Trilayer ionic EAP actuators exhibit nonlinear electrical and mechanical properties as a function of their oxidation state making it more challenging to accurately predict their mechanical behavior. In this study, an analytical multi-physics model of the conducting polymer actuators is proposed to predict their non-linear dynamic mechanical behavior. To demonstrate the accuracy of the model, a trilayer actuator composed of a solid polymer electrolyte sandwiched between two poly(3,4-ethylenedioxythiophene) (PEDOT) electrodes was fabricated and characterized. This system consists of an electrical subsystem, an electro-mechanical coupling matrix, and a mechanical subsystem described by using a rigid finite element method. The electrical conductivity and the volumetric capacitance, an empirical strain-to-charge ratio, and Young's modulus of the actuator as a function of the PEDOT electrode charge state were also implemented into the model, using measured values. The proposed model was represented using a Bond Graph formalism. The concordance between the simulations and the measurements confirmed the accuracy of the model in predicting the non-linear dynamic electrical and mechanical response of the actuators. In addition, the information extracted from the model also provided an insight into the critical parameters of the actuators and how they affect the actuator efficiency, as well as the energy distribution including dissipated, stored, and transferred energy.