Electrical modeling of cylindrical dielectric elastomer transducers

Dielectric elastomer transducers (DETs) are commonly modeled by lumped-element models (LEMs), however such models do not capture the cutoff behavior that manifests at relatively low frequencies due to the high resistivity of the stretchable electrodes. Moreover, the contribution of the electrodes into the lumped series resistance is not accurately known. The aim of this work is to define the accuracy and frequency limits of the LEM and to derive the exact values of its lumped components. This is achieved by developing a detailed three-dimensional distributed-element model (DEM) of the transducer structure. Based thereon, analytical expressions are developed for the LEM components and limits are explored. Through numerical evaluation of the DEM it is found that only two-third of the single-polarity electrode resistance contributes to the lumped series resistance, which is three times lower than predicted by existing models. Comparison between the LEM and DEM further shows that the LEM is adequate for frequencies significantly below the cutoff frequency. Thereafter, capacitance and resistance fall off as a result of signal propagation limitations. This has been experimentally verified. The developed DEM and established validity range of the simple LEM allows for more accurate sensors and better optimized transducers designs, with up to three times less electrode material.