A Thermo-Electro-Viscoelastic Model for Dielectric Elastomers

Dielectric elastomers (DEs) are a class of electro-active polymers (EAPs) that can deform under electric stimuli and have great application potential in bionic robots, biomedical devices, energy harvesters, and many other areas due to their outstanding deformation abilities. It has been found that stretching rate, temperature, and electric field have significant effects on the stress-strain relations of DEs, which may result in the failure of DEs in their applications. Thus, this paper aims to develop a thermo-electro-viscoelastic model for DEs at finite deformation and simulate the highly nonlinear stress-strain relations of DEs under various thermo-electro-mechanical loading conditions. To do so, a thermodynamically consistent continuum theoretical framework is developed for thermo-electro-mechanically coupling problems, and then specific constitutive equations are given to describe the thermo-electro-viscoelastic behaviors of DEs. Furthermore, the present model is fitted with the experimental data of VHB4905 to determine a temperature-dependent function of the equilibrium modulus. A comparison of the nonlinear loading-unloading curves between the model prediction and the experimental data of VHB4905 at various thermo-electro-mechanical loading conditions verifies the present model and shows its ability to simulate the thermo-electro-viscoelastic behaviors of DEs. Simultaneously, the results reveal the softening phenomena and the instant pre-stretch induced by temperature and the electric field, respectively. This work is conducive to analyzing the failure of DEs in functionalities and structures from theoretical aspects at various thermo-electro-mechanical conditions.