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arXiv 2003.07245cond-mat.soft
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电荷控制软介质板的稳定性分析

Stability analysis of charge-controlled soft dielectric plates

Hannah Conroy Broderick, Michele Righi, Michel Destrade, Ray W. Ogden

摘要:

我们研究了软介质板的稳定性变形的机械预应力施加在其侧面和电场施加通过其厚度下的电荷控制的耦合效应。电场是通过在板的主面上喷射电荷来产生的:尽管在实践中这种驱动模式比电压驱动变形更难实现,但我们发现它在理论和模拟中更加稳定。首先,我们表明,机电不稳定性的基础上的海森准则与系统的自由能不会发生在所有的电荷驱动的电致伸缩的电位移是线性的电场。然后,我们表明,在电压控制下产生的板的表面上的小振幅皱纹的形成相关的几何不稳定性不会发生在电荷控制下。这与电压控制驱动完全相反,在电压控制驱动中,一旦达到特定的临界电压,就会发生Hessian不稳定性和Ergling不稳定性。对于机械预应力,可以在实践中实施的两种模式被使用:等双轴和单轴。我们确认的分析和数值稳定性结果的均匀变形模式与有限元模拟的真正的驱动,不均匀的领域可能会发展。当预应力是由静载重量引起时,我们发现在等轴向情况下完全一致,在单轴向情况下非常接近一致。在后一种情况下,模拟表明,小的非均匀效应发展附近的夹具,并最终出现压缩横向应力,导致故障的数值。

英文摘要:

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.

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