Application of viscoelasticity to nonlinear analyses of circular and spherical dielectric elastomers

Abstract

Time-dependent dissipative behaviors of circular and spherical dielectric elastomer (DE) membranes were investigated, and viscoelastic models based on nonlinear theory were developed. Using these formulas, one can easily understand the electromechanical performance of DEs. By combining the Maxwell stress, mechanical stress, energy principle, Gent model (for circular membranes), and neo-Hookean model (for balloon-shaped membranes), we derived governing equations that describe membrane deformation. The voltage versus stretch curves of VHB-based thin films was N-shaped, and the peak applied voltage decreased as the viscoelastic stretch grew. Membranes with smaller original radii required shorter relaxation times. When the viscoelastic relaxation time was very short, the viscoelasticity could be negligible. There were clear differences between the theoretical analyses of circular and spherical DE membranes. For example, the radial stretch was different and the ideal gas law was used for DE balloons but not for circular films. Our experiments indicated large deformations of both types of DE membranes at 5 kV. However, electromechanical instability can appear over time. According to our theoretical analysis, a DE membrane can reach equilibrium after viscoelastic relaxation. The presence of viscoelasticity lowered the response speeds but increased the mean stretch of DE films. These models are expected to provide guidance for DE device design and application.