Bloch wave approach for the analysis of sequential bifurcations in bilayer structures

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A wide variety of surface morphologies can be formed by compressing a bilayer comprising a thin film bonded to a compliant substrate. In particular, as the applied strain is increased, secondary instabilities are triggered and the initial sinusoidal wrinkles evolve into new complex patterns. Here, we propose a robust numerical analysis based on Floquet–Bloch boundary conditions to detect the primary and secondary instabilities triggered upon compression. Because the proposed method is based on unit cell simulations, it is computationally very efficient. Moreover, it accurately predicts not only the critical strains, but also the corresponding critical modes and their wavelengths, enabling us to follow the evolution of the surface morphology as the applied strain is progressively increased.