# Dielectric elastomers of interpenetrating networks

[Edited by Jianyu Li, AP 225, Fall, 2010]

## Summary

This paper reports a theoretical model for interpenetrating elastomers consisted of long and short chains with the aim to explain why the network can bear large deformation without break. The result shows that long chains make elastomer complaint at deformation, by contrast, short chains prevent the elastomer thinning excessively.

## Electromechanical Instability

The elastic energy of the network depends on the in-plane streches, $\lambda_1,\lambda_2$. For interpenetrating networks of A and B, $W(\lambda_1,\lambda_2)=\phi^A W^A (\lambda_1^A,\lambda_2^A)+\phi^B W^B (\lambda_1^B,\lambda_2^B)$. Then, they used the eight-chain model of Arruda and Boyce to represent the free energy function, where $W=\frac{kT}{\nu}(\frac{\zeta}{tanh \zeta}-1+log \frac{\zeta}{sinh \zeta})$. After getting the expression of the free energy, the stresses can be calculated by, $\sigma _1=\lambda_1 \partial W(\lambda_1,\lambda_2)/ \partial \lambda_1-\epsilon E^2, \sigma_2=\lambda_2 \partial W(\lambda_1,\lambda_2)/ \partial \lambda_2-\epsilon E^2$. The preserved stretch is displayed in figure 2, which matches the neo-Hookean limit well.

## Under Electric Field

This paper further analyzed the behavior under electric field. The relation between the voltage and thickness is followed, $V=hE=(\lambda^p/\lambda)^2 h^p E$. Through changing the parameters $\lambda, n^A and n^B$, they compared the results of prestretched and native networks, as illustrated in figure 3 and 4.