  We analyse here the problem of large deformation of dielectric elastomeric
membranes under coupled electromechanical loading. Extremely large deformations
(enclosed volume changes of 100 times and greater) of a toroidal membrane are
studied by the use of a variational formulation that accounts for the total
energy due to mechanical and electrical fields. A modified shooting method is
adopted to solve the resulting system of coupled and highly nonlinear ordinary
differential equations. We demonstrate the occurrence of limit point,
wrinkling, and symmetry-breaking buckling instabilities in the solution of this
problem. Onset of each of these "reversible" instabilities depends
significantly on the ratio of the mechanical load to the electric load, thereby
providing a control mechanism for state switching.
