On the Electro-Mechanical Stability of Elastomeric Coaxial Fibers

The stability of cylindrical coaxial fibers made from soft elastomeric materials is studied for electro-static loadings. The general configuration considered is a three-component axisymmetric fiber having a conducting core bonded to a dielectric annulus in turn bonded to an outer conducting annular sheath. A voltage difference between the conducting components is imposed. The stresses and actuated elongation in the perfectly concentric fiber are analyzed, and the critical voltage at which stability of the concentric configuration is lost is determined via solution of the non-axisymmetric bifurcation problem. The role of the geometry and moduli contrasts among the components is revealed, and the sub-class of two-component fibers is also analyzed. The idealized problem of a planar layer with conducting surfaces that is bonded to a stiff substrate on one surface and free on the other exposes the importance of short wavelength surface instability modes.