Effect of an electric field on the deformation of incompressible rubbers: Bifurcation phenomena

Well above their glass transition temperatures, polymers behave like rubber materials. In the rubbery state, the elastic modulus is low enough to allow large deformations. Rubbery materials also deform under the application of an electric field. Rubbers can be referred as electromechanically active elastomers (EMAE) or lightweight materials that convert electrical into mechanical energy and vice versa [H. Xu, Z.-Y. Cheng, D. Olson, T. Mai, Q.M. Zang, G. Kavarnos, Ferroelectric and electromechanical properties of poly(vinylidene-fluoride-trifluoroethylene-chlrotrifluoroethylene) terpolymer, Appl. Phys. Lett. 78 (2001) 2360–2362]. Possible applications include biomedical prostheses, actuators, energy harvesters and robots [R.E. Pelrine, R.D. Kornbluh, J.P. Joseph, Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation, Sens. Actuators, A 64 (1998) 77–85; G. Kofod, W. Wirges, Energy minimization for self-organized structure formation and actuation, Appl. Phys. Lett., 90 (2007) 81916–81918; J.S. Plante, S. Dubowsky, Large-scale failure modes of dielectric elastomer actuators, Int. J. Solids Struct. 43 (2006) 7727–7751]. However, although the engineering applications of EMAE are quite recent, the theoretical foundations of continua under simultaneous electrical and mechanical force fields date back the 1960s. In this paper we present the basis of the nonlinear electroelasticity according to the formulation by Dorfmann and Ogden [A. Dorfmann, R.W. Ogden, Nonlinear Electroelastic Deformations, J. Elasticity 82 (2006) 99–127; A. Dorfmann, R.W. Ogden, Nonlinear electroelasticity, Acta Mechanica 174 (2005) 167–183] and discuss the influence of an electrical field on the bifurcation phenomena appearing in some cases of electromechanical deformation in rubber materials.