First applications of a novel unified model for global and local buckling of sandwich columns

Due to the intrinsic heterogeneity of sandwich structures, phenomena at various scales can co-exist in these layered-like assembly of thick-soft and thin-stiff materials. Especially under in-plane compression loadings, geometrical instabilities can occur at both global (structure) and local (skins) scales. Therefore, the in-plane compressive response of sandwich structures is of major concern in designing structural applications. In the present paper, the first applications of a novel unified model for sandwiches are presented, with closed-form solutions for both global and local buckling. For the perfect structure, analytical critical loads are extracted for a simply supported beam, through the calculation of two eigenvalues leading to three buckling modes: it appears that the eigenvalue associated with the antisymmetrical mode can correspond to the occurrence of either global or local (wrinkling) buckling. These global and local loads from the present unified model are shown to compare very well with the predictions given by the most complete specific models from the literature. Moreover, it is shown that conversely to the classical models, our approach yields critical loads that depend only on rigorous well-founded mechanical hypotheses. The simple but general analytical expressions from the unified model permit to select quickly configurations against local and global buckling. In this simplified framework, conclusions can be drawn from this unified model capable of properly predicting the phenomena at both scales. This simplified study is essential in getting an insight in the role played by each geometrical and material parameter, the combination of which is of importance for subsequent non-linear interactive post-buckling analyses (Léotoing et al., 2001).