The torsional buckling of a cruciform column under compressive load with a vertex plasticity model

The torsional buckling of a plastically deforming cruciform column under compressive load is investigated. The problem is solved analytically based on the von Kármán shallow shell theory and the virtual work principle. Solutions found in the literature are extended for path-dependent incremental behaviour as typically found in the presence of the vertex effect that is present in metallic polycrystals.At the critical load for buckling the direction of straining changes by an additional shear component. It is shown that the incremental elastic–plastic moduli are spatially nonuniform for such situations, contrary to the classical J₂ flow and deformation theories. The critical shear modulus that governs the buckling equation is obtained as a weighted average of the incremental elastic–plastic moduli over the cross-section of the cruciform.Using a plasticity model proposed by the authors, that includes the vertex effect, the buckling-critical load is computed for a aluminium column both with the analytical model and a FEM-based eigenvalue buckling analysis. The stable post-buckling path is determined by the energy criterion of path-stability. A comparison with the experimentally obtained classical results by Gerard and Becker (1957) shows good agreement without relying on artificial imperfections as necessary in the classical J₂ flow theory.