On the influence of the unilateral damage behaviour in the stability of cracked beam/columns

This paper deals with the buckling analysis of cracked beam-columns. The crack is modelled with a unilateral elastic bending-stiffness behaviour, represented by a unilateral rotational spring. This model takes into account the crack closure effect associated with the phenomenon of breathing crack. The rotational spring may model a one-sided crack (or a unilateral joint for other applications in biomechanics or civil engineering). The unilateral elastic constitutive law of the crack is introduced from a variational procedure based on energy arguments. It is shown that this constitutive law can be formulated as a function of a physically-based damage parameter. A one-crack and a two-crack hinged-hinged beam-column are theoretically investigated to illustrate the unilateral effect of the crack behaviour on the buckling load. It is shown that the open crack analogy can be adopted for the one-crack beam-column, whereas this simplified assumption cannot be retained for the two-crack beam-column. In this last case, the crack closure effect strongly affects the buckling load, with respect to the open crack analogy of the same problem. More specifically, the crack-closure phenomenon tends to increase the buckling load, with respect to the open crack assumption mainly retained in the literature.