Electrochemo-poromechanics of ionic polymer metal composites: Towards the accurate finite element modelling of actuation and sensing

Ionic polymer metal composites (IPMCs) consist of an electroactive polymeric membrane, plated with metal electrodes, and including a fluid phase of ions in a solvent, whose diffusion allows for actuation and sensing applications. We build on a previous finite-deformation theory of our group that accounts for the cross-diffusion of ions and solvent and couples the mass balances of these species with the stress balance and the Gauss law. Here, we abandon the assumption that the fluid phase is a dilute solution, with benefits on both modelling and computation. A reliable finite element (FE) implementation of electrochemomechanical theories for IPMCs is challenging because the IPMC behaviour is governed by boundary layers (BLs) occurring in tiny membrane regions adjacent to the electrodes, where steep gradients of species concentrations occur. We address this issue by adopting the generalized FE (GFE) method to discretise the BLs. This allows unprecedented analyses of the IPMC behaviour since it becomes possible to explore it under external actions consistent with applications, beside obtaining accurate predictions with a reasonable computational cost. Hence, we provide novel results concerning the influence of the membrane permittivity on the species profiles at the BLs. Additionally, by leveraging on the mobility matrix, we establish that the initial peak deflection in actuation strongly depends on the constitutive equations for the species transport and discuss the predictions of some experimental results from the literature. Overall, we demonstrate the potential of the proposed model to be an effective tool for the thorough analysis and design of IPMCs.