Finite Deformation Plate Theory for Wrinkling in Thin Electroelastic Sheets

Abstract This work derives an O(h3) electroelastic plate theory for thin dielectric sheets from a three-dimensional variational formulation, incorporating material nonlinearity and Maxwell stresses. The theory captures wrinkling behavior in the presence of mechanical traction and externally applied electric fields. The resulting two-dimensional formulation is specialized to an isotropic, incompressible material obeying reflection symmetry about the sheet mid-surface, and field-dependent explicit expressions are obtained for the elasticity tensor, electroelastic coupling coefficient, and permittivity. The strong-form equations are then derived from the two-dimensional variational formulation by setting the first variation of the potential to vanish. These equations are employed to analyze the wrinkling response of a stretched rectangular sheet subjected to a uniform electric field about a biased reference state. Approximate analytical solutions are obtained via linearization of the plate equations for small slopes, to understand the influence of electric field intensity and applied stretch on the onset and amplitude of wrinkling. The results show that increasing voltage raises the critical loads and wrinkle amplitude while reducing wrinkle count, thereby establishing voltage as a tunable parameter to control wrinkling.