Instabilities in thin films on hyperelastic substrates by 3D finite elements

Abstract

Spatial pattern formation in thin films on rubberlike compliant substrates is investigated based on a fully nonlinear 3D finite element model, associating nonlinear shell formulation for the film and finite strain hyperelasticity for the substrate. The model incorporates Asymptotic Numerical Method (ANM) as a robust path-following technique to predict a sequence of secondary bifurcations on their post-buckling evolution path. Automatic Differentiation (AD) is employed to improve the ease of the ANM implementation through an operator overloading, which allows one to introduce various potential energy functions of hyperelasticity in quite a simple way. Typical post-buckling patterns include sinusoidal and checkerboard, with possible spatial modulations, localizations and boundary effects. The proposed finite element procedure allows accurately describing these bifurcation portraits by taking into account various finite strain hyperelastic laws from the quantitative standpoint. The occurrence and evolution of 3D instability modes including fold-like patterns will be highlighted. The need of finite strain modeling is also discussed according to the stiffness ratio of Young’s modulus.