## 2 Numerical and Analytical Methods Description  
Among various joints configurations, the single lap joint (SLJ) is frequently employed due to its simplicity and effectiveness in load transfer, making it a standard specimen in both experimental and numerical studies, according to the ASTM D1002 [34]. The single lap joint considered in this study represents a common configuration used to evaluate adhesive performance under different loading conditions. Aluminum alloys, such as the one used in this study, are often selected for lap joints due to their favorable strength-weight ratio, corrosion resistance, and widespread application in industries where joint reliability is critical. The chosen aluminum alloy adherent, simulated as an elastic-plastic isotropic material, reflects the material's typical mechanical properties, ensuring that the findings of this study are relevant to real-world applications. The adhesive used in this study is FM 73M OST, a commercially available film adhesive frequently employed in aerospace and automotive applications for its robust mechanical properties and strong bonding performance with aluminum alloys. Its widespread industrial use reflects a balance of cost, manufacturability, and mechanical performance factors which are crucial for many large-scale engineering applications [28]. In a typical SLJ experiment, adherends (often metallic, composite, or a combination) are bonded using a structural adhesive over a prescribed overlap length, then cured according to the adhesive manufacturer's specifications--commonly under elevated temperature and pressure, although some adhesives are ambient-cured. After curing, the joints are cut or machined to ensure consistent dimensions and then tested on a universal testing machine such as an MTS or Instron system. The ends of the adherends are clamped in grips with sufficient friction to prevent slippage, and a uniaxial tensile load is applied at a controlled displacement rate until failure [35]. In this study, the commercial software Abaqus (v2019) was used to perform this numerical analysis due to the embedded sophisticated cohesive zone models. The purpose of these analyses is to offer a thorough examination of the behavior of joints and to compare different adhesive model representations and values of overlap length based on the pro vided criteria. This study used a simulation that was three-dimensional and geometrically non-linear. The elastic properties of the aluminum and the FM 73M OST are provided in Table 1. The aluminum alloy substrate used was simulated as an elastic-plastic isotropic material, and the longitudinal plasticity parameters are shown in Table 2. Longitudinal and transverse labels for the plastic strain versus flow stress-tabulated values refer to the rolling direction of the aluminum plates under consideration [36]. In this study, the SLJ follows the guidelines of ASTM D1002 [34] as depicted in Figure 1, while specific geometrical parameters are varied to assess the consistency of different modeling methods. The adherend thicknesses (\(t_{\text{P}}\)) are varied among four values (0.5 mm, 1 mm, 2 mm, and 3 mm) and the overlap (\(L_{\text{o}}\)) is investigated at four increments (10 mm, 15 mm, 20 mm, and 25 mm). These variations enable the study of how each adhesive modeling approach responds to a broad range of material and geometric dimensions. Meanwhile, the adhesive thickness, \(t_{\text{A}}\) = 0.2 mm, the grip length, \(L_{\text{G}}\) = 25 mm, and the adherend length, \(L_{\text{A}}\) = 100 mm, are held at constant values according to the standard ASTM D1002 [34]. An adhesive thickness of 0.2 mm was chosen to balance the competing demands of mechanical performance, manufacturability, and practical application. [PERSON] et al. [37] noted that although a 2 mm bond line might not yield the highest fracture toughness, scaling the adhesive layer beyond that thickness often introduces defects and proves impractical for most engineering purposes.