True method to analyze electromechanical stability of dielectric elastomers

A layer made of a dielectric elastomer can be voltage actuated to behave as actuator, but needs to avoid the electromechanical instability of excessive thin down accompanied with electric breakdown. We develop a true method to analyze the electromechanical stability of dielectric elastomers by adopting the positive definiteness of the true tangential modulus matrix, and demonstrate that the previous method is valid for the special case of zero prestress and can lead to sufficiently accurate results when the deformation is not too large. Our new method is applicable for arbitrary prestress cases including zero prestress, with predictions consistent with the available experimental measurements. Our theoretical results demonstrate the significant effects of prestress on critical voltage and critical actuation stretches.