into the electric Gibbs free energy, both the direct and converse flexoelectric effects can be captured. The general solution to the differential governing equation is a linear combination of modified Bessel functions and the electromechanical fields are obtained by solving boundary value problems. The influences of the material surfaces and the electric circuit conditions on the electromechanical coupling behavior of the dielectric nano-ring have also been considered. It is found that the flexoelectricity and the surface effect on the electromechanical fields are substantial, and they are affected by the size of the ring structure. Moreover, the flexoelectric effect is sensitive to the material length scales introduced by the new theory and the electric circuit conditions. From simulation results, it is also suggested that nano-scaled electromechanical coupling devices could be built based on dielectric materials through flexoelectricity, which thereby opens up new perspectives for nano-technology.