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We investigate the finite bending and the associated bending instability ofan incompressible dielectric slab subject to a combination of applied voltageand axial compression, using nonlinear electro-elasticity theory and itsincremental version. We first study the static finite bending deformation ofthe slab. We then derive the three-dimensional equations for the onset ofsmall-amplitude wrinkles superimposed upon the finite bending. We use thesurface impedance matrix method to build a robust numerical procedure forsolving the resulting dispersion equations and determining the wrinkled shapeof the slab at the onset of buckling. Our analysis is valid for dielectricsmodeled by a general free energy function. We then present illustrativenumerical calculations for ideal neo-Hookean dielectrics. In that case, weprovide an explicit treatment of the boundary value problem of the finitebending and derive closed-form expressions for the stresses and electric fieldin the body. For the incremental deformations, we validate our analysis byrecovering existing results in more specialized contexts. We show that theapplied voltage has a destabilizing effect on the bending instability of theslab, while the effect of the axial load is more complex: when the voltage isapplied, changing the axial loading will influence the true electric field inthe body, and induce competitive effects between the circumferentialinstability due to the voltage and the axial instability due to the axialcompression. We even find circumstances where both instabilities cohabit tocreate two-dimensional patterns on the inner face of the bent sector.

Finite bending and pattern evolution of the associated instability for a dielectric elastomer slab