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When a voltage is applied between the internal and external surface of a dielectric elastomer spherical shell, positive charges appear on one surface and negative charges on the other. This gives rise to Coulomb forces between opposite charges, generating a pressure. Thus, the shell reduces in thickness and stretches in area, and a higher electric field is produced. This positive feedback may make the shell continually thin down, eventually causing electrical instability. In this paper we use the neo-Hookean model and the Arruda-Boyce model to analyze the electromechanical instability of the thick-walled shell respectively. The electric field in the shell is inhomogeneous and varies with the radius of the shell. The instability in spherical shells with different thicknesses and boundary conditions is discussed. When the elastomer obeys the Arruda-Boyce model, the stability is related to the parameter n. The spherical shell will appear with snap-through instability and pull-in instability for different values of the parameter n.

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