Linear Electromechanical Model of Ionic Polymer Transducers -Part I: Model Development

A linear electromechanical model is developed for ionic polymer materials. The model is based on an equivalent circuit representation that is related to the mechanical, electrical, and electromechanical properties of the material. Expressions for the quasi-static and dynamic mechanical impedance are derived from beam theory. The Golla-Hughes-McTavish model of viscoelasticity is incorporated into the model to include effects due to a rate dependent modulus. Similar to previous research, the electrical impedance is modeled as a series combination of resistive and capacitive elements. The major contribution of this work is the derivation of an electromechanical coupling term that is related to an effective bending strain coefficient. This parameter is also frequency dependent to model the low-frequency relaxation that has been measured in certain ionic polymer materials. The resulting linear electromechanical model is based on the measurement of the effective permittivity, elastic modulus, and effective strain coefficient. All input-output relationships related to sensing and actuation can be derived using these three material parameters and the transducer geometry. This model also emphasizes a reciprocity between sensing and actuation that has not been discussed before in relation to these materials. The result of this work is a comprehensive model that enables the design of devices and material systems that incorporate ionic polymer materials as either sensors or actuators.