Non-dimensional parameters governing the crashworthy performance of tubes with complex cross-sections

•A comparative study is conducted on the crashworthiness of various thin-walled tubes.•All the tubes are made from identical material and possess identical apparent cross-sectional area, height and mass.•Six indicators are employed to characterize the crashworthiness of the tubes.•Two new non-dimensional indices, geometric complexity index (RG) and topological index (RT), are introduced to greatly simplify the regression of the mean crushing force and energy absorption of tubes.•The mean crushing force and specific energy absorption of tubes vary almost linearly with a governing parameter ω, which is a function of RG and RT. The crashworthiness of thin-walled tubes with various designs under axial compression has been extensively investigated. Despite this, the parameters that govern the performance of tubes and can be applied across different cross-sectional topologies have not hitherto been available. In this paper, twenty types of thin-walled tubes with different cross-sectional shapes (e.g., multi-celled, bi-tubular, and hierarchical square, hexagonal and circular tubes) have been numerically simulated and theoretically analysed. All the tubes are made from identical material and possess identical apparent cross-sectional area, height and mass. Six indicators are employed to characterise the crashworthiness performance of the tubes. Two novel non-dimensional indices, the geometric complexity index (RG) which is the ratio of the total length of solid segments in the cross-section of a tube to that of the square tube, and the topological index (RT) which is the non-dimensional coefficient in the expression of plastic energy dissipation closely related to the types and numbers of the wall junctions in cross-section, are identified for the first time. Both the indices RG and RT are used in a regression analysis of the indicators that characterise the crashworthiness of the tubes. The results reveal that the crashworthiness indicators of the tubes, the mean crushing force (MCF), the specific energy absorption (SEA) and the effectiveness of energy absorption (EEA) do not exclusively vary with RG. Instead, MCF, SEA and EEA are all properly fitted by linear relations with a single non-dimensional parameter ω, which is a simple function of RG and RT, i.e., ω=RT/RG. Increasing the magnitude of ω ultimately improves the crashworthiness of tubes, including enhanced specific energy absorption, effectiveness of energy absorption and crushing force efficiency, while