Axial crushing of circular structures with rectangular multi-cell insert

•Axial crushing of circular tubes with rectangular multi-cell insert is investigated using numerical simulation.•A formula for the analytical evaluation of the mean crushing force is derived and the results are evaluated.•Parameters associated with the formula and the feasibility of solutions are discussed.

The axial crushing of circular structures with rectangular insert was investigated. Literature available experimental data were used to validate the numerical models of the structures investigated. Results are compared in order to set up the simulation layout. To increase the efficiency of the simulation process a software module was developed and some explanations related to the generation of the numerical model are provided.Based on the theoretical models of the symmetric crushing of circular tubes and the model developed to investigate multi-cell square thin-walled structures a formula for the evaluation of the mean crushing force for the proposed structure was derived.Results obtained from the experiments and different numerical simulations of structures with different number of cells, different thicknesses and main dimensions were evaluated and compared with theoretical results. The theoretical model predicted the mean crushing force with and error of 20% in case of structures with a reduced number of cells (four cells) or with a very thin insert while for structures with a higher number of cells or thicker insert (comparable with the thickness of the tube) the predicted value is within 5% range. Some plots based on the theoretical model are presented and can provide the start point for an optimisation process.