The recent discovery of electroactive polymers has shown great promises in the field of soft robotics and was logically followed by experimental, numerical, and theoretical developments. Most of these studies were concerned with systems entirely covered by electrodes. However, there is a growing interest for partially active polymers, in which the electrode covers only one part of the membrane. Indeed, such actuation can trigger buckling instabilities and so represents a route toward the control of three-dimensional shapes. Here, we study theoretically the behavior of such partially active electroactive polymer. We address two problems: (1) the electrostatic elastica including geometric nonlinearities and partially electroactive strip using a variational approach. We propose a new interpretation of the equations of deformation, by drawing analogies with biological growth, in which the effect of the electric voltage is seen as a change in the reference stress-free state. (2) We explain the nature of the distribution of electrostatic forces on this simple system, which is not trivial. In particular, we find that edge effects are playing a major role in this problem.

中文翻译：

---

电膜的力学和能量学

最近发现的电活性聚合物在软机器人领域显示出巨大的前景，并且顺理成章地伴随着实验、数值和理论的发展。这些研究中的大多数都涉及完全由电极覆盖的系统。然而，人们对部分活性聚合物的兴趣越来越大，其中电极仅覆盖膜的一部分。事实上，这种驱动可以触发屈曲不稳定性，因此代表了控制三维形状的途径。在这里，我们从理论上研究了这种部分活性电活性聚合物的行为。我们解决了两个问题：（1）静电弹性包括几何非线性和使用变分方法的部分电活性条。我们提出了对变形方程的新解释，通过与生物生长进行类比，其中电压的影响被视为参考无应力状态的变化。(2) 我们解释了这个简单系统上静电力分布的性质，这不是微不足道的。特别是，我们发现边缘效应在这个问题中发挥着重要作用。