## 1 Introduction  
Sheet metal forming is widely used across various industries and is one of the most popular manufacturing technologies to produce finished products [1, 2, 3, 4]. Its applications are especially prominent in the automotive and aerospace industries, as well as in the food and domestic appliance sectors [5, 6]. Key advantages of this technology include the ability to produce parts without requiring highly skilled labor, as well as its ease of production, excellent mechanical properties of the formed parts, and minimal waste generation. However, its major drawbacks include the high cost of tooling, the extended time needed for tool production, and the lengthy iterative process to achieve the final geometry [1; 2; 3; 4]. This iterative process can significantly delay the optimization of tooling production [7; 8]. In today's industries, rapid product development is crucial for maintaining competitiveness [9; 10; 11; 12]. Flat sheets can be transformed into complex three-dimensional components using processes such as bending and deep drawing [2; 13]. Advanced operations include welding [14], bolting, adhesive bonding [15], and the use of clips [16; 17], among others. There is a growing demand for customized components and small-batch production. Rapid prototyping presents a significant opportunity to reduce both product development time and manufacturing costs [5; 6; 7; 8]. Tooling processes that allow sheet metal forming without relying on conventional (metal) tools are increasingly important, particularly for short production runs where conventional tooling costs are prohibitive. Prototyping aims to optimize manufacturing processes and detect potential defects. Due to the high production time and cost of conventional tools, sheet metal-forming technology is primarily suitable for large-scale production. To address this, the use of additively manufactured tools and alternative materials, such as aluminum and synthetic resins, has gained attention. Additive manufacturing offers greater flexibility and resource savings, making it ideal for rapid prototyping and low-volume production. Market demand has driven significant interest in additive manufacturing technologies and 3D printing [18; 19; 20; 21]. 3D printing is rapidly advancing, enabling the production of complex parts that are challenging to create using other methods. This process starts with a digital CAD file that is converted into an STL format. Specialized slicing software generates a G-code file containing layer-specific instructions, which the 3D printer uses to create the part layer by layer [22; 23; 24]. Similar technologies have been applied to unique applications, such as 3D printing railway ballast aggregates [25; 26] and studying ballast track deformation [27; 28]. Various polymeric materials have proven valuable in the development of sheet-forming tools, particularly for low-volume production, offering significant cost savings and shorter lead times [20; 29]. PLA (polylactic acid) is a popular and inexpensive 3D printing material with excellent printability. Research has shown that 3D-printed PLA tools can effectively shape sheet metal, delivering results comparable to those achieved with metal tools in terms of formability [9; 30]. From a tooling perspective, fused deposition modeling (FDM) is one of the most promising 3D printing technologies. Studies highlight significant potential for the use of FDM tools across various industries. This technology builds parts by depositing layers of molten plastic. While the raw material (plastic filament) is cost-effective, the resulting parts exhibit lower strength compared to those made via conventional injection molding due to slight porosity [1; 18]. FDM plastic tools in sheet metal forming offer shorter lead times than conventional tooling. However, due to their lower yield strength and elastic modulus, plastic tools are more prone to failure and have reduced dimensional accuracy.