Instability mode interaction: From Van Der Neut model to ECBL approach

In the case of an ideal structure, the theoretical equilibrium bifurcation point and the corresponding load, Ncr, are obtained at the intersection of the pre-critical (primary) force–displacement curve with the post-critical (secondary) curve. For a real structure, affected by a generic imperfection the bifurcation point does not appear anymore and, instead, the equilibrium limit point is the one characterizing the ultimate capacity, Nu, of the structure. The difference between Ncr and Nu represents the Erosion of the Critical Bifurcation Load (ECBL), due to the imperfections. This model applies in the instability mode interaction. The meaning of mode interaction inherently refers to the erosion of critical bifurcation load in case of interaction of two (or more) buckling modes associated with the same, or nearly the same, critical load. A well-known example of such a mode interaction is the one resulting from the coupling of local or distortional buckling with overall buckling in the case of thin-walled cold-formed members. Van der Neut [1] stated the erosion due to coupling and imperfection effects is maximum in the local–global coupling point. The ECBL approach extracts its basic principle from this conclusion. This is a review paper of which purpose is to summarize the mode interaction problem and ECBL approach, presenting the last results obtained by the authors.