单轴拉伸和电场作用下介电膜的非均匀变薄
Inhomogeneous thinning of dielectric membranes under uniaxial tension and electric fields
- Dongguan University of Technology（东莞理工学院）
- Keele University（基尔大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究单轴拉伸和电场作用下的介电膜，用变分渐近法推导简化模型，经线性和弱非线性分析，揭示黑塞稳定性准则与零波数分岔的联系及非均匀变薄现象，为分析介电膜不稳定性提供框架。
AI中文摘要：
介电弹性体因机械变形与电场耦合呈现丰富机电不稳定性。常用的赵和锁（2007年）提出的黑塞稳定性准则可确定均匀变形失稳起始，但无法确定失稳后变形发展。本文研究单轴拉伸和电场作用下的介电膜，推导简化模型，分析表明黑塞稳定性准则等同于零波数分岔条件，零波数分岔导致局部颈缩，即膜的非均匀变薄。
英文摘要：
Dielectric elastomers exhibit rich electromechanical instabilities arising from the coupling between mechanical deformations and electric fields. A widely used approach for analyzing instabilities in dielectric elastomers is the Hessian stability criterion proposed by Zhao and Suo (2007), which identifies the onset of instability of a homogeneous deformation but does not determine how the deformation develops beyond the instability threshold. To address this problem, we investigate dielectric membranes subjected to uniaxial tension and an electric field. Starting from a three-dimensional nonlinear electroelastic formulation, we derive asymptotically consistent reduced models, including a membrane model and a plate model, using the variational-asymptotic method. A linear bifurcation analysis first shows that the Hessian stability criterion is equivalent to a zero-wavenumber bifurcation condition, thereby establishing a direct connection between energy-based stability analysis and bifurcation theory. A subsequent weakly nonlinear analysis demonstrates that the zero-wavenumber bifurcation gives rise to localized necking, manifested as inhomogeneous thinning of the membrane. The weakly nonlinear predictions are further validated by numerical simulations. Furthermore, for the plane-stress configuration considered here, the membrane model accurately captures both the onset of instability and the associated localization behavior, while bending effects remain small. These results identify the deformation associated with the Hessian instability and provide a framework for understanding electromechanical instabilities in dielectric membranes.
