Nonlinear dynamic modeling of ultrathin conducting polymer actuators including inertial effects

Trilayer conducting polymer (CP) actuators are potential alternatives to piezoelectric and electrostatic actuators due to their large strain, and recently demonstrated operation at hundreds of Hertz. However, these actuators exhibit nonlinear electrical and mechanical properties as a function of their oxidation state, when operated over their full strain range, making it more challenging to accurately predict their mechanical behavior. In this paper, an analytical multi-physics model of the CP actuators is proposed to predict their nonlinear 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 represented by an RC equivalent circuit, 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 nonlinear 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. These are the key parameters for designing, optimizing, and controlling the actuation behavior of a trilayer actuator.