An analytical investigation on the crushing behavior of thin-walled tubes filled with a foam with strain hardening region

In this paper, the axial crushing behavior of a foam-filled thin-walled circular tube, assuming the strain hardening for the foam. The theoretical model is based on the super folding element and unlike the previous researches, the interaction effect between the wall of the tube and the foam which had a tangent modulus (Et) in the plateau region is considered. The governing equations of energy absorption consist of four types of consuming energy mechanisms: membrane deformation, bending deformation, the interaction between the tube and foam, and axial crushing of the foam. In order to validate the theoretical model, the results of the model are compared with numerical simulations presented in this paper and previous experimental results and reveal good agreement. Furthermore, the effects of different values of tangent modulus (Et) of the foam material on the folding length, crushing force, energy absorption, and specific energy absorption of the foam-filled circular tube are also investigated and the changes in the energy-consuming mechanisms are fully described. According to the results, as the value of the tangent modulus of the foam material increased, the value of mean crushing force, energy absorption, and specific energy absorption of the foam-filled circular tube increased, too, and the folding length decreased. •A novel theoretical model is proposed based on the super folding element.•The proposed model can accurately predict the crushing behaviors of circular tubes.•The effect of eccentricity factor on the interaction coefficients is investigated.•Increasing the tangent modulus will increase the mean crushing force of tubes.