Investigation on the Plastic Buckling Paradox for Metal Cylinders

© 2018 World Scientific Publishing Europe Ltd. This chapter investigates the so-called "plastic buckling paradox," which states that the deformation theory of plasticity tends to provide values of the buckling loads which are in better agreement with experimental results than those given by the flow theory of plasticity. The paradox lies in the fact that the latter is physically more sound because it assumes that the current stress depends not only on the current value of the total strain but also on how this strain value has been attained. Instead, the deformation theory of plasticity is based on the assumption that, at any point on the loading path, the stress is uniquely determined by the current state of strain only. The plastic buckling paradox has been observed in a wide range of shell structures, such as plate assemblies, torispherical domes and circular cylinders, under different loading conditions and using different boundary conditions. Among these, the problem of relatively thick cylindrical shell structures subject to either axial compression or combined axial tension and external pressure has attracted substantial interest due to its importance in engineering applications, which has led to a vast literature with many benchmark tests and results. The outcomes from recent studies by the authors are discussed in detail, and it is shown that, when an accurate and consistent FE model is set up, both the flow and deformation theories can predict buckling loads with acceptable plastic strains. In fact, contrary to the common belief, buckling pressures calculated numerically by means of the flow theory are found to be in better agreement with the experimental data. Analytical and semi-analytical formulations are also employed to shed light on the underlying causes of this apparent paradox.