Soft dielectric elastomer tubes in an electric field

Soft dielectric elastomers with high relative permittivity, very low modulus and high electric breakdown strength have emerged as promising materials for various applications as sensors, actuators and in energy harvesting and soft robotics. We study the intricate deformation behaviour of a soft dielectric elastomer tube of finite length and closed ends, that carries a dead load, is internally pressurised by an injected fluid and has a high electric potential applied across its walls. As for soft tubes in the absence of a potential, this electro-hyperelastic problem involving very large deformations, exhibits a multitude of possibilities, including homogeneous deformation, inhomogeneous bifurcation, snap-through instabilities and post bifurcation behaviour in the form of propagation of axisymmetric bulges. We develop a coupled Finite Element procedure for the situation where the domains of the mechanical and electrostatic problems coincide. The procedure can handle volume flow rate controlled electro-elastic problems. We use it to study the many aspects of the deformation behaviour and limitations placed by competing failure mechanisms on practical utilisation of the large areal strains and axial actuations that can be produced. If electrical breakdown can be avoided by ingenious design of loading sequences, the large volume increase in the tube due to the triggering of instabilities can be harnessed and has far-reaching technological implications