A quasi-static and low-velocity impact crushing investigation on a metal square tube

The crushing of a metal square tube under quasi-static and low-velocity impact loading is investigated, theoretically and numerically. A modified Wierzbicki's static model in the crush analysis of hexagonal honeycomb is extended to the crushing of metal square tubes. Rewriting the internal energy terms and the external work in the energy method through the basic element folding by considering the true cylindrical curvature effects and the flow stress of the tube material leads to a better prediction of the mean crushing force and the half-wavelength of the folding mode of these energy absorbers under quasi-static loading. Afterwards, the present static model is extended to the low-velocity impact crushing of the metal square tube, and for the first time, an analytical model is presented for the study of the low-velocity impact crushing of these energy absorbers. The required initial velocity of the projectile for decreasing the length of these structures from the initial value to a desired value is calculated. A finite-element model (FEM) is developed in the ABAQUS software and the validity of the FEM is demonstrated by comparisons of numerical results with the experimental data available in the literature. Afterwards, results for mean crushing load and half-wavelength of the folding mode in the static loading and initial velocity of the projectile in the impact loading are compared to those of the present and previous theoretical models for various wall thicknesses and widths. A good agreement between results obtained using FEM and present models are observed.