School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 01238, USA.
Philos Trans A Math Phys Eng Sci. 2013 May 20;371(1993):20120422. doi: 10.1098/rsta.2012.0422. Print 2013 Jun 28.
The role of substrate nonlinearity in the stability of wrinkling of thin films bonded to compliant substrates is investigated within the initial post-bifurcation range when wrinkling first emerges. A fully nonlinear neo-Hookean bilayer composed of a thin film on a deep substrate is analysed for a wide range of the film-substrate stiffness ratio, from films that are very stiff compared with the substrate to those only slightly stiffer. Substrate pre-stretch prior to film attachment is shown to have a significant effect on the nonlinearity relevant to wrinkling. Two dimensionless parameters are identified that control the stability and mode shape evolution of the bilayer: one specifying arbitrary uniform substrate pre-stretch and the other a stretch-modified modulus ratio. For systems with film stiffness greater than about five times that of the substrate the wrinkling bifurcation is stable, whereas for systems with smaller relative film stiffness bifurcation can be unstable, especially if substrate pre-stretch is not tensile.
在薄膜初始出现褶皱的分岔后初始范围，研究了基底非线性性在结合于柔性基底的薄膜褶皱稳定性中的作用。分析了一个由薄膜和深基底组成的完全非线性neo-Hookean 双层结构，研究了薄膜-基底刚度比的广泛范围，从与基底相比非常硬的薄膜到仅略硬的薄膜。在薄膜附着之前的基底预拉伸显示对褶皱相关的非线性性有显著影响。确定了两个控制双层稳定性和模态形状演化的无量纲参数：一个指定任意均匀基底预拉伸，另一个指定拉伸修正的模量比。对于薄膜刚度大于基底刚度约五倍的系统，褶皱分岔是稳定的，而对于薄膜刚度相对较小的系统，分岔可能不稳定，特别是如果基底预拉伸不是拉伸的。
