基于COMSOL有限元挠曲电圆筒的力电耦合行为分析

挠曲电效应是一种新型的力电耦合效应。不同于压电效应，挠曲电效应是极化对应变梯度的响应，指的是电介质中的离子由于应变梯度的存在打破了反演对称性，从而导致电介质发生极化或者变形的现象。作为一种类似压电效应的机电耦合效应，因其在材料、机械工程、自动化、仪器仪表等学科中的独特优势而受到越来越多的关注。由于目前所有的商业有限元软件中都缺少挠曲电模块，因此挠曲电问题的数值模拟需用有限元自主编程进行计算。得益于COMSOL Multiphysics的偏微分方程模块（PDE模块），本文展示在COMSOL软件中对考虑挠曲电效应的力电耦合问题直接进行数值模拟的方法。并针对固定边界位移的挠曲电圆筒进行数值计算，与已有的解析解进行对比，验证了有限元数值计算方法的正确性。此外，本文研究了挠曲电系数及材料不同梯度指数对圆筒力电耦合的影响。该工作可以为挠曲电效应数值计算及挠曲电结构设计提供帮助。

Analysis of electromechanical coupling behavior of flexoelectric cylinder based on COMSOL finite element

The flexoelectric effect is a new type of electromechanical coupling effect. Different from piezoelectric effect, flexoelectric effect is the response of polarization to strain gradient, which refers to the phenomenon that the ions in the dielectric break the inversion symmetry due to the existence of strain gradient, resulting in polarization or deformation of the dielectric. As a kind of electromechanical coupling effect similar to piezoelectric effect, it has attracted more and more attention because of its unique advantages in materials, mechanical engineering, automation, instrumentation and other disciplines. Due to the lack of flexoelectric module in all commercial finite element software, the numerical simulation of flexoelectric problem needs to be calculated by finite element self-programming. Thanks to the partial differential equation module ( PDE module ) of COMSOL Multiphysics, this paper demonstrates a direct numerical simulation method for the electromechanical coupling problem considering flexoelectric effect in COMSOL software. The numerical calculation of the flexural electric cylinder with fixed boundary displacement is carried out. Compared with the existing analytical solutions, the correctness of the finite element numerical calculation method is verified. In addition, the effects of flexoelectric coefficient and different gradient indexes of materials on the electromechanical coupling of cylinders are studied. This work can provide help for the numerical calculation of flexoelectric effect and the design of flexoelectric structure.