Time-dependent electromechanical phase transition and bulging propagation in a viscoelastic dielectric elastomer tube

When a dielectric elastomer (DE) tube is subjected to mechanical pressure and electrical voltage, electromechanical (EM) phase transition may happen. In recent experiment, it has been shown that the EM phase transition process can be highly time-dependent: the bulged section can propagate along the tube under fixed voltage. In this article, we adopt a nonlinear viscoelastic model for the DE material to investigate the time-dependent EM phase transition of a DE tube under fixed amount of air and fixed voltage. Using the model of viscoelasticity, we demonstrate that a DE tube may experience a transition from a homogeneous shape to an inhomogeneous shape with bulged and unbulged sections coexisting in the tube under electrical loading, then the bulged section can gradually propagate at the expense of the unbulged section under the fixed initial coexistent voltage, which well captures the experimental observations. We have further shown that the EM phase transition condition and propagation of the bulged section of the DE tube also depend on the volume of the air chamber connected to the tube and the ramping rate of the applied voltage. (paper)