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

Abstract : 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.
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Fan Xu, Michel Potier-Ferry. A multi-scale modeling framework for instabilities of film/substrate systems. Journal of the Mechanics and Physics of Solids, Elsevier, 2016, 86, pp.150-172. ⟨10.1016/j.jmps.2015.10.003⟩. ⟨hal-01515198⟩



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