In order to enhance the load-carrying and energy-absorbing capacity of the energy-absorbing structure, a new energy-absorbing mode of a metal foam-filled sandwich circular tube (MFSC-Tube) expanded by a conical–cylindrical die under axial compression is designed. An analytical model of expansion of the MFSC-Tube under axial compression is established, considering the bending, stretching, and strain hardening of inner and outer tubes as well as compression of the metal foam core. Subsequently, finite element calculations are performed. Both analytical solutions and deformation modes agree well with the finite element calculation results, which proves the validity of the analytical model. The effects of material and geometrical parameters on the expansion of MFSC-Tubes are considered in detail based on the proposed analytical model. It is found that the load-carrying and energy-absorbing capacity of the expansion of the MFSC-Tube can be enhanced by adjusting such parameters as the ratio of the foam thickness to the wall thickness of the metal circular tube and the semi-angle of the die. Last but not least, the specific energy absorption (SEA) of the MFSC-Tube under expansion is significantly improved compared with that of hollow tubes under expansion.

The axial compressive deformed configurations of traditional and lightweight energy absorption thin-walled tubes are uncontrollable, while the introduction of internal and external induction grooves can control the deformed configuration at predetermined intervals to improve the stability of axial collapse. Thus, by introducing induction grooves and the concept of gradient into the design of energy-absorbing structures, an efficient energy absorber consisting of biomimetic foam-filled diameter-gradient tube with internal and external gradient induction grooves (FD-GIG Tube) is proposed. The axial compressive experiments of the FD-GIG Tubes filled with density uniform foam are carried out, and the deformation-related failure modes are clearly observed. An analytical model for axial crushing behaviour of a FD-GIG Tube filled with density gradient foam is established. The axial crushing behaviour of FD-GIG Tube filled with density gradient foam is analytically and numerically studied. The analytical average force-displacement curves of FD-GIG Tubes filled with density gradient / uniform foam, match well with experimental and numerical results. Increasing cone angle, density gradient factor, induction groove height factor and induction groove depth factor can all effectively increase the specific energy absorption (SEA) of the FD-GIG Tube up to 81.8% maximum.

The failure behavior of geometrically asymmetric sandwich beams with a metal foam core is analytically and experimentally investigated. New initial failure modes of the asymmetric sandwich beams are observed under three-point bending, i.e., face yield, face wrinkling, core shear A, core shear AB, core shear A-AB, and indentation. It is shown that the initial failure modes of sandwich beams depend on the span of the beam, the thicknesses of top and bottom face sheets, core height and material properties. We derived the analytical formulae for the initial failure loads and then constructed the initial failure mechanism maps for the geometrically asymmetric sandwich beams. It is shown that the analytically predicted initial failure mechanism maps are in good agreement with the experimental results, which are clearly different from the symmetric sandwich beams. As a preliminary application, the minimum weight designs are presented for asymmetric metal sandwich beams.