A multi-physics coupled beam model for ionic polymers: Solutions for static and dynamic responses

Ionic polymers, with Nafion as a typical representative, have been widely applied in various fields. In this paper, we develop a new model that reveals the multi-physics coupling properties of ionic polymer beams. A key advantage of this model is its ability to provide analytical solutions, eliminating the need for finite element methods while effectively capturing the various responses of ionic polymer beams. Through this model, we systematically investigate the static and harmonic vibration characteristics of ionic polymer-metal composites (IPMCs) as force sensors and perform a comprehensive parametric analysis. Specifically, we explore how diffusion coefficient, permittivity, molar volume of hydrated cations, and anion concentration influence IPMC performance. The results highlight the strong applicability of the model in describing the multi-physics coupled behavior of ionic polymers, making it a powerful tool for the design and optimization of this class of sensors.