We analyse here the problem of large deformation of dielectric elastomeric membranes under coupled electromechanical loading. Extremely large deformations (enclosed volume changes of 100 times and greater) of a toroidal membrane are studied by the use of a variational formulation that accounts for the total energy due to mechanical and electrical fields. A modified shooting method is adopted to solve the resulting system of coupled and highly nonlinear ordinary differential equations. We demonstrate the occurrence of limit point, wrinkling, and symmetry-breaking buckling instabilities in the solution of this problem. Onset of each of these “reversible” instabilities depends significantly on the ratio of the mechanical load to the electric load, thereby providing a control mechanism for state switching.

在这里，我们分析了在耦合机电载荷下介电弹性膜的大变形问题。通过使用变分公式研究了环形膜的极大变形（封闭体积变化为100倍或更大），该变形公式考虑了由于机械和电场而产生的总能量。采用改进的射击方法来求解耦合的和高度非线性的常微分方程组。在此问题的解决方案中，我们证明了极限点，起皱和对称破坏屈曲不稳定性的发生。这些“可逆”不稳定性中的每个不稳定性的发生在很大程度上取决于机械负载与电负载的比率，从而提供了用于状态切换的控制机制。