A multi-scale modeling framework for instabilities of film/substrate systems. (January 2016)

• Record Type: Journal Article
• Authors: Xu, Fan; Potier-Ferry, Michel
• Is Part Of: Journal of the mechanics and physics of solids. Volume 86(2016:Jan.)
• Page Start: 150
• Page End: 172
• Publication Date: 2016-01
• Subjects: Wrinkling -- Post-buckling -- Multi-scale -- Fourier series -- Path-following technique -- Finite element method; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2015.10.003
• Languages: English
• ISSNs: 0022-5096

Abstract

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. Abstract : Graphical abstract: Abstract : Highlights: A multi-scale modeling framework for film/substrate systems is first developed. The reduced-order model provides an efficient way to simulate large-scale instability problems with numerous undulations. The proposed macroscopic model can significantly reduce DOF and CPU time by 90% and 98%, respectively. Bifurcation portrait and post-buckling evolution are investigated from a quantitative standpoint. A new bifurcation scenario with alternating packets of large and small undulations has been found numerically.