Wrinkling in bilayer systems consisting of a thin film on a softer substrate has been extensively studied in literature using various experimental setups as well as analytical and numerical methods. In this work we present a finite element model to simulate a tri-layer system with thin elastic film on top of a viscoelastic (VE) layer which in turn rests on a substrate. The loading conditions imposed on this tri-layer system are motivated by the experiments involving induction of instabilities in the thin film via viscous stresses. Effects of strain rate and VE layer thickness on the tri-layer system bifurcations are first studied for what we call as the moderate substrate pre-stretch scenario with compressive strains around 7%. With only wrinkling of the film observed for moderate pre-stretch scenario, we look into variation of critical wrinkling strain, wrinkle wavelength and wrinkle amplitude w.r.t compressive strain rate and viscoelastic layer thickness, with reasonable explanations provided for these variations based on the analytical results available for bilayer systems in the literature. Further we look into the role of substrate pre-stretch by varying it up to 2.0 i.e 100% nominal strain and applying nominal compressive strain upto 40%. Two different secondary bifurcation modes namely, ridge formation and period doubling are observed for different combinations of parameters. These two bifurcations are studied in detail by defining geometric quantities and by looking into their variation with compressive strain. Bifurcation curves obtained for these secondary bifurcations and tertiary bifurcations following them are provided to gain insight into the deformation of the film. These observations are compared to the secondary bifurcations reported for the bilayer systems in the literature in order to explain effect of different parameters on the tri-layer system. We present bifurcation diagrams to better understand role of compressive strain rate, VE layer thickness and substrate pre-stretch in producing different bifurcations in the film. Cutoff VE layer thickness, substrate pre-stretch and compressive strain rates are found for the two bifurcations based on bifurcation diagrams. General trend suggests that higher substrate pre-stretch and lower VE layer thickness combined with lower compressive strain rates leads to evolution of wrinkles to ridges, while higher substrate pre-stretch and higher VE layer thickness combines with higher compressive strain rates leads to wrinkling followed by period doubling. Evolution of bifurcations is observed beyond compression by holding the tri-layer system at a specific compressive strain, which reveals that ridge formation is irreversible and turns out to be the final equilibrium configuration. Films might continue to evolve new ridges or grow existing ones however it does not evolve back into sinusoidal wrinkling. Contrary to ridge formation we observe the period doubling to evolve back into wrinkling on holding the tri-layer system.


Rate-Dependent Wrinkling and Ridge Formation of an Elastic Thin Film on a Viscoelastic Layer

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Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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