A new Fourier-related double scale analysis for wrinkling analysis of thin films on compliant substrates

In this paper, a new Fourier-related double scale approach is presented to study the wrinkling of thin films on compliant substrates. By using the method of Fourier series with slowly variable coefficients, the 1D microscopic model proposed by Yang et al. (2015) is transformed into a 1D macroscopic film/substrate model whose mesh size is independent on the wrinkling wavelength. Numerical tests prove that the new model improves computational efficiency significantly with accurate results, especially when dealing with wrinkling phenomena with vast wavenumbers. Besides, we propose a strategy to efficiently trace the wrinkling pattern corresponding to the lowest critical load by accounting for several harmonics of Fourier series in this new model. The established nonlinear system is solved by the Asymptotic Numerical Method (ANM), which has advantages of efficiency and reliability for stability analyses.