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

Abstract

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.

Direct numerical simulations of three-dimensional surface instability patterns in thin film-compliant substrate structures

“…The simulation domain is defined in such a way to represent a unit cell of a periodic structure. This periodic-cell approach is built upon our earlier 1D wrinkling study 37 and is now extended to full 3D simulations. One embedded imperfection is placed in the substrate adjacent to the film-substrate interface, as shown in Fig.…”

“…Surface wrinkling can be captured without the need of any tedious or multi-step numerical treatments. This approach was first developed for 1D sinusoidal wrinkling simulations 35 – 37 , and was recently extended to simple forms of 3D surface wrinkles 38 . The current paper presents our first comprehensive study on surface patterns encompassing the full range of in-plane compressive loading.…”

Flower Inspiration: Broad‐Angle Structural Color through Tunable Hierarchical Wrinkles in Thin Film Multilayers

“…Similar surface morphologies were investigated on a buckled free‐standing thin film bilayer. [ 39,49 ] Therefore, under very high strains, the loss of the majority of small wrinkles (except the very limited amount in the valleys) effectively reduces the intensity of the optical diffraction.…”

Nonlocal wrinkling instabilities in bilayered systems using peridynamics

“…The analytically predicted trends for the influence of the main controlling parameters, e.g. the stiffness ratio of the film and the substrate as well as the film thickness, have been confirmed in experimental studies [6,20,[32][33][34][35][36] as well as numerical simulations [20,25,28,29,[37][38][39][40][41][42][43][44]. To date, the numerical method of choice is the finite element method (FEM).…”

“…To date, the numerical method of choice is the finite element method (FEM). To trigger the instabilities, it is customary to introduce small perturbations to the system through the mesh, boundary conditions or material properties [39]. In order to eliminate the need for subjective perturbations that might affect the resulting wrinkling pattern, in [16,37] the FEM simulation is enhanced by an eigenvalue analysis.…”