The deformation mechanism analysis of a circular tube under free inversion

• For a circular tube under free inversion, curvature varying is confirmed by equilibrium analysis.
• In first stage of inversion, curvature increases continuously, different to semi-circle.
• Theoretical model of free inversion tube is improved considering bending and tension interaction.
• Predictions of current model agree well with finite element simulations and experimental data.

As a popularly adopted design of thin-walled energy absorber, a circular tube under free inversion has been studied theoretically since 1960s However, in all the existing models, the profile of inversion is assumed to be a semi-circle, i.e., the curvature in the region of inversion is a constant. In this study, from equilibrium of a representative element, the curvature is found to be varying, due to bending moment distribution. The conclusion of varying curvature is verified by the corresponding finite element simulations.Then the deformation mechanism of a tube under free inversion is theoretically investigated by establishing a curvature varying model. Considering the interaction of bending and tension, the steady inversion load and knuckle radius predicted by current model agree well with those obtained from FE simulations as well as the experimental data published in literature.