## 3 Results and Discussion
### Stress Distribution of the Adhesive
By contrast, the continuum single-row model shows higher amplitude stress emphasizing the purely elastic-plastic adherend response without cohesive failure in the adhesive. Moving on to Figure 13d, the asymmetry in the continuum model's stress distribution becomes more pronounced. In the CZ-based approaches, local adhesive damage triggers load redistribution, though the cohesive zone models allow for progressive edge softening rather than pure plastic rotation of the adherends. Consequently, each method's stress contour evolves uniquely under large deformations, with the continuum model showing more pronounced asymmetry once plastic hinges begin to form in the adherend material near the overlap edges. Figure 14: Adhesive stress distributions at the mid-thickness of the adhesive layer (0.5 mm thick adherend, 10 mm overlap) at the elastic region: (**a**) peel stress; (**b**) shear stress. The figure-to-figure consistency of the CZ models in the elastic regime--where they remain close to the continuum model and analytical predictions--confirms that their traction-separation \"stiffness\" is large enough to avoid artificial compliance before damage. The minor differences among CZ approaches arise largely from how each formulation handles local stress distributions and potential failure initiation. Hence, even though the SRCE model offers a more simplified representation of the adhesive layer, it still matches overall elastic behavior quite well, while the more refined cohesive models may capture localized stress peaks or failure paths in greater detail. Analyzing the effect of different adherend thicknesses using the single-row cohesive element method revealed a progressive increase in peel and shear stress as the thickness decreased. For the same load step at the elastic region, the 3 mm thick adherend produced peel and shear stresses of 14.1 MPa and 7.6 MPa, respectively. In contrast, the 2 mm thick adherend showed peel and shear stresses of 14.3 MPa and 9.2 MPa, respectively. This trend continued with the 1 mm thick adherend, producing 14.6 MPa and 10.6 MPa, and the 0.5 mm thick adherend yielding the highest stresses of 14.8 MPa and 12.1 MPa, in Figure 15. These results indicate that thinner adherends experience higher stress, making them more susceptible to initiating degradation in the cohesive zone at the outer edges of the overlap under similar loading conditions compared to thicker adherends. The analytical formulation in Figure 15c,d also replicated this progressive increase in stress with decreasing thickness, further validating the numerical results and confirming the mechanical behavior predicted by the simulations. In this thickness variation study, a 25 mm overlap was chosen in accordance with ASTM D1002 guidelines, which prescribe standardized dimensions for SLJ. Under these  
Figure 15: (**a**) Numerical peel; (**b**) numerical shear; (**c**) analytical peel; (**d**) analytical shear stress distributions at the mid-thickness of the adhesive layer of different adherend thicknesses at the elastic region. conditions, the distribution of peel stresses was found to vary with adherend thicknesses. For the thickest adherend (3 mm), peel stresses were more evenly distributed across the overlap length due to the larger size, whereas thinner adherends exhibited more pronounced peel stresses at the edges. Thicker adherends possess a large moment of inertia, thus exhibiting greater stiffness in bending. Consequently, they experience less out-of-plane displacement under tensile loading, effectively shifting the joint's response toward shear-dominated behavior rather than bending-dominated behavior. As a result, the load transfer is more uniform, reducing stress concentrations at the overlap edges and improving the joint's overall durability. By contrast, thinner adherends are more susceptible to edge-peel failures because their reduced bending stiffness localizes deformation at the edges, promoting higher stress concentrations that can trigger premature damage (Figure 15).