Voltage-controlled instability transitions and competitions in a finitely deformed dielectric elastomer tube

This work compares the transition and competitive mechanism between three types of instabilities of an incompressible dielectric tube: wrinkling, pull-in instability and electric breakdown. We also see how to select one type of instability mode on demand. First, we investigate the finite response and the wrinkling of a tube subject to a combination of applied radial voltage, torsion and axial force (or stretch). We use the surface impedance matrix method to determine the wrinkling threshold, and obtain the corresponding two-dimensional pattern shape of wrinkled surface. Second, we look at illustrative numerical calculations for ideal Mooney-Rivlin dielectrics and study the effects of actuation methods, electric voltage, torsion and geometrical parameters on the three types of instabilities. Results show that the deformation of the solid will influence the true electric field in the solid, and induce competitive effects between the applied voltage and the mechanical loading. We find that in addition to the expected contractile buckling, buckling may also occur in extension in an electrically actuated dielectric tube, a departure from the purely elastic wrinkling. Moreover, the electro-elastic behavior of the DE elastomer can be enhanced by introducing torsion. We also find that large stable actuation can be achieved and that the wrinkling pattern can be selected on demand in the tube by finely tuning the actuation, voltage, torsion and geometry, without encountering material failure.