超弹性薄膜与可压缩基底双层结构表面失稳分析

当上层超弹性硬质薄膜和下层可膨胀基底构成的双层结构受压时,薄膜的自由表面可通过形成褶皱降低系统能量.研究表明,上下两层的模量比不同时,上层弹性硬质薄膜将表现出不同的表面失稳模式.本文提出了一种新颖的方法可有效抑制双层软材料的表面失稳,即改变基底材料的泊松比,这种方法同时适用于不具有应变硬化的软材料.首先基于Neo-Hookean模型发展了小变形条件下双层结构表面失稳的理论模型,通过半解析的方法得到了表面失稳的临界应变;然后通过有限元计算与模拟,进一步验证了负泊松比基底可延缓表面失稳.结果表明:(1)当双层结构基底泊松比为正且趋于0.5(不可压缩)时,双层结构在较小的压缩应变下出现表面失稳;(2)当基底的泊松比为负且趋于-1时,可被压缩至46%而不出现表面失稳,即可膨胀基底能有效抑制薄膜的表面失稳.本文发展的方法及主要结果可为延展性电子器件的设计提供指导.

STUDY OF SURFACE INSTABILITY ABOUT HYPERELASTIC FILMS ON AUXETIC SUBSTRATES UNDER COMPRESSION

When a bilayer structure consisting of a thin stiff film and a thick compliant substrate subjected to compressive deformation, its free surface would be wrinkled to minimize the energy of the system, and different wrinkle patterns may appear for different ratios of the modulus of the film to that of the substrate. In this article, we developed a novel approach to suppress the surface instability of such bilayer materials under severe compression by adjusting the Poisson's ratio of the substrates. This approach is also applicable to the bilayer consisting of a soft substrate and a film with elastic modulus similar to that of the substrate. We developed an analytical approach for surface instability of the bilayer based on NeoHookean model in the case of small deformation, and obtained the critical strain of the bilayer with a semi-analytical method. Then, we used finite element approach (FEA) to illustrate that the instability of the thin film can be delayed if the substrate has a negative Poisson's ratio. We showed that:(1) when the Poisson's ratio of the substrate is positive and close to 0.5 (nearly incompressible), the surface instability may occur to the bilayer system at a very small compressive strain; (2) if the Poisson's ratio of the substrate is negative and close to -1, the film can be compressed up to 46% without occurence surface instability. The approach developed and the results obtained in this article imply a great potential of auxetic materials used to enhance the compressibility of thin films, which can provide guidance for the design of laminate ductile electronic devices.