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Numerical aspects of pattern formation modeling of film-substrate systems

Abstract : Wrinkles of a stiff thin layer attached on a soft substrate have been widely observed in nature and these phenomena have raised considerable interests over the last decade. In terms of stability study, several theoretical and numerical works have been devoted to linear perturbation analysis and nonlinear buckling analysis. However, most previous works have been mainly constrained to determine the critical conditions of instability and the corresponding wrinkling patterns near the instability threshold. The post-buckling evolution and mode transition of surface wrinkles are only recently being pursued. Pattern formation modeling and post-buckling analysis deserve new numerical investigations, especially through finite element method that can provide the overall view and insight into the formation and evolution of wrinkle patterns in any condition. Therefore, we propose a whole numerical framework to study surface wrinkling of film-substrate systems: from 2D to 3D modeling, from classical to multi-scale perspective [1, 2, 3, 4, 5]. The main objective is to apply advanced numerical methods for multiple-bifurcation analyses of film-substrate systems , especially focusing on post-buckling evolution and surface mode transition. These advanced numerical approaches include path-following techniques, bifurcation indicators, bridging techniques, multi-scale analyses, etc. Through incorporating them with finite element method, it can predict the occurrence and whole evolution of wrinkling patterns in various boundary and loading conditions as well as complex geometries. The point of this framework lies in, but is not limited to, the application and improvement of the following numerical methods to the instability pattern formation of film-substrate systems: • Finite element method to be able to deal with all the geometries, behaviors and boundary conditions; • Path-following technique for nonlinear problem resolution and post-buckling tracing; • Bifurcation indicator to detect bifurcation points and the associated instability modes;
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Submitted on : Friday, January 19, 2018 - 3:17:01 AM
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Fan Xu, Michel Potier-Ferry. Numerical aspects of pattern formation modeling of film-substrate systems. 30th International Workshop on Statistical Modelling (IWSM 2015), Statistical Modelling Society, Jul 2015, Linz, Austria. pp.203-222, ⟨10.1016/j.ijnonlinmec.2014.12.006⟩. ⟨hal-01513497⟩



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