Axial crushing behaviors of metal density gradient foam-filled square taper tubes: Analytical model and numerical calculation

Metal tube is a traditional energy-absorbing structure, and metal foam is a lightweight material with advantages, i.e. high energy absorption and high specific strength. The foam-filled square tube can improve the crashworthiness and has better energy absorption, which is higher than the sum of the energy absorption of the tube and foam. Axial crushing behaviors of metal density gradient foam (DGF) filled square taper tubes are studied analytically and numerically in this paper. An analytical model is presented to study the crushing behavior of DGF filled square taper metal tube under axial loading, in which the interaction between square taper tube and DGF is considered. The numerical calculation is conducted, and the deformation mode is obtained. The analytical predictions are well consistent with the experimental and numerical results. The influences of taper angle, foam strength, maximum relative density and minimum relative density of gradient foam on the compressive behavior of metal DGF filled square taper tube under axial loading are considered. It is demonstrated that when the taper angle is less than 85°, the average crushing force increases as the minimum density of the DGF increases. However, when the taper angle is greater than 85°, the average crushing force decreases with the increase of the minimum density of gradient. This proposed analytical model can effectively predict the axial crushing behaviors of metal DGF filled square taper tube.