# Investigation of Functionality of Vehicle Crumple Zones Recovered after a Traffic Accident
## 1 Introduction
The review of various research publications on this topic has suggested the following few issues that have recently been under greater focus: positions of the stiffening ribs in structural elements [18; 19; 20; 21]; residual stresses in the elements [22]; the effect of holes, cracks, and other stress concentrators [23; 24; 25]; complex and time-dependent loads [26; 27; 28]; and preceding geometric deviations of surfaces [29; 30]. Review of the calculation techniques for the stability of thin-walled structural elements subjected to buckling has shown that the critical buckling force obtained by analytical calculation usually exceeds the results obtained by experiments because of various factors. The critical buckling force depends on the geometric deviations and other factors which are fairly difficult to accurately account for when using analytical methods. The classical analysis of the shells of structural elements was initially focused more on identifying the value of critical buckling force. This helped to identify the capacity of a specific structure to hold loads of a certain value. As the analytical expression of the critical force was found to significantly exceed the real values obtained by experiments, the results of the experimental database have started to be widely used in engineering calculations [31]. The dependency between the initial geometric deviations and the value of critical force still does not have a solid functional relationship. Recently, there have been attempts to assess the effect of geometric deviations on buckling by using probabilistic forecasting methods [32; 33]. [PERSON] and [PERSON] identified three types of methodologies to model vehicle behaviour during abnormal loads [34]. The first type of methodology is discrete modelling of distributed masses [35]. The aim of discrete modelling of distributed masses is to design simplified mathematical models for the investigation of the characteristics of dynamic processes during a traffic accident and the analysis of the effect thereof on humans [36; 37; 38]. Here, the calculation system is based on the solution of differential equations. The structure is simplified down to the systems with a few degrees of freedom by using the distributed masses interconnected with elastic elements. The discussed models of one or more distributed masses are basic, yet convenient for qualitative assessment of the dynamic process and are widely used for the modelling of various types of vehicle collisions. Models of this type have been explored fairly extensively and are widely used in the initial vehicle design phase [39; 40]. The second type of methodology is the spatial modelling of vehicle structure using the Finite Element Method (FEM) [41; 42]. Analysis of the process of development of crumple zones in the structures has shown a preference toward closed thin-walled sections because the course of their deformation can be predicted the most accurately. The effect of geometric characteristics, material mechanical characteristics, and production technologies on the efficiency of elements is determined during the analysis. Currently, methodologies for the calculation of this type of section using FEM have performed fairly well [43; 44; 45]. The third type of methodology combines both methods of analysis. These studies have confirmed that the shell structures used in Europe failed to comply with safety specifications as the design mainly focused on the minimization of mass. This led to the design of a rigid and strong interior frame, and special elements were used that performed the additional functions of a load bearing structure. Recent research has placed a considerable focus on the analysis of this process, and guidelines have been developed on the design of these elements. However, the accumulated data on the effect of potential operational damages and the behaviour of the damaged elements during a traffic accident are insufficient. Moreover, no theoretical models have been developed, and the experimental investigations are insufficient.