Direct numerical simulation of buckling instability of thin films on a compliant substrate

Abstract

Surface buckling (wrinkling) driven by mechanical instability is commonly observed in thin-film structures with a compliant substrate. The resulting undulation, while sometimes undesirable, has been increasingly exploited to enhance mechanical and/or functional performances of many thin film devices. In this study a practical finite element modeling approach is introduced to simulate wrinkle formation in thin films atop a compliant substrate. The proposed technique is robust and easy to implement, and it overcomes typical challenges in computationally modeling the buckling instability. Using a two-dimensional geometry under the plane strain or generalized plane strain conditions, with randomly distributed imperfections bearing different material properties at the film/substrate interface, we demonstrate the model’s capability in triggering surface instability during direct compression and out-of-plane tensile loading. With sufficient mesh refinement, the predicted wrinkling wavelength, amplitude, and critical strain to activate wrinkle formation are shown to be close to analytical solutions. The effect of imperfection distribution is systematically studied, and a valid range of imperfection spacing is identified. The present numerical approach can be applied to predicting buckling instability in the design and analysis of thin film/compliant substrate systems over a wide range of material and geometric conditions. Directions for future studies are also discussed.