IPMC mechanoelectrical transduction: its scalability and optimization

Abstract

Ionic polymer–metal composite (IPMC) mechanoelectrical transduction is described with a system of partial differential equations—the Poisson equation, the Nernst–Planck equation, and the Navier equations for the displacements. Modeling of this system of four equations is challenging due to the differences in the physical fields—namely, one physical field can be very smooth while others have steeper gradients. When using the conventional finite element method (FEM), the problem size in terms of number of degrees of freedom can be very large. Additionally, it is challenging to find an optimal mesh due to the fact that the physical fields are time dependent. Last but not least, due to the coupled nature of the system, it is necessary to have a way to estimate the error to ensure the desired accuracy of the solutions. In this work, we propose a novel hp-FEM modeling method for solving the system of equations. hp-FEM is a modern version of the FEM that is capable of exponential convergence. It is also demonstrated how the multi-meshing reduces the problem size while maintaining the prescribed error limit. The solution domain that describes IPMC can be scaled without a significant increase in the number of degrees of freedom and solution time. Additionally, PID controller based time step optimization is incorporated. The model is implemented in Hermes, which is a free hp-FEM solver.