Keywords: buckling, sandwich, interaction, localization, plasticity.

Sandwich structures exhibit a high specific flexural stiffness but also a complex mechanical behaviour. This last particularity is emphasized when in­plane compression is considered. Indeed, geometrical instabilities can appear at the global scale of the structure or at the local scale of the components (core and skins). The aim of this work is to model analytically and numerically the global and local buckling of a sandwich beam, but also the possible interactions between instabilities at these two scales.

First, an analytical beam model based on a high order theory is established, which permits to isolate simple critical loads (Equations (83.1)) associated with global buckling of the beam ( ) and symmetrical and antisymmetrical wrinkling of the skins ( ) and ( ). The dimensionless parameters introduced (, , , ) stand respectively for the thicknesses ratio (skin thickness / core thickness), the moduli ratio (skin Young's modulus / core Young's modulus), the slenderness of the beam (length / ( core thickness)) and the core moduli ratio (Young's modulus / shear modulus). Coefficient B is positive and depends on geometrical and material parameters.

Thanks to the analysis of the sign of the difference between these three critical loads, design diagrams (Figure 83.1) are built which are useful to quickly identify sandwich beam configurations locally or globally unstable, but also likely to develop interactive buckling . Concerning this last form of buckling, the analytical model is successfully used to characterize the occurence and the stability of an interactive buckling form. Moreover, for this configuration, the drop in the maximum applied load due to an initial global curvature is analytically studied and plainly identified.

Then, a "simplified" non-conform FE model (beam elements for the skins and bi-dimensional elements for the core) is built and assessed which permits to find a good correlation between the numerical and the previous analytical critical loads and wavelengths. The low time­consuming calculation of this model leads to an efficient characterization of the complete response of the sandwich beam in a material and/or geometrical nonlinear framework. The stability of the different buckling forms are discussed, as well as the high sensitivity towards global or local geometrical imperfections. In order to model the actual behaviour of crushing foams, an elastoplastic constitutive law (yield stress ) is introduced in the core. This nonlinear material behaviour leads to a very sub­critical response, characterized by a drastic drop in the global stiffness of the beam due to the localization of plastic strains (Figure 83.2).

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