Analytical and numerical crashworthiness uncertainty quantification of metallic thin-walled energy absorbers

Abstract

Thin-walled tubular components are featured in transport structures for increased occupant protection in the event of a crash. However, when the limits of their design are sought through deterministic procedures, components often become unreliable due to uncertainties which may cause them to underperform or even fail. Seeking a deeper understanding of the effect of incertitudes on the thin-walled tubes' performance, this research focuses on the crashworthiness quantification of diverse sources of uncertainties in the progressive collapse of these components under axial loads. For a broader insight on the tubes’ behavior, diversity is considered and scrutinized on all the main fields involved in the research; studying two cross-sections, three sources of uncertainties, and the two epitomical crashworthiness metrics, namely the average and peak crushing loads. The process is undertaken via three different methods, combining analytical formulas, numerical simulations, and surrogate modeling. Results show that the best approximation is offered by the multivariate adaptive regression splines metamodel, yielding similar mean values as with the statistical propagation of the analytical formulas, while the standard deviation is overestimated by 1%–3%. The numerical noise quantified for the simulations results shows oscillation frequencies below 40% and a breadth of three-sigma under 9% for both metrics. The uncertainty quantification of both tubes offers a similar response when studying geometric uncertainties, with the plate thickness having a more relevant effect on the results than diameter or edge length. However, material uncertainties affect the absorbers in an opposite manner, as variations in the elastic modulus contribute the most to the square section metrics, while the circular tube is more affected by variations in the equivalent flow stress. Incertitudes in the operational conditions lead to reduced peak load values when the impact angle varies from a perfect axial collision, consequently delivering reduced mean values and high standard deviations.