## 1 Introduction  
Losing a limb profoundly impacts an individual's physical and psychological health, affecting not only the patient but also their family. Research indicates that psychological disorders among limb amputees range from 32% to 84%, with depression rates reaching nearly 63% and Post-Traumatic Stress Disorder (PTSD) occurring in 3.3% to 56.3% of cases [1,2]. Trans-tibial amputations have become increasingly common due to trauma, malignancy, and diabetes [3,4]. Assistive devices like prostheses play a vital role in rehabilitation, helping restore mobility and improve quality of life. Lower-limb prostheses typically comprise a pylon, socket, and foot, with the socket serving as the critical interface between the residual limb and the prosthesis [5]. The coupling and alignment of these components determine the effectiveness of the prosthesis, ensuring a proper fit and comfort [6]. Common socket types include the Patellar Tendon Bearing (PTB) and Total Surface Bearing (TSB) designs. While PTB sockets concentrate the load on pressure-tolerant areas, TSB sockets distribute weight evenly across the stump, reducing pressure points and enhancing comfort [7,8]. Additionally, the increased contact area in TSB sockets minimizes stress concentration on pressure-tolerant regions and reduces slip or sliding between the residual limb and the socket [9]. Traditionally, prosthetic socket fabrication involves several manual steps, including creating a Plaster of Paris (PoP) negative cast of the residual limb, forming a positive mold by filling the PoP cast, rectifying the positive mold for an optimized fit, and developing the socket from the rectified positive cast [10]. However, the advent of additive manufacturing (AM) has streamlined this process by generating positive cast CAD models directly from 3D scans, CT, or MRI data of the residual limb [11; 12]. AM techniques, such as selective laser melting [13], selective laser sintering [14], fused deposition modeling [15], and liquid droplet binding [16], enable the tool-less fabrication of prosthetic sockets directly from CAD models. While AM significantly enhances the customization and efficiency of prosthetic socket fabrication, it also introduces complexities in ensuring optimal socket performance, particularly in terms of fit, comfort, and biomechanical integrity. This is where Finite Element (FE) modeling becomes crucial. FE modeling provides a detailed biomechanical analysis of prosthetic devices by enabling the prediction and optimization of stress, strain, and contact pressures within the socket-stump interface [17; 18; 19; 20; 21; 22]. This integrated approach ensures that the innovative designs produced by AM meet the functional and comfort requirements of the user. Thus, FE analysis facilitates the evaluation of different materials and geometries in a virtual environment, addressing the challenges AM poses in achieving optimal socket performance. Past studies have demonstrated the utility of FE tools in examining the effects of socket modifications (e.g., rectifications and material properties) [23; 24; 25] and changes in the coefficient of friction at the stump/socket interface [26]. The first FE analysis of a lower-limb prosthesis was conducted by [PERSON] et al. [27]. They used CT scans to create a linear model and predict stump-socket normal interface stresses. [PERSON] et al. [28] simulated contact in the PTB socket with the assumption of no slip at the interface, but their model was limited during loading transitions. [PERSON] et al. [29] developed a non-linear 3D FE model for the PTB socket, incorporating slip movement to calculate normal and shear stresses at the interface. [PERSON] et al. [30] further improved upon this by implementing automatic surface-to-surface contact modeling to simulate interface stresses and the donning effect. [PERSON] et al. [31] demonstrated that TSB sockets experience considerably less frictional slip compared to Kondyl-Bettung-Munster (KBM) sockets. [PERSON] et al.