A multi-scale modeling framework for instabilities of film/substrate systems

作者：Xu, Fan^*; Potier-Ferry, Michel

来源：Journal of the Mechanics and Physics of Solids, 2016, 86: 150-172.

DOI：10.1016/j.jmps.2015.10.003

• Wrinkling
• Post-buckling
• Multi-scale
• Fourier series
• Path-following technique
• Finite element method

Spatial pattern formation in stiff thin films on soft substrates is investigated from a multi-scale point of view based on a technique of slowly varying Fourier coefficients. A general macroscopic modeling framework is developed and then a simplified macroscopic model is derived. The model incorporates Asymptotic Numerical Method (ANM) as a robust path-following technique to trace the post-buckling evolution path and to predict secondary bifurcations. The proposed multi-scale finite element framework allows sinusoidal and square checkerboard patterns as well as their bifurcation portraits to be described from a quantitative standpoint. Moreover, it provides an efficient way to compute large-scale instability problems with a significant reduction of computational cost compared to full models.

• 出版日期2016-1
• 单位复旦大学