A modified self-consistent computational model for an electrostrictive graft elastomer

An electrostrictive graft elastomer, as recently developed by NASA, is a type of electro-active polymer. In this paper, a 2D computational model with a self-consistent boundary is developed. Firstly, three-dimensional deformations, induced by both bending angle and dihedral torsional angle changes, are projected onto a two-dimensional plane. Using both theoretical and numerical analyses, the projected 2D equilibrium bending angle is shown to have the same value as the 3D equilibrium bending angle. The 2D equivalent bending stiffness is derived using a series model based upon the fact that both bending and dihedral torsion produce a configurational change. Equivalent stiffness is justified by polymer chain end-to-end distance characteristics. Secondly, a self-consistent scheme is developed to eliminate the boundary effect. Eight images of the unit cell are created peripherally, with the original unit cell in the center. Thus the boundary can only affect the rotation of the eight images, not the central unit cell. A computational model is employed to determine the electromechanical properties of the electrostrictive graft elastomer. Relations between electric field induced strain and electric field strength are calculated. The effect of molecular scale factors, such as free volume fraction, graft weight percentage and graft orientation, are also discussed.