A general visco-hyperelastic model for dielectric elastomers and its efficient simulation based on complex frequency representation

A general visco-hyperelastic model for dielectric elastomers (DE) is presented in this paper, derived from the Quasi-Linear Viscoelastic (QLV) framework. To gain a physical insight into the time-dependent constitutive relation and solve it efficiently, a complex frequency representation of the convolution integral equation, with the legible form of block-scheme, is specifically constructed, in which the viscoelastic stress is interpreted considering the instantaneous response (depicted by Yeoh strain energy potential) as a signal filtered by a linear system (superposition of characteristic modes of the time relaxation function, i.e., Prony series). By incorporating the effects of electrostatic pressure, the model is further extended to the electromechanical coupling state, which can be expediently implemented by the general software, MATLAB/Simulink. Comparisons of the theoretical predictions from the proposed model with the experimental results previously reported (for VHB elastomers) show good agreements over a wide range of stretch rates (from 10^{-4 to ~ 1 s}-1), whether the membrane is only subjected to large mechanical deformations, or undergoes electric loads simultaneously.