## 1 Introduction  
Sheet metal forming is a worldwide manufacturing process, where sheet blanks with a basic outline are plastically deformed between dies to obtain parts with complicated shapes and desired tolerances. It is a sector that has a significant economic impact and is at the forefront of manufacturing processes. Sheet metal-forming processes usually leave little scrap and manufacture the final part in a very short time: usually a few strokes of a press. As a result, many parts are produced in less time, which helps in large production quantities, where tool costs can be easily amortized. They are used extensively throughout the automobile, aerospace, electronics and household appliance industries to produce complex parts [1; 2; 3; 4]. Despite its many obvious advantages, sheet metal forming has some drawbacks. Dies with aggressive geometry, and the abusive use of small radii, are often some of the key aspects that generate the fracture [5] of metal sheets during the forming process [6]. Fracture caused by excessive stretching in sheet metal forming has been extensively investigated [7]. Wrinkling occurs when compressive stresses in the flange reach a critical point of instability [8], most likely in regions where the work piece is unsupported or when the blank-holder force is insufficient. The wrinkling can be prevented by increasing the blank-holder force and by redesigning the draw beads in order to create tensile stress in those flanges to compensate the compressive stresses. The springback phenomenon is related to the elastic strain recovery, and it consists of the change in the shape of a part at the end of the deformation process when it is released from the forming tool-associated forces [9]. It is physically driven by the stress state reached at the end of the forming process and by the elastic response of the formed part. This phenomenon pushes parts away from their design and targeted dimensions. Minimizing springback issues can shorten the overall project timeline by reducing the need for iterative testing and adjustments during the design phase. Improved control over springback leads to quicker product iterations and a reduced time to market, which is critical in the competitive home appliances industry. Stamping tooling accounts for a substantial fraction of the investment in home appliance projects, and excessive springback can necessitate costly modifications or even complete redesigns of tooling, impacting the project budget and additional delays. Historical efforts to reduce the collateral effects created by springback have usually been carried out by trial and error methods. Manufacturing a physical part to verify the functional and dimensional assessment is a costly procedure. It also includes the design stage of the piece itself and the tooling involved in the manufacturing process, which is usually one die per stage and also the trimming tools. Once the physical die is set up, first pieces are manufactured. Those parts are checked to determine if the piece complies with all the dimensional and functional requirements. In the event that the part requirements are not fulfilled, the process must be repeated from the beginning. This process, depending on the part, can take months of trial and error looping. This long process and the costs related put a great pressure on the viability of different projects. Hence, a great concern in sheet metal-forming design is making an appropriate prediction of the final shape of a formed part without the need for prototyping or trial and error with the springback playing a key role in this final shape of the part. Numerical tools are needed to reduce trial and error cycling on physical prototypes. Of all the numerical techniques described so far, the Finite Element Method (FEM) has become established and nowadays is the preferred choice [10] for springback prediction following forming processes. On the face of it, the concept of springback seems simple, but the prediction of springback has proven to be quite challenging.