Anomalous bulging behaviors of a dielectric elastomer balloon under internal pressure and electric actuation

When a clamped membrane of elastomer is subject to a lateral pressure, it bulges into a hemispherical balloon. However, for a clamped membrane of dielectric elastomer (DE) under a lateral pressure as well as a voltage through the thickness, it may bulge into a regular hemispherical balloon or an irregular shape. This work focuses on the anomalous bulging behaviors (i.e. the irregular bulging shape) of a DE balloon under electromechanical coupling loading. The full set of the equilibrium configurations of the DE balloon is theoretically derived within the framework of thermodynamics, based on which we find that with the increase of the applied voltage, the pressure-volume relationship changes from the single-N shape for the case of purely mechanical loading to a double-N shape, where five or more equilibrium configurations exist including both regular and irregular bulging shapes. Through stability analysis we find that the anomalous bulging is a common behavior for the DE balloon under electromechanical coupling loading and all types of irregular bulging shapes can be achieved by following carefully designed loading paths. Besides, the irregular bulging region usually has the largest local strain which may initiate the failure of the DE membrane. Guided by the theoretical analysis, we conducted experiments on a DE balloon under the internal pressure and electrical actuation. Typical irregular shapes were successfully observed and the entire evolution of the shape changing agrees very well with theoretical predictions. These findings enrich understandings of highly nonlinear behaviors for soft materials under electromechanical coupling loading.