A novel hp-FEM model for IPMC actuation

The system of Poisson and Nernst-Planck (PNP) equations is used to describe the charge transport in ionic polymer-metal composite (IPMC) materials. This process is a key mechanism for the electromechanical transduction of the material. As the system coupled with elastostatic equations is nonlinear and for a domain with two electrodes, the charge concentration differences occur in a very narrow region near the boundaries, the required computing power for a full scale finite element (FE) model is, especially in 3D, rather significant. Furthermore, it is challenging to find a mesh that would be optimal in terms of calculation time, required computing resources, and calculation accuracy. Most of the commercially available FE software for multi-physics problems has rather strict restrictions in terms of element types, mesh types, and choice of polynomial degrees. In this paper, we explore the option of using hp-FEM modeling to solve the PNP and elastostatic equation system. First, we demonstrate how the multi-meshing and the time dependent adaptivity help to control the error of the solution and also how the problem size is reduced. This is done by studying Poisson-Nernst-Planck system of equations in a 2D domain with different hp-adaptivity types. Both 2D and 3D versions of the model are implemented in Hermes which is a space- and space-time adaptive hp-FEM solver. Full mathematical derivation of the weak formulation of the system of equations is presented. Furthermore, we show how the features of Hermes can be useful in modeling more complicated full scale actuation of IPMC.

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