Electro-cavitation and electro-assisted snap-through instability of a hollow sphere of dielectric elastomers

Abstract

Soft dielectric elastomers can be easily deformed when they are subjected to electromechanical loadings. The process of large deformation accompanies highly nonlinear electromechanical couplings and various failure modes that inevitably inhibit the application of dielectric elastomer in advanced soft machines. The existence of material imperfection like a cavity would be a potential unsafe factor for using dielectric elastomers. Under certain critical loading conditions, the cavity within the material would grow rapidly with a significant change in size (known as cavitation), resulting in the rupture of elastomers. In this paper, we study the electromechanical behaviors of a soft sphere with a concentric hole. We give the total free energy of the electrostatic system and formulate a boundary-value problem. We solve the problem analytically by using neo-Hookean dielectrics. For a small cavity in a soft sphere, we demonstrate that the cavitation occurs at first, and then the snap-through instability is followed. So far, the co-existence of cavitation and snap-through instability is seldom reported in dielectric elastomers. Increasing the cavity size makes the hollow sphere become a spherical shell in which only the electro-assisted snap-through instability exists. This paper is desirable to further the understanding of electromechanical behaviors and instabilities of imperfect dielectric elastomers.