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The Poisson-Nernst-Planck system of equations is used to simulate the charge dynamics due to ionic current and resulting time-dependent displacement of ionic polymer-metal composite (IPMC) materials. Measured data show that currents through the polymer of IPMC cause potential gradients on the electrodes. Existing physics based models of IPMC do not explicitly consider how this affects the charge formation near the electrodes and resulting actuation of IPMC. We have developed an explicit physics based model that couples the currents in the polymer to the electric current in the continuous electrodes of IPMC. The coupling is based on the Ramo-Shockley theorem. The circular dependency concept is used to explain how the dependency between the ionic current and the potential drop in the electrodes is calculated and how they affect each other. Simulations were carried out using the finite element method. Calculated potential gradients, electric currents, and tip displacement of IPMC were validated against experimental data. We also show how the model is general in respect to the different types of currents in the polymer and how it can be used in more complicated cases such as 3D simulations.