Abstract：Flexoelectricity, the special electromechanical coupling between strain gradient and polarization, exists in all dielectric materials. It has received wide attention in multiple fields including energy harvesting, sensing and actuation. However, the effect of elastic strain gradient on flexoelectric response has typically been ignored or underestimated in the studies of flexoelectricity of nano-dielectric structures, which is solved in this paper. According to the general strain gradient elasticity theory, it is strictly proved that only three length-scale parameters are independent, and the applications of strain gradient theory with one or two scale parameters in the literature are only in its simplified forms. Based on this theory, a theoretical model of three-dimensional dielectric structure considering the generalized strain gradient elasticity is established. Then, using this model, the governing equations and boundary conditions of a bending nanobeam are obtained by Hamilton’s variational principle. The one-dimensional cantilever nano-beam is taken as an example to study the flexoelectric response of its bending and energy harvesting characteristics. The results show that the flexoelectric response of structure exhibits size effect, and the elastic strain gradient influences this effect to some extent, especially when the structural scale is smaller than the length-scale parameters. On the other hand, the results show that extreme values of displacement and energy efficiency exist with the increase in structural scale, when the elastic strain gradient theory is considered. Furthermore, it is found that flexoelectricity coupling with external voltage will lead to the beam’s inhomogeneous boundary conditions. In short, the elastic strain gradient significantly impacts the displacement, polarization, electric potential, and energy efficiency of a dielectric nanobeam with incorporation of flexoelectricity. This work provides a theoretical basis for further understanding of the mechanism of flexoelectricity at nanoscale and the effect of elastic strain gradient theory on flexoelectricity. It can be helpful for the design of nanoscale flexoelectric energy harvesters.
2019, Vol. 40 
