For structures consisting of a thin film bonded to a compliant substrate, wrinkling of the thin film is commonly observed as a result of mechanical instability. Although this surface undulation may be an undesirable feature, the development of new functional devices has begun to take advantage of wrinkled surfaces. The wrinkled structure also serves to improve mechanical resilience of flexible devices by suppressing crack formation upon stretching and bending. If the substrate has a reduced thickness, buckling of the entire structure may also occur. It is important to develop numerical design tools for predicting both wrinkle and buckle formations. In this paper we report a comprehensive finite element-based study utilizing embedded imperfections to directly simulate instabilities. The technique overcomes current computational challenges. The temporal evolution of the wrinkling features including wavelength and amplitude, as well as the critical strains to trigger the surface undulation and overall structural buckling, can all be predicted in a straightforward manner. The effects of model dimensions, substrate thickness, boundary condition, and composite film layers are systematically analyzed. In addition to the separate wrinkling and buckling instabilities developed under their respective geometric conditions, we illustrate that concurrent wrinkling and buckling can actually occur and be directly simulated. The correlation between specimen geometry and instability modes, as well as how the deformation increment size can influence the simulation result, are also discussed.

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.

Surface instability via wrinkle formation is a common feature in thin films attached to a compliant substrate. Wrinkled thin-film structures have been increasingly exploited to enhance device performance. In this study, a numerical technique utilizing embedded imperfections is employed for direct simulations of wrinkle formation, extending from a single-film structure to composite films involving two or more layers. The incorporation of material elements, bearing different elastic properties at the film-substrate interface, assists in triggering buckling instability when the compressive strain reaches a critical value. The wrinkle wavelength and amplitude obtained from the numerical modeling show excellent agreements with available theoretical solutions involving bi-layer composite films, over the entire span of volume ratios of the constituent layers. A valid range of imperfection distribution, resulting in uniform wrinkle formation, is identified. The current numerical approach is robust and easy to implement and yields great promises in generating reliable wrinkling patterns. It can be readily applied to cases where realistic features cannot be captured by theories, such as the generalized plane strain deformation, indirect compression, and multilayer composite films.

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