Wrinkling of a film/substrate bilayer with periodic material properties: An assessment of the Winkler foundation model

The Winkler foundation model is often used to analyze the wrinkling of a film/substrate bilayer under compression, and it can be rigorously justified when both the film and substrate are homogeneous and the film is much stiffer than the substrate. We assess the validity of this model when the substrate is still homogeneous but the film has periodic material properties in the direction parallel to the interface. More precisely, we assume that each unit cell is piecewise homogeneous, and each piece can be described by the Euler–Bernoulli beam theory. We provide analytical results for the critical compression when the substrate is viewed as a Winkler foundation with stiffness modeled either approximately (as in some previous studies) or exactly (using the Floquet theory). The analytical results are then compared with those from Abaqus simulations based on the three-dimensional nonlinear elasticity theory in order to assess the validity of the Euler–Bernoulli beam theory and the Winkler foundation model in the current context. •Buckling of a periodic film/substrate bilayer is analyzed using a beam model.•The response of the substrate is described analytically using the Floquet theory.•A semi-analytical bifurcation condition is derived using the PWE method.•A formula is given that determines whether a whole wave consists of one or two unit cells.•Validity of various assumptions is assessed by comparing with Abaqus simulations.