基于广义应变梯度理论的纳米梁挠曲电效应研究

挠曲电效应是应变梯度与电极化的耦合，它存在于所有的电介质材料中。在纳米电介质结构的挠曲电效应研究中，应变梯度弹性对挠曲电响应的影响一直以来被低估甚至被忽略了。根据广义应变梯度理论，应变梯度弹性中独立的尺度参数只有三个，而文献中所采用的一个或两个尺度参数的应变梯度理论只是它的简化形式。基于该理论，论文建立了考虑广义应变梯度弹性的三维电介质结构的理论模型，并以一维纳米梁为例研究了其弯曲问题的挠曲电响应及其能量俘获特性。结果表明，纳米梁的挠曲电响应存在尺寸效应，并且弹性应变梯度会影响结构挠曲电的尺寸效应，特别是当结构的特征尺寸低于尺度参数时。论文的工作为更进一步理解纳米尺度下的挠曲电机理和能量俘获特性提供理论基础和设计依据。

The flexoelectric response of nanobeam based on the general strain gradient theory

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.