## 3 FE Model  
The finite element method (FEM) is commonly used in the literature [40; 41; 42; 43] for the prediction of the structural behavior of such structural components as bonded joints. This section presents the modeling approach, based on FEM, for the simulation of the structural behavior of bonded joints. All analyses are performed through Abaqus(r) v. 2021 [44] commercial FE code. The FE model, shown in Figure 2a, refers to nominal dimensions shown in Figure 1a. The FE model counts a total of 90,520 linear hexahedral C3D8R elements (from Abaqus(r) finite element library), 8 nodes with 3 degrees of freedom, used for the modeling of all adherends, and 1456 linear hexahedral COH3D8 elements (from Abaqus(r) finite element library), 0.001 mm thick, 8 nodes with 3 degrees of freedom, used to simulate the adhesive. The cohesive element layer, depicted in gray in Figure 2b, opportunely placed on the adherend area covered by the adhesive, permits us to predict both debonding initiation and evolution without providing to the FE model indications of the zone where the phenomenon starts. Moreover, element nodes of adherends and adhesive layers are merged at the interfaces to guarantee their connectivity, these being characterized by the same in-plane mesh size. Particular attention has been paid to the material characterization of the adhesive. In detail, the traction--separation law is defined, considering for each opening I mode the bilinear law shown in Figure 3, where \(\sigma_{i}\) represents stress and \(\delta_{i}\) represents the separation displacement. This technique is widely used in FE analyses and provides a simplified representation of the mechanical behavior of adhesive joints. However, it does not capture the scale effect, which is critical in scenarios where the thickness of the adhesive layer influences the stress distribution and mechanical performance. As highlighted by [PERSON] et al. [45], the scale effect becomes particularly significant when adhesive layers are reduced to micrometer or nanometer thicknesses (that does not represent the specific case of this study), leading to deviations from classical mechanics predictions. The inability to account for these size-dependent behaviors can result in an underestimation or overestimation of joint strength, especially in applications involving thin adhesive layers. Regarding the cohesive thickness \(t\), when a traction--separation approach is used to define the cohesive element response, Abaqus assumes by default that the constitutive thickness is set to one. This default setting is based on the premise that the geometric thickness of cohesive elements is typically zero or negligible in applications where a traction--separation-based response is appropriate, such as in the presented model. This choice ensures that nominal strains directly correspond to the relative separation displacements. According to Figure 3, the traction--separation law consists of a first linear A-B path, characterized by a prefixed slope (penalty stiffness \(K_{p}\)), where \(\sigma_{\text{ic}}\) and \(\delta_{0i}\) represent the critical stress value and the displacement at the debonding initiation. The following B-C path represents the debonding evolution phase. The complete decohesion, and then the cohesive element deletion, occurs when \(\delta_{\text{max,i}}\) is reached. For inclusion within the simulation, the effects of the combination of multiple opening modes on debonding the quads' damage criterion and the power law [44] are implemented as initiation and evolution criteria, respectively. Concerning the former, debonding is assumed to initiate when a quadratic interaction function involving the nominal stress ratios reaches a value of one, Equation (1).