## 1 Introduction
[PERSON] et al. [17] conducted a comprehensive study that included both experimental and computational studies to investigate the tensile properties of CFRP single-strap repairs. The study examined various patch thicknesses and overlap lengths. A mixed-mode cohesive damage model was created to simulate the initiation and propagation of cracks accurately in structural repairs. The experimental and numerical findings showed a strong agreement in terms of failure modes, failure load, and equivalent stiffness of the repair. Using experimentation and numerical analysis, [PERSON] et al. [18] investigated the adherend failure and adhesive failure on composite SLJ material. They tested SLJs experimentally using various adhesives and overlap lengths, and they contrasted the experimental findings with basic analytical predictions and numerical predictions. [PERSON] et al. [19] conducted an experimental study to assess the stiffness of adhesives on the impact performance of bonded joints. They examined two types of adhesives: one that was brittle and another that was ductile. The joints were thereafter subjected to multiple impacts at varying energy levels. Although the more compliant and ductile adhesive performed better in the initial impact, the stiffer and brittle adhesive outperformed it in subsequent impacts. [PERSON] and [PERSON] [20] utilized a closed form analytical solution to apply three distinct constitutive models to an epoxy adhesive: a basic model, a model with linear elastic characteristics for the adhesive, and a model with linear softening. Validation of all the models was conducted by comparison with analytical solutions. The researchers discovered that when stiffness values are high, the precision of the Young's modulus value does not affect the results. [PERSON] et al. [21] conducted a study on the precise application of adhesive joints in the automotive industry. A flexible epoxy glue was utilized in a CFRP single lap joint with multiple overlap lengths. Numerical and experimental experiments were conducted under both quasi-static and dynamic circumstances, including impact scenarios. The CZ numerical models were verified for both situations. An augmentation in the maximum load was seen when the overlap was increased for both static and impact loadings. Furthermore, it was determined that carbon fiber-reinforced polymer adherends exhibit superior vibration absorption capabilities in comparison to steel adherends. Various traction-separation law (TSL) shapes have been proposed to represent the interfacial behavior of adhesive layers, each capturing the details of damage initiation and propagation. For instance, bilinear, trapezoidal, and exponential TSLs [22] offer distinct ways to model the adhesive's brittle or ductile response, influencing the predicted stress distributions and the onset and growth of damage. Although the present study does not explore the geometric placement of cohesive elements or their local versus continuum representations, the chosen TSL shape still significantly impacts the predicted joint performance. In particular, accurately anticipating adhesive debonding, cohesive fracture, or mixed-mode failures depends on selecting a TSL that best reflects the material's fracture process. These distinctions are particularly important in experimental tests where these failure modes are frequently observed. Moreover, each adhesive model representation inside the CZ model framework provides distinct perspectives on the mechanical behavior of the joint under different loading circumstances. For example, a bilinear model could effectively capture the initial stiffness and linear softening behavior, whereas a trapezoidal model may more accurately depict the plateau in the stress-strain curve, which indicates plastic deformation before total separation. An exponential model would more accurately represent the progressive decline in stress as separation increases [23].