# Dielectric Elastomer Actuator for Soft Robotics Applications and Challenges
## 3 Modeling of DEA
To outline the modeling trend for DEAs, one actuator from each category has been selected. Their modeling trend is listed in Table 2, and their configurations are represented in Figure 4. The actuator shown in Figure 4a,b is a circular planar actuator. It is composed of a single DE film and a pair of concentric circular electrodes placed on the top and bottom of the film. Upon voltage activation, the coated part of the actuator undergoes in-plane expansion. Figure 3: DE actuation schematic. (**a**) Reference state; (**b**) Current state; (**c**) Rheological model. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Year**, **Config.** & **Electrode** & **Modeling Method** & **Material Model** & **Viscoelastic Model** &
\begin{tabular}{c} **Static/Dynamic** \\ **Analysis** \\ \end{tabular} & **Strain Rate** & **Pre-Stretch** & **Sim** & **Exp.1** \\ \hline
2005, Circular [37] & Bentem gold & Numerical & Yeoh & Prony series & Static & No & No & Yes & Yes \\
2006, Circular [5] & Hydrological & Numerical & Ogden & Rheological model & Static & Yes & Yes & Yes & Yes \\  & & & Yesh. & & & & & & \\
2007, Circular [88] & Graphite/Silicone & Numerical & Arruda-Boyce, & - & Static & No & Yes & Yes & Yes \\  & & & Ogden & & & & & & \\
2011, Circular [99] & Carbon grease & Analytical & Gent, Nevo-Hookean & - & Static & No & Yes & Yes & Yes \\
2012, Circular [40] & - & Analytical & Gent & Rheological model & Both & Yes & Yes & Yes & No \\
2014, Circular [41] & Carbon grease & Analytical & Gent & Rheological model & Static & Yes & Yes & Yes & Yes \\
2018, Circular [28] & Carbon grease & Analytical & Gent & Rheological model & Both & Yes & Yes & Yes & Yes \\
2019, Circular [24] & Carbon grease & Analytical & Gent & Rheological model & Static & Yes & Yes & Yes & No \\
2006, Spring Roll [42] & - & Analytical & - & - & Static & No & Yes & Yes & Yes \\
2006, Spring Roll [43] & - & Numerical & - & - & Static & No & Yes & Yes & Yes \\
2007, Spring Roll [45] & - & Numerical & Yeoh & - & Static & No & Yes & Yes & No \\
2008, Spring Roll [45] & - & Analytical & Gaussian & - & Static & No & Yes & Yes & No \\
2008, Spring Roll [46] & Carbon grease & Numerical & & - & Static & No & Yes & Yes & Yes \\
2015, Spring Roll [35] & Carbon grease & Analytical & Neo-Hookean & Rheological model & Both & Yes & No & Yes & No \\
2016, Spring Roll [35] & Carbon grease & Numerical & Yeoh & - & Static & No & No & Yes & Yes \\ \hline \hline \end{tabular}  
* Criteria for checking whether formulated model has been verified experimentally.  
\end{table} 
Table 2: Modeling trend of dielectric elastomer actuators (DEAs). In the top half of Table 2, the modeling trend for the circular DEA is shown. There are two main branches in the modeling method. One is modeling with a numerical model, such as the finite element model, and the other is with an analytical model, such as the non-equilibrium thermodynamic model. In the 2000s, the viscoelasticity of the DE was either neglected or modeled with the Prony series. After the research on the non-equilibrium Helmholtz free energy analysis, a combination of the Gent material model and the rheological viscoelastic model became the standard in the corresponding modeling branch. Yet, DE behavior analysis is still focused more on its static actuation than dynamic actuation. The actuator in Figure 4c,d is a spring roll DEA. This actuator is also composed of DE films. It is fabricated by wrapping DE film around a spring core. The DE film may be pre-stretched and the spring may be compressed before wrapping. As a result, upon voltage activation, the planar expansion of the DE film is converted into linear movement in the axial direction. The bottom half of Table 2 shows the trend for a spring roll type DEA. Unlike the circular actuator, there are fewer attempts in modeling and analyzing the spring roll actuator with a viscoelastic model. This is most likely due to the greater complexity in fabrication and modeling.