Dielectric elastomer(DE) is a kind of promising material bearing excellent activate properties including large deformations (up to 380%), high energy densities (up to 3.4 J/g), high efficiency, high responsive speed, good reliability and durability. Thus the DE actuator, sensors and energy harvester is widely used in the field of aeronautics and smart bionics. When an electric field is applied on the compliant electrodes of the dielectric elastomers, the polymer shrinks along the electric field and expands in the transverse plane. In consequence, the electric field becomes higher. This kind of positive feedback may cause the elastomer to thin down, resulting in an electromechanical stability. An analysis on the electromechanical stability of dielectric elastomer using arbitrary free-energy function with constant dielectric constant has been presented in Suo’s papers. In many research on the electromechanical stability analysis of DE actuator, DE’s dielectric constant is assumed to be a constant. This is only the truth if the dielectric elastomer undergoing limited deformation. Actually, a typical dielectric elastomer is a kind of crosslinked polymer. The structural symmetry of the macromolecular, the crosslinking degree, along with the tensile deformation can affect the dielectric permittivity enormously. For dielectric elastomers with higher crosslinking degree, or higher degree of molecular structural symmetry, its permittivity is relatively low. In addition, stretching can guide the macromolecule to be arranged in order, this can increase the intermolecular forces and reduce the activities of polar group, as a results, the dielectric constant will decrease. However, if the crosslinking degree is low and the deformation is well below the extension limit, the molecular units in the polymers can be polarized as freely as in a polymeric liquid. In this case the corresponding permittivity is unaffected by the deformation. Recent experimental research results also proved that the dielectric permittivity of dielectric elastomer changed while undergoing large deformation. According to Pelrine, the dielectric constant of the DE film is variable and it is a function of the area increase ratio which depends on stretch ratio. In this paper, approach for the electromechanical stability of a dielectric elastomer having variable dielectric constant is developed. The critical breakdown electric field is obtained. Simulation results proved that the prestretching process can enhance remarkably the electromechanical stability of dielectric elastomer. These results agree well with the experimental data and can be used as guidances in the design and fabrication of dielectric elastomer actuators.
Pre-stretch and frequency variation effect on the dielectric permittivity of a dielectric elastomer: an amended permittivity model
