Surface instabilities on the top surface of a soft elastomeric dielectric layer bonded on its bottom to a stiff substrate are investigated for two electro-static conditions: (I) a voltage difference imposed across the top and bottom surfaces of the layer which are both conducting, and (II) a voltage difference imposed across a rigid planar electrode above the layer and the conducting top surface of the layer. In the absence of surface energy, the critical voltage associated with the onset of instability of the planar state is shown to be a surface mode with any wavelength that is short compared to the layer thickness. With no layer pre-stretch and no surface energy, the uniform state in (I) has hydrostatic compression while that of (II) has hydrostatic tension, nevertheless the critical voltage is the same for both problems if the permittivity is the same for both systems. The role of equi-biaxial pre-stretch and surface energy is presented for both problems for neo-Hookean materials and for the Gent generalization. The thrust of the study is the investigation of the post-bifurcation behavior involving nonlinear interactions among the simultaneous surface modes associated with the critical voltage. The post-bifurcation response of Problem I is a crease-like mode with the top surface probing downward towards the lower surface. The opposite occurs for Problem II with the formation of a sharp ridge protruding towards the upper electrode. The bifurcation behavior is highly unstable leading to an extreme sensitivity to small imperfections. The study complements earlier work and highlights unresolved issues.

研究了在两种静电条件下，软弹性介电层的底部粘合到硬质基材上的表面不稳定性：（I）施加在均导电的层的上下表面之间的电压差； （II）在该层上方的刚性平面电极和该层的导电顶表面上施加的电压差。在没有表面能的情况下，与平面状态的不稳定性开始相关的临界电压显示为具有与层厚度相比任何短的波长的表面模式。在没有层预拉伸且没有表面能的情况下，（I）中的均匀状态具有静水压缩，而（II）中的均匀状态具有静水张力，但是，如果两个系统的介电常数相同，则这两个问题的临界电压都相同。提出了等双轴预拉伸和表面能对新霍克材料的问题和Gent概化的作用。研究的重点是研究分叉后的行为，该行为涉及与临界电压相关的同时表面模式之间的非线性相互作用。问题I的分叉后响应是一种折痕状模式，其顶面朝下表面探测。对于问题II，相反的情况是形成朝着上部电极突出的尖脊。分叉行为是高度不稳定的，从而导致对小缺陷的极端敏感性。该研究是对早期工作的补充，并突出了未解决的问题。