## 1 Introduction  
In the global context in which it is mandatory to reduce the use of resources in all areas of activity, the auto industry is strongly influenced by the decisions taken at the design level of the various resistance structures. For weight and cost reduction of parts, the use of assemblies made of tailor-welded blanks--from now on referred to as TWB--is a technology implemented in both car manufacturing and aerospace industries. Research shows that weight reduction of the vehicle by just 1% leads to a fuel consumption decrease by 0.6-1% [1]. In the case of weight and cost reduction aluminium, magnesium, or composite materials are used, but they do not show the flexibility and elasticity offered by steel [2]. An opportunity promising to satisfy these requirements is represented by using TWB parts. TWBs initially appeared as a method of using waste resulting from other production processes. This way, the evident benefits of combining different material thicknesses, different grades, or protective coating were available. Joining different metal sheets is often used in the car industry because it reduces manufacturing costs, improves the resistance of new structures, and decreases total weight [3]. TWB semi-finished parts are used to make the following components: front and rear door interior, longitudinal brackets, engine support brackets, stiffening structures, bottom panels, and crash boxes as shown in Figure 1. TWBs are also used for applications such as uprights (A, B, and C) and side members [4]. TWBs are widely used in the production of household goods, packaging, or construction. Generally, any product that requires different properties of the material in different areas can be made of TWB. Metal assemblies made of TWBs are also used in the production of tubular elements (rectangular, elliptical, or conical) within the resistance structure of motor vehicles. Figure 1 shows such an element integrated into a car's structural subassembly, designed to absorb the energy developed in case of impact. In real applications, such a system for absorbing impact energy can be made of thin-walled tubular structures, such as rectangular crash boxes. They are widespread in the automotive industry, meeting the objectives of impact behaviour quite well, protecting both the occupants of the vehicle and the structure itself [5]. Generally, the study of the vehicle involved in a collision is made considering some of the following aspects: the ability of the vehicle to avoid the accident (primary safety), its dynamics during and after the impact, the movement of occupants, and most importantly, the behaviour of deformed structures [6]. The impact force response and the energy absorption capacity are two parameters directly influenced by the deformation mode, the relative deformation, and the inertia effects. A very difficult problem to solve is the accurate estimation of springback in the case of TWB. In this case, the weld line and the two materials with different properties or thicknesses are involved. Moreover, there is a thermally affected area for each material, which often has different properties from the base material [7], and therefore five materials are involved in springback estimation. The mechanical behaviour of the thermally influenced area is quite difficult to characterize mathematically by a springback estimation analytical model. Implementing the thermally affected area in the finite element analysis negatively influences the springback corresponding to TWB composed of different steel grades [8; 9]. This effect is caused by the fact that the thermally affected area has a higher modulus of elasticity. A high value of the modulus of elasticity and the yield strength has opposite effects on the springback [10; 11; 12]. In the case of TWB made of different steels, simulations showed that thickness reduction of the metal sheets and increase of the forming punch radius led to a rise in the springback intensity [13].