An improved theoretical model of a metal tube under free external inversion

Due to the long stroke and stable reaction force, circular tubes under inversion are always adopted in the design of energy absorbers. Although a few studies were conducted, the existing theoretical predictions on the knuckle radius and the reaction force of the circular tube during its free inversion displayed large discrepancy from the experimental observations [1–3]. s paper, currently existing two-dimensional theoretical models of the free inversion tube are carefully reviewed. After realizing the defects of these models, Reddy׳s model [2] is improved by adopting the appropriate external work rate and material yield condition, for tubes made of rigid, perfectly plastic material. In order to validate the improved theoretical model, experiments of the free inversion of circular aluminum tubes, and finite element simulations of tubes made of the elastic, perfectly plastic material are all carried out. It is confirmed that compared with the experimental data and the FE simulations, the current model provides more accurate predictions on both the knuckle radius and the steady inversion load for the quasi-static free inversion of circular tubes.