Analysis of the free external inversion of circular tubes based on deformation theory

• A deformation theory based theoretical analysis is proposed for a free inversion circular tube.
• Predictions with the two-stage thickness assumption agree well with FE and experimental data.
• In previous 2D models, neglecting axial stretching energy is found to be the reason of deviation.

Inversion of tubes can be used in the design of energy absorbers. In this study, by comparing the initial state and the final state of the inverted tube, a deformation theory based theoretical analysis is proposed to predict the knuckle radius and the inversion load of a tube under an external free inversion. Employing the rigid, perfectly plastic (RPP) material idealization, three kinds of deformation mechanisms are compared. It is concluded that for tubes within a certain range of geometrical parameters, the analytical results based on a two-stage assumption about tube thickness agree well with those obtained from FE simulations as well as the experimental data. By re-visiting the existing theoretical models, the reasons of deviations in their predictions are discussed, indicating that neglecting the energy dissipation due to the axial stretching will lead to an overestimate of the knuckle radius.