We examine the stability of a soft dielectric plate deformed by the coupled effects of a mechanical pre-stress applied on its lateral faces and an electric field applied through its thickness under charge control. The electric field is created by spraying charges on the major faces of the plate: although in practice this mode of actuation is harder to achieve than a voltage-driven deformation, here we find that it turns out to be much more stable in theory and in simulations.

First we show that the electromechanical instability based on the Hessian criterion associated with the free energy of the system does not occur at all for charge-driven dielectrics for which the electric displacement is linear in the electric field. Then we show that the geometric instability associated with the formation of small-amplitude wrinkles on the faces of the plate that arises under voltage control does not occur either under charge control. This is in complete contrast to voltage-control actuation, where Hessian and wrinkling instabilities can occur once certain critical voltages are reached.

For the mechanical pre-stresses, two modes that can be implemented in practice are used: equi-biaxial and uni-axial. We confirm the analytical and numerical stability results of homogeneous deformation modes with Finite Element simulations of real actuations, where inhomogeneous fields may develop. We find complete agreement in the equi-biaxial case, and very close agreement in the uni-axial case, when the pre-stress is due to a dead-load weight. In the latter case, the simulations show that small inhomogeneous effects develop near the clamps, and eventually a compressive lateral stress emerges, leading to a breakdown of the numerics.

我们研究了软介电板的稳定性，该软介电板由于在电荷控制下施加于其侧面的机械预应力和通过其厚度施加的电场的耦合效应而变形。电场是通过在板上的主要表面上喷射电荷而产生的：尽管在实践中，这种驱动模式比电压驱动的变形更难实现，但在这里我们发现它在理论上和稳定性上要稳定得多。模拟。

首先，我们表明，对于电荷驱动的电介质，基于电场的线性位移，基于Hessian准则与系统自由能相关的机电不稳定性根本不会发生。然后我们表明，在电压控制下，与在板面上形成小振幅皱纹有关的几何不稳定性在电荷控制下均不会发生。这与电压控制致动完全相反，电压控制致动一旦达到特定的临界电压，就会发生粗麻布和起皱不稳定性。

对于机械预应力，可以在实践中使用两种模式：等双轴和单轴。我们用实际驱动的有限元模拟来确认均质变形模式的解析和数值稳定性结果，其中可能会出现非均匀场。当预应力归因于静载重量时，我们发现在等双轴情况下完全一致，而在单轴情况下非常接近一致。在后一种情况下，仿真表明，在夹具附近会产生小的不均匀影响，最终会产生压缩侧向应力，从而导致数值崩溃。