Dielectric rods have been employed in various electromechanical applications, including energy harvesters and sensors. This paper develops a general framework to model large deformations in dielectric rods, considering both direct and converse flexoelectric effects. Initially, we derive the governing differential equations for a three-dimensional dielectric continuum solid to model large deformations, incorporating converse flexoelectricity. Then, we derive the equilibrium equations for the flexoelectric strain-gradient special Cosserat rod. Subsequently, we establish its constitutive relations and identify the corresponding work conjugates. To solve these governing differential equations numerically, we implement a quaternion-based numerical approach and obtain flexoelectricity-based solutions corresponding to the follower load. Moreover using these constitutive relations, we have also obtained nonlinear analytical solutions for bending under the follower load that show an excellent agreement with our numerical results. Bending under the follower load is also compared with the transverse load to understand the electric field generation. Unlike, under the application of the transverse load, where the electric field increases monotonically, for the follower load, the electric field gradually switches its sign. The role of direct and converse flexoelectric coefficients has also been examined, and several interesting conclusions have been drawn. Finally, we analyze the effect of mechanical and electrical length scale parameters. The electromechanical response from the follower load can be utilized to fabricate flexoelectric sensors for nanoelectromechanical systems.

中文翻译：

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模拟软电介质棒中的正反挠曲电及其对从动负载的应用


介电棒已用于各种机电应用，包括能量收集器和传感器。本文开发了一个通用框架来模拟介电棒中的大变形，同时考虑了正向和反向挠曲电效应。最初，我们推导出三维介电连续体固体的控制微分方程，以模拟大变形，并结合逆向挠曲电。然后，我们推导出了挠曲电应变梯度特殊 Cosserat 棒的平衡方程。随后，我们建立其本构关系并确定相应的工作共轭。为了以数值方式求解这些控制微分方程，我们实现了一种基于四元数的数值方法，并获得了对应于从动器负载的基于柔性电的解。此外，使用这些本构关系，我们还获得了从动载荷下弯曲的非线性解析解，与我们的数值结果非常吻合。还将从动负载下的弯曲与横向负载进行比较，以了解电场的产生。与在横向负载下电场单调增加不同，对于从动负载，电场会逐渐改变其符号。还研究了正向和反向挠曲电系数的作用，并得出了几个有趣的结论。最后，我们分析了机械和电气长度尺度参数的影响。来自从动负载的机电响应可用于制造用于纳米机电系统的柔性电传感器。