## 3 Results and Discussion
### Mechanical Behavior of SLJ Reference Configuration  
In analyzing the force-displacement response of lap joints, the transition of stresses, particularly von Mises and shear stresses, can be observed distinctly across the elastic (A), hardening (B), and maximum failure regions (C). Initially, in the elastic region, the applied load causes a proportional increase in both von Mises and shear stresses within  
Figure 6: Different BC study (**a**) without grips; (**b**) with grips.  
Figure 7: Force-displacement plot of a lap joint with and without grips.  
the adhesive layer. The SLJ configuration considered in Figure 7 will be explored in this section to illustrate these three regions.  
The different stress variations are shown in Figure 8. The shear stress distribution exhibits a pattern which shows that the shear stress is dominant in the mechanics of the lap joint. In the elastic range, there are high stresses at the edges, primarily due to the non-uniform distribution of stress due to the eccentric load path and the geometric discontinuity. At the start of the analysis, the overlap region experiences a combination of normal and shear stresses, and the abrupt changes at the edges create a stress riser, leading to an increase in the shear stress values compared to the central region of the joint. Similarly, shear stress concentration occurs at the edges because the adhesive layer must accommodate differential deformations between the adherends. The effect of the shear stresses at the edges makes these regions critical for initiating damage and failure in the adhesive layer, which is visible in the peel stress plot and the adhesive layer representation. The graphics in Figure 9 correlate with the plots in Figure 8, illustrating the variations in adhesive stress distributions.  
As the load increases in the single-row cohesive zone model, stress concentrations develop at the overlap edges, but the plastic behavior is localized in the adherends rather than in the CZ adhesive layer. Because a single-row cohesive element uses a traction-separation law to represent the adhesive, there is no provision for plasticity or strain hardening within that interface. Instead, the von Mises stress exceeding the yield strength applies primarily to the adherends just outside the overlap. This localized plasticity in the adherends can exhibit strain hardening, further raising the overall load-bearing capacity. Meanwhile, the shear stress in the cohesive elements continues to increase, since the critical stress is a higher value than the adherend yield stress. Hence, the adherends not the cohesive adhesive layer undergo plastic deformation and hardening, even though their deformation may appear closely coupled with the failure process at the joint edges.  
Upon reaching the maximum failure region, the effects of peel and shear stresses cause the cohesive elements at the edges to degrade fully. This leads to crack initiation and propagation from the edges towards the center of the lap joint. The adhesive layer starts to experience significant damage, with micro-cracks coalescing into larger fractures. As the load continues to increase, these cracks propagate, reducing the effective load-carrying area of the adhesive layer and further increasing the local stress concentration, as shown in Figure 9. Eventually, the lap joint reaches its ultimate load-bearing capacity, and complete separation occurs, characterized by a rapid decline in both von Mises and shear stresses  
Figure 8: (**a**) Shear stress; and (**b**) peel stress distributions at the adhesive mid-thickness as a function of normalized overlap length.  
as the adhesive layer fails. This failure process highlights the critical role of edge stress concentrations in determining the overall structural integrity and failure behavior of single lap joints.