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.

Surface Instability of Composite Thin Films on Compliant Substrates: Direct Simulation Approach

“…For random imperfection distributions with the maximum or minimum S imp beyond the specified range, the wrinkle pattern will deviate from the theoretical form and can become non-uniform and complex, with the actual configuration dictated by the placement of imperfections. The present results, based on higher-order finite elements, are generally consistent with those obtained previously using linear elements (Nikravesh et al, 2019), with the upper limit of the S imp /λ s ratio remaining at 55 and the lower limit being 10 instead of 6.…”

“…In our previous analysis using four-noded linear elements, mesh convergence can be reached but the converged solution deviated from the theoretical value slightly (Nikravesh et al, 2019). In the present case of eight-noded quadrilateral elements, an excellent agreement between numerical and theoretical solutions is obtained.…”

“…The pre-existing material defects [referred to as the embedded imperfections (Nikravesh et al, 2019)] are incorporated into the numerical model as shown in Figure 2. The defects are regular finite elements in the substrate immediately below the film/substrate interface.…”

“…In this study, all thin film and substrate materials are assumed to follow linear elasticity. It was built upon our previous development (Nikravesh et al, 2019) but now involves higher-order finite elements, more realistic model layouts with a composite film stack, and a systematic analysis on the effect of imperfection properties and distribution. The assumption of linear elasticity for the entire film-substrate system may not be realistic from the physical standpoint (Hutchinson, 2013).…”

Instabilities of Thin Films on a Compliant Substrate: Direct Numerical Simulations from Surface Wrinkling to Global Buckling

“…In this approach, termed "embedded imperfections," perturbed elastic properties are assigned to one or more regular elements at the interface of the film-substrate structure, for the purpose of triggering the formation of wrinkles without the need of any multi-step process. This work is originated from our recent development 36,37 , but is now expanded into a comprehensive study of the effects of model dimensions and boundary condition, using only one embedded imperfection, to fully assess the modeling capability. Most importantly, we illustrate that the formation of surface wrinkles and overall structural buckles can both be predicted from a single numerical implementation, and that concurrent wrinkling and buckling can actually occur and be directly simulated.…”