Multi-scale techniques to analyze instabilities in sandwich structures

Two multi-scale techniques will be applied in this paper to analyze buckling and wrinkling phenomena in sandwich structures. The first one is a Fourier-related analysis, where the unknowns are slowly variable Fourier coefficients of the basic fields. As shown in [19], it permits to describe the coupling between global and local buckling without describing the details of the spatial oscillations. This leads to a macroscopical model similar to Landau-Ginzburg envelope equations, but the latter is not able to account for local-global coupling and it is accurate only near the bifurcation. Nevertheless it is sometimes difficult to associate boundary conditions with this Fourier-related approach because the assumption of a nearly periodic response of the structure is not always valid near the boundary. In [17] it has been proposed to apply the initial model near the boundary, the macroscopical model in the bulk and to relate them by the Arlequin method. In this paper, we associate the Fourier-related analysis and the Arlequin method to study the instability of sandwich structures.