## 1 Introduction  
For several decades, to reduce the weight of the parts used in the transport sector and, therefore, the fuel needed to move them, steel parts have been replaced by light alloys based on aluminum or magnesium. The semi-finished product, in the form of sheet metal, is generally subjected to an ironing or drawing process both at room temperature (only aluminum alloy sheets) and hot (both aluminum alloy and magnesium alloy sheets). Conventional stretching processes at room temperature have two important drawbacks: light alloys are generally not easily formable and the thickness distribution produced is not uniform in the part subjected to deformation. 5 xxx aluminum alloys have cold formability better than that of the 6 xxx and 7 xxx series alloys [1]. More generally, light alloys have reduced formability compared to steel and generate greater problems in terms of elastic return. To overcome, in part, the problem of failure of the sheet metal, in [2] it was proposed to operate properly on the force or pressure exerted on the blank holder. In [3, 4], attention was paid to the flexibility of the dies and the adoption of an original blank holder. However, to increase the formability of the material, reference is increasingly made to hot sheet metal working techniques. In a review work on sheet metal working techniques [5], it was shown that a sheet can be heated directly or indirectly (by heating the equipment) and then subjected to the forming process. In other cases, the sheet is pushed inside a die heated by the use of pressurized gas. In [6], a series of works related to materials and processing techniques of superplasticforming was collected. In [6; 7], a complete overview of the quick plastic forming technology is presented. To make the thickness distribution of a sheet metal component formed by a hot forming process as uniform as possible, in recent years, multiphase processes have been proposed. In [8], a two-stage superplastic forming process was designed and validated experimentally, while in [9], the thickness profile of a PbSn60 superplastic sheet metal component was optimized by adopting a two-phase gas forming process and making use of a fracture criterion during the design phase. However, the hot working techniques present a series of drawbacks that are mainly related to the heating methods and, for some materials, to the reduction of the resistance properties. Therefore, in [10; 11] incremental sheet forming (ISF) and multi-point forming (MPF) were used as flexible forming processes to increase the formability of the material at room temperature. These processes are suitable to produce components of high value and belonging to small lots. The ISF process allows reaching deformations deeper than the traditional forming process [12], while the main limit is represented by longer processing times. The MPF process makes it possible to obtain three-dimensional surfaces by adjusting the used punches [13]. The main limit is related to the presence of defects on the surface of the sheet due to the action of the punches. These defects were inevitable even in the presence of an elastic rubber sheet on the die surface [14]. Moreover, the size of the punches can limit the shape of the geometry of the workpiece to produce. To overcome the limits indicated above for flexible forming processes, in [15; 16] processes have been proposed to be carried out in several forming steps. In [15], the sheet to be deformed is first subjected to an MPF process and then to an ISF process. In [16], a sheet pre-deformed by a process using a pressurized fluid is subsequently subjected to an ISF process. For the sole purpose of standardizing the thickness of simple parts in superplastic material, in [17; 18; 19; 20] methods to design the profile of the initial thicknesses of the sheet were proposed.