Formation of surface wrinkles and creases in constrained dielectric elastomers subject to electromechanical loading

This paper investigates issues that have arisen in experimental and theoretical studies of the stability of a dielectric elastomeric layer bonded to a stiff substrate and subject to a voltage difference across the top and bottom conducting surfaces of the layer. The role of equi-biaxial pre-stretch of the layer prior to bonding to the substrate is a central factor in the investigation. The focus is the competition between wrinkling and creasing and how this competition is affected by pre-stretch. A finite element model of the system is employed to generate wrinkling bifurcation and advanced post-bifurcation solutions in the form of localized modes, either crease-like or groove-like depending on the pre-stretch. The constitutive model includes elastic compressibility, but the formulation produces accurate solutions for nearly incompressible materials which coincide with the neo-Hookean solid in the incompressible limit. The numerical simulations reveal that localized crease solutions exist at voltages below the critical voltage for wrinkling bifurcation for equi-biaxial pre- stretches below about 2.4. In this range, the wrinkling bifurcation is highly unstable, creasing rather than wrinkling can be expected, and a discontinuous transition is predicted with a finite energy barrier that may be overcome due to the presence of surface defects. With an equi-biaxial pre-stretch greater than 2.4, a continuous transition is predicted with no energy barrier, forming a localized groove due to nonlinear interactions among the unstable wrinkling modes.