# Difference between revisions of "Method to analyze electromechanical stability of dielectric elastomers"

## Information

Fig. 1. Schematic diagram of the system in the paper Fig. 2. derived Hessian for the system in the fig. 1. Fig. 3. Behavior of a dielectric elastomer actuator under several levels of equal biaxial prestresses: �(a)� nominal electric field vs nominal electric displacement, (�b)� true electric field vs nominal electric displacement, and (�c)� nominal electric field vs actuation stretch. The critical points for instability are marked as crosses.

Wiki entry by : Dongwoo Lee, AP225 Fall 2010.

Paper in this Wiki : Xuanhe Zhao, Z. Suo, Method to analyze electromechanical stability of dielectric elastomers, Applied Physics Letters 91, 061921 (2007).

## Summary

The authors talk about the analysis of electromechanical stability of dielectric elastomers. When the thickness of a layer of a dielectric elastomer reduces because of an electric voltage input, the elastomer experiences drastic shrinking, resulting in an electrical breakdown. It is possible to analysis this phenomenon with Hessian of the free-energy function. Fig. 1 shows the schematic diagram of the system that is considered in this paper, and Fig. 2 contains the derived equation for the system; Hessian. The authors show that the electromechanical instability occurs when the Hessian of the free-energy function ceases to be positive definite. In the figure 3, the function $\tilde{E}$ has a peak. the left-hand side of each curve has a positive definite Hessian, the right side has a non-positive-definite Hessian, and the peak has det(H)=0.

## Discussion

The authors introduce a method to analyze the stability of dielectric actuator. The stability of the system was closely related to Hessian of the free energy function and the results (fig. 3.) showed a good agreement with previous experimental data. Further analysis can be conducted for various configurations of the actuators to find the optimal parameters for increasing strain without breakdown.