Global and local interactive buckling behavior of a stiff film/compliant substrate system

Wang, C. G., Y. P. Liu, and H. F. Tan. “Global and Local Interactive Buckling Behavior of a Stiff Film/Compliant Substrate System.” International Journal of Solids and Structures 102–103 (December 15, 2016): 176–85. https://doi.org/10.1016/j.ijsolstr.2016.10.006.

This paper elucidates the global and local interactive buckling behavior of a stiff film resting on a compliant substrate under uniaxial compression. The resulting governing non-linear equations (non-autonomous fourth-order ordinary differential nonlinear equations with integral conditions) are then solved by intro-ducing a continuation algorithm, which offers considerable advantages to detect multiple bifurcations and trace a complex post-buckling path. The critical conditions for local and global buckling and respective post-buckling equilibrium paths are carefully studied. Two different evolution mechanisms of buckling modes and processes from destabilization to restabilization (snap-back) are observed beyond the onset of the primary sinusoidal wrinkling mode in the post-buckling range. In addition, the shear modulus of an orthotropic substrate acts as a dominant role in the bifurcation portrait. Our results offer better understanding of the global and local buckling behaviors of such a bilayer system, and can open up new opportunities for the design and applications of novel nanoelectronics.

本文研究了附于柔性基底上刚性薄膜在非轴向压缩下的全局和局部屈曲行为。提出了非线性的控制方程，并利用延拓算法进行求解，这种算法的优势在于可以检测多分岔以及记录复杂的后屈曲路径。细致分析了局部和全局屈曲以及各自对应的后屈曲平衡路径的严格条件。后屈曲阶段中，在原有的三角褶皱模型下，研究了两种不同的力学屈曲演化模型，以及由扰动到在稳定的过程。另外，在分岔模型中，正交各向异性基底的剪切模量起主导作用。研究结果提供了一种对这类双层系统的全局和局部屈曲行为的更好解释，同时给新型纳米电子材料的设计和应用提供了的新的研究方向。