Interval methods for lack-of-knowledge uncertainty in crash analysis

This paper deals with lack-of-knowledge uncertainty in complex non-linear simulations on a component level, i.e., a crashbox during frontal impact of a vehicle. Specifically, the focus lies on using interval field techniques to model the uncertain boundary conditions during impact simulations. The uncertainty considered in this work is the unknown mechanical response from the adjacent structure. This uncertainty is considered to be epistemic, representing the case where this adjacent structure is unknown at the time the impact analysis is performed. In practice, this refers to the situation where the adjacent structure is still under development, e.g., at a different department or even outsourced. In addition, the safety critical performance of both, the component and the overall structure should be guaranteed under a wide range of circumstances, which are typically encountered in real-life situations. Typically, car manufacturers use multidisciplinary optimisation to identify component designs that perform best on all requirements in a deterministic sense, while minimising the overall weight. Unfortunately, the results of such optimisation schemes are known to converge to an often non-robust optimum. As a result, the response of the structure may be sensitive to small changes in input parameters or boundary conditions. As an answer to these challenges, this paper proposes an interval field approach that accounts for the epistemic, i.e., lack-of-knowledge, uncertainty of the adjacent structures, even in an early design stage. This is accomplished by introducing a spatially varying uncertain mechanical compliance in elements that connect the component to the adjacent structures. These elements have an interval valued stiffness, which is varied along the component following the realisations of an interval field. The bounds on the interval-valued response quantities of interest, i.e., mean force and peak force, are identified using a differential evolution algorithm. This method is demonstrated on four case studies of a full overlap crash analysis of a rectangular crash box, which represents a generic component within the front structure of a vehicle. These case studies demonstrate the applicability and the potential of the proposed method. In addition, in the last case it is shown that the performance of the component can be assessed under an increasing range of uncertainty.