Viscoelasticity plays an important role in the instability and performance of soft transducers. Wrinkling, an instability phenomenon commonly observed on soft materials, has been studied extensively. In this paper, we theoretically investigate the viscoelastic effect on the wrinkle formation of a dielectric-elastomer (DE) balloon subjected to combined electromechanical loads. Results show that the critical voltage for the wrinkle formation of a DE balloon gradually decreases as the material undergoes viscoelastic relaxation and finally reaches a stable value. The wrinkles in the lateral direction always have critical voltages equal to or lower than those in the longitudinal direction. What is more, the nucleation sites of wrinkles always move from the apex to the rim of DE balloon with the viscoelastic relaxation of DE. It takes less time for the DE balloon with higher pressure to reach the stable state. Higher pressure also leads to the stable wrinkle nucleation site moving closer to the fixed edge of the DE balloon. An experiment is conducted to illustrate the effect of viscoelasticity on the wrinkle propagation of a DE balloon, and the results agree well with the model predictions. This study provides a guide in the wrinkling control of a DE balloon and may help the future design of DE transducers.

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