Carbon emissions from commercial aircraft are expected to reach more than twice as much as the current levels by 2050. Unconventional aircraft, such as the Flying-V, are projected to achieve more than 20% fuel savings when compared to conventional configurations. However, these unconventional aircraft configurations pose a unique set of design challenges, being one of them the crashworthiness of wing-fuselage structures, which have an oval-shaped cross section that leads to a significant reduction in space underneath the cabin floor. Evaluating the feasibility of a design early in the design phase is vital to avoid cost overruns and minimize the need for drastic design changes. For assessing crashworthiness early in the design phase, the development of low-fidelity models is an attractive as well as a viable option because these models offer both low computational cost and the capability to conduct parametric studies on the crash structure. To develop and implement such low-fidelity models, we propose to explore the analytical modeling of various energy-absorbing mechanisms, namely axial crushing, plastic bending, and joint failure. In the present study, we present the modelling of plastic bending for beam-like structural members. We also present an envisaged method applying user-defined elements to simulate plastic bending in structural members for cases where the location of plastic hinges cannot be predetermined.

The authors regret to inform that an error has been identified in the numerical dataset presented in the original paper (Appendix C.1) for square tubular structures. The mean force values were taken for the entire range (including the peak) instead of the plateau phase of the crushing due to a scripting error. This has an effect on some of the coefficient of determination values, error ranges in Table 2 and causes a change in the generalized equation. However, the coefficient of determination of the generalized model remains unchanged. This corrigendum presents the changes in text and the updated figures and tables. The authors would like to apologise for any inconvenience caused.

To design crash structures for disruptive aircraft designs, it is required to have fast and accurate methods that can predict crashworthiness of aircraft structures early in the design phase. Axial crushing is one of the key energy absorbing mechanisms during a crash event. In this study, various analytical models proposed for calculation of mean crushing force for thin-walled tubular structures are compared with a database of numerical and experimental values to ascertain their accuracy. Improvements to some of the models have also been proposed. Finally a generalized model based on the studied and improved analytical models for prediction of mean crushing force for closed section thin-walled tubular structures is introduced. The generalized model demonstrates high accuracy when compared against experimental/numerical dataset as evidenced by a high coefficient of determination (R²) value of 0.97 and can therefore be used to estimate the mean crushing force for closed-section thin-walled metallic tubular structures with various cross-sectional shapes and crushing modes early in the design phase.

This paper reviews analytical models proposed by Abramowicz et al.[1, 2] and Stefan et al.[3] for the axial crushing of metallic tubular structures with square and circular cross-sections. First, a database of experiments for square and circular tubes was created based on the literature. Subsequently, the predictions obtained using these analytical models were compared against the database of experiments to determine the accuracy of these analytical models. The database of experiments was also compared against some results generated using Finite-Element Method (FEM). Furthermore, the sensitivity of the analytical models to various material and geometrical parameters was studied to determine the influence of these parameters on the mean crushing force. Both models were found to be highly sensitive to the thickness of the tubular structures. It was observed that the models proposed by Abramowicz et al.[1, 2] showed better agreement with experimental results, although an over-prediction was observed for square tubular structures made of materials with a significant difference between the values of yield and ultimate stress. The model proposed by Stefan et al.[3] slightly over-predicted for square tubes and showed reasonable accuracy for circular tubes.