  A dielectric elastomer whose edges are held fixed will buckle, given
sufficient applied voltage, resulting in a nontrivial out-of-plane deformation.
We study this situation numerically using a nonlinear elastic model which
decouples two of the principal electrostatic stresses acting on an elastomer:
normal pressure due to the mutual attraction of oppositely charged electrodes
and tangential shear ("fringing") due to repulsion of like charges at the
electrode edges. These enter via physically simplified boundary conditions that
are applied in a fixed reference domain using a nondimensional approach. The
method is valid for small to moderate strains and is straightforward to
implement in a generic nonlinear elasticity code. We validate the model by
directly comparing the simulated equilibrium shapes with the experiment. For
circular electrodes which buckle axisymetrically, the shape of the deflection
profile is captured. Annular electrodes of different widths produce azimuthal
ripples with wavelengths that match our simulations. In this case, it is
essential to compute multiple equilibria because the first model solution
obtained by the nonlinear solver (Newton's method) is often not the
energetically favored state. We address this using a numerical technique known
as "deflation". Finally, we observe the large number of different solutions
that may be obtained for the case of a long rectangular strip.
