Ionic polymer metal composites (IPMCs) are soft electroactive materials that are finding increasing use as actuators in several engineering domains, where there is a need of large compliance and low activation voltage. Similar to traditional sandwich structures, an IPMC comprises a hydrated ionomer core that is sandwiched by two stiffer electrodes. The application of a voltage across the electrodes drives charge migration within the ionomer, which, in turn, contributes to the development of an eigenstress, associated with osmotic pressure and Maxwell stress. Critical to IPMC actuation is the variation of the eigenstress through the thickness of the ionomer, which is responsible for strain localization at the ionomer-electrode interfaces. Despite considerable progress in the development of reliable continuum theories and finite element tools, accurate structural theories that could beget physical insight into the inner workings of IPMC actuation are lacking. Here, we seek to bridge this gap by contributing a principled methodology to structural modeling of IPMC actuation. Our approach begins with the study of the IPMC electrochemistry through the method of matched asymptotic expansions, which yields a semi-analytical expression for the eigenstress as a function of the applied voltage. Hence, we establish a total potential energy that accounts for the strain energy of the ionomer, the strain energy of the electrodes, and the work performed by the eigenstress. By projecting the IPMC kinematics on select beam-like representations and imposing the stationarity of the total potential energy, we formulate rigorous structural theories for IPMC actuation. Not only do we examine classical low-order and higher-order beam theories, but we also propose enriched theories that account for strain localization near the electrodes. The accuracy of these theories is assessed through comparison with finite element simulations on a plane-strain problem of non-uniform bending. Our results indicate that an enriched Euler-Bernoulli beam theory, with three independent field variables, is successful in capturing the main features of IPMC actuation at a limited computational cost.

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关于离子聚合物金属复合材料的结构理论：准确性和简单性之间的平衡

离子聚合物金属复合材料 (IPMC) 是软电活性材料，在需要大柔顺性和低激活电压的多个工程领域中越来越多地用作致动器。与传统的夹心结构类似，IPMC 包含一个水合离聚物核，该核被两个更硬的电极夹在中间。在电极上施加电压会驱动离聚物内的电荷迁移，这反过来又会导致与渗透压和麦克斯韦应力相关的本征应力的产生。IPMC 驱动的关键是本征应力随离聚物厚度的变化，这导致离聚物-电极界面处的应变局部化。尽管在可靠的连续统理论和有限元工具的发展方面取得了长足的进步，缺乏可以对 IPMC 驱动的内部工作原理进行物理洞察的准确结构理论。在这里，我们试图通过为 IPMC 驱动的结构建模贡献一种有原则的方法来弥合这一差距。我们的方法从通过匹配渐近展开方法研究 IPMC 电化学开始，该方法产生作为施加电压函数的本征应力的半解析表达式。因此，我们建立了一个总势能，它考虑了离聚物的应变能、电极的应变能和本征应力所做的功。通过将 IPMC 运动学投影到选择的梁状表示上并强加总势能的平稳性，我们为 IPMC 驱动制定了严格的结构理论。我们不仅研究了经典的低阶和高阶梁理论，而且还提出了解释电极附近应变局部化的丰富理论。这些理论的准确性是通过与非均匀弯曲平面应变问题的有限元模拟进行比较来评估的。我们的结果表明，具有三个独立场变量的丰富 Euler-Bernoulli 梁理论成功地以有限的计算成本捕获了 IPMC 驱动的主要特征。