# Computational Methodology for the Development of Wrinkled Tubes by Plastic Deformation
## 1 Introduction  
Thin-walled metal tubes are widely used in naval engineering, civil construction, and the automotive sector [1]. In various applications, the tubes can be wrinkled, which can be achieved through welding processes or forming methods, depending on the specific purpose and required mechanical strength [2, 3]. The welding processes have limitations related to differences in the mechanical and metallurgical properties of materials [4, 5]. Threaded, pressed, welded, brazed, or bonded connections are commonly used to join the ends of tubes. Threaded connections are simple to design, easy to assemble and disassemble, and come in standard sizes [6]. Another option is the use of pressure in the fitting, which is not limited by aesthetic requirements, flanges, or standard sizes, but may be constrained by the required extraction force and water or gas tightness [7]. Bonded joints are alternatives to welded joints in situations where high temperatures are not applicable or when different materials (such as metals and polymers) are used [8]. Adhesive joints eliminate most of the limitations associated with other types of joints. Still, they require careful surface preparation with tight tolerances, and the curing time of the adhesive must also be considered [9]. Mechanical forming techniques have increasingly been used to minimise these limitations in manufacturing wrinkled tubes [10]. Given their commercial importance and wide range of applications, extensive research has been conducted on these processes. Key evaluation parameters include the energy absorbed during the process, the stress exerted during deformation, and changes in mechanical properties in areas where dimensional and geometric alterations occur in the formed structure. Wrinkled tubes obtained by sheets are presented in [11] as one of the innovative joining processes. According to the authors, the challenges for current and future engineers are obtaining mechanical joints with ultra-high-strength steels and applying materials with greater property dispersion (mechanical and geometric properties, including sheet thickness), which require more flexible and robust processes [12]. Studies are focused on optimising structures, geometries, and the amount of material required for tube manufacturing, as well as reducing failures that occur during the process, such as bends, cracks, impact analysis, and the resistance of the materials used [13; 14]. An example is the study of the effect of diameter expansion methods on the bending fracture resistance of Fe-SMA tube joints at various strain rates. The authors investigated the following methods for expanding the diameter of Fe-SMA joints: radial tube expansion, and unidirectional and bidirectional imposed pressure. The joints obtained were tested, and their bending fracture resistance was evaluated [15]. Currently, research is being conducted on aluminium tube joining processes using plastic forming. The study conducted in [16; 17] discusses experimental tests with tools designed to create the most suitable joints for tube joining using the tube expansion principle, to position the contact surfaces of the two tubes adequately for subsequent joining, which is achieved through plastic instability and simultaneous pressure flanging. One of the main objectives of this study was to determine appropriate joining parameters, such as tool distance or edge conicity, for further investigations [16; 17]. However, there is still a lack of research that combines numerical studies with experimental testing of wrinkled tubes or other tube-joining processes aiming to optimise the process and its parameters, particularly with the detailed methodology for the numerical study and optimised dimensions in die geometry. To reduce the number of experimental tests, production costs, and design expenses, numerical simulations have been applied to solve technical problems [18].