On second–order determination of the constitutive constants of an hyperelastic dielectric

Electro-active polymers, particularly dielectric elastomers, for their rapid and reversible electromechanical response, exhibit great potential for the next-generation of soft actuators. In this paper, we describe a methodology for determining the second-order constitutive constants of a homogeneous, isotropic, and hyperelastic dielectric material that can be applied to compressible and incompressible dielectrics. A Lagrangian framework is employed to address the quasi-electroelastostatic problem, with a detailed comparison of free energy formulations proposed in literature for compressible and incompressible hyperelastic dielectrics. An analytical solution is derived for a controllable state in a simple geometry, and a new experimental setup is introduced to take into account boundary layer effects produced by the electric field. This setup could be used as a basic device to design experimental procedures for determining the material’s constitutive constants.