A numerical investigation into the plastic buckling paradox for circular cylindrical shells under axial compression

• Numerical investigations are conducted for the plastic buckling paradox of cylinders subjected to axial compression.
• It is found that the flow theory of plasticity predicts more accurate buckling stresses than the deformation theory.
• Numerical results are validated by classic experimental results.
• The apparent paradox is found to be due to the assumptions on the bucking shape made in analytical investigations.

It is widely accepted that for many buckling problems of plates and shells in the plastic range the flow theory of plasticity leads to a significant overestimation of the buckling stress while the deformation theory provides much more accurate predictions and is therefore generally recommended for use in practical applications. The present work aims to contribute to further understanding of the seeming differences between these two theories with particular regards to circular cylindrical shells subjected to axial compression. A clearer understanding of the two theories is established using accurate numerical examples and comparisons with some widely cited accurate physical test results. It is found that, contrary to common perception, by using a geometrically nonlinear finite element formulation with carefully determined and validated constitutive laws very good agreement between numerical and test results can be obtained in the case of the physically more sound flow theory of plasticity. The reasons underlying the apparent buckling paradox found in the literature regarding the application of deformation and flow theories and the different conclusions reached in this work are investigated and discussed in detail.