Large deformation of soft dielectric cylindrical tubes under external radial electric field

We study the nonlinear deformation of a soft dielectric tube subjected to an external electric field induced by two outer fixed electrodes. The tube follows an electro-elastic, ideal dielectric, neo-Hookean free energy and is longitudinally either constrained or free; in general, it deforms by shrinking and finding an equilibrium configuration closer to the inner electrode. The non-homogeneous system of governing equations is solved numerically with details given for each type of boundary conditions. The notion of contraction limit is introduced and emergence of electromechanical instability for both problems is noted with the relevant modes studied at some relevant points of the stretch–voltage actuation curve.