Electrostrictive polymer plates as electro-elastic material surfaces: Modeling, analysis, and simulation

In this article we discuss modeling of electrostrictive polymer plates as electro-elastic material surfaces. A complete direct approach is developed without the need to involve the three-dimensional formulation. Ponderomotive forces and couples as well as constitutive coupling by means of electrostriction are accounted for. We propose a rational formulation for the augmented free energy of electro-elastic material surfaces incorporating electrostriction by a multiplicative decomposition of the surface stretch tensor and an additive decomposition of the surface curvature tensor into elastic and electrical parts. Numerical results computed within the framework of this complete direct approach are compared to results computed with a method that requires the numerical integration of the three-dimensional augmented free energy through the thickness of the plate and to alternative formulations reported in the literature.