The static actuation of dielectric elastomer actuators: how does pre-stretch improve actuation?

It has previously been shown that providing dielectric elastomer actuators with a level of pre-stretch can improve properties such as breakdown strength, actuation strain and efficiency. The actuation in such actuators depends on an interplay between the highly nonlinear hyperelastic stress-strain behaviour with the electrostatic Maxwell's stress; however, the direct effects of pre-stretch on the electromechanical coupling have still not been investigated in detail. We compare several experimental results found in the literature on the hyperelastic parameters of the Ogden model for the commonly used material VHB 4910, and introduce a more detailed and thus more accurate fit to a previous uniaxial stress-strain experiment. Electrostatic actuation models for a pure shear cuboid dielectric elastomer actuator with pre-stretch are introduced, for both intensive and extensive variables. For both intensive and extensive variables the constant strain (blocked stress or force) as well as the actuation strain is presented. It is shown how in the particular case of isotropic amorphous elastomers the pre-stretch does not affect the electromechanical coupling directly, and that the enhancement in actuation strain due to pre-stretch occurs through the alteration of the geometrical dimensions of the actuator. Also, the presence of the optimum load is explained as being due to the plateau region in the force-stretch curve, and it is shown that pre-stretch is not able to affect its position. Finally, it is shown how the simplified Ogden fit leads to entirely different conclusions for actuation strain in terms of extensive variables as does the detailed fit, emphasizing the importance of employing accurate hyperelastic models for the stress-stretch behaviour of the elastomer.