Saddle-like deformation in a dielectric elastomer actuator embedded with liquid-phase gallium-indium electrodes

We introduce a dielectric elastomer actuator (DEA) composed of liquid-phase Gallium-Indium (GaIn) alloy electrodes embedded between layers of poly(dimethylsiloxane) (PDMS) and examine its mechanics using a specialized elastic shell theory. Residual stresses in the dielectric and sealing layers of PDMS cause the DEA to deform into a saddle-like geometry (Gaussian curvature K < 0). Applying voltage U to the liquid metal electrodes induces electrostatic pressure (Maxwell stress) on the dielectric and relieves some of the residual stress. This reduces the longitudinal bending curvature and corresponding angle of deflection #. Treating the elastomer as an incompressible, isotropic, NeoHookean solid, we develop a theory based on the principle of minimum potential energy to predict the principal curvatures as a function of U. Based on this theory, we predict a dependency of # on U that is in strong agreement with experimental measurements performed on a GaIn-PDMS composite. By accurately modeling electromechanical coupling in a soft-matter DEA, this theory can inform improvements in design and fabrication.