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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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https://hal.univ-lorraine.fr/hal-01512998
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Submitted on : Thursday, April 27, 2017 - 9:11:45 AM
Last modification on : Friday, February 26, 2021 - 2:48:02 PM

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  • HAL Id : hal-01512998, version 1

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Fan Xu, Michel Potier-Ferry. A multi-scale modeling framework for instabilities of film/substrate systems. 3rd ECCOMAS Young Investigators Conference (YIC) & 6th GACM Colloquium on Computational Mechanics, Jul 2015, Aix-la-Chapelle, Germany. pp.150-172. ⟨hal-01512998⟩

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