基于不同板理论的嵌于柔性层中薄膜的皱曲分析

论文对于柔性层-薄膜-柔性层三层结构系统，基于经典板理论、一阶剪切变形理论和高阶剪切变形理论，分别推导给出薄膜皱曲的控制方程。对于两个柔性层，则把它们处理成具有有限厚度的平面应变弹性体。针对上下柔性层固支边界或自由边界条件，利用线性扰动动方法得到柔性层对薄膜的横向压力差，最终获得确定薄膜具有周期性正弦型皱曲的临界载荷方程。同时，对结构系统建立了有限元数值模型，通过模拟结果与三种板理论的结果进行了比较，验证了理论解的精确性和适用性。最后，进行了参数和极限情况分析，阐述了上下层边界条件、薄膜和柔性层的材料和几何参数对临界值的影响。

Wrinkling Analysis of Film Embedded in Compliant Layers Based on Different Plate Theories

In this paper, the governing equations for the wrinkling of a film sandwiched between two compliant layers are derived based on classical plate theory, first-order shear deformation theory and high-order shear deformation theory, respectively. The two compliant layers are treated as elastic bodies with finite thickness under plane strain condition along one inplane direction. The Airy stress function is then employed to solve the stress field in the two compliant layers subject to clamped and free boundary conditions. With the calculated pressure difference between the upper and lower layers, the governing equations are solved by the linear perturbation method and the critical load expression is thus obtained, which determines the periodic sinusoidal wrinkling of the film. As a validation, the finite element method is also employed to solve the wrinkling of the sandwich structure and the results are compared with our analytical solutions. Good agreement is achieved between the finite element and analytical results. It is shown that, albeit small differences exist, the results obtained based on the classical plate theory can provide sufficient accuracy compared with the shear deformation theories of different orders. Finally, the parameter analysis is conducted to illustrate the influences of boundary conditions, material properties and thicknesses of the film and the compliant layers on the critical loading. The limiting cases, where the thickness of the compliant layers is set to be zero or infinite, are also discussed. The results can serve as guidelines for the optimal designs of various substrate/film structures such as stretchable electronics.