## 6 Numerical Investigation and Validation
### Double-Lap Test
The vertical force was measured in the steel plate, and the vertical displacement is the relative movement between the steel plate and the GFRP plate (AB distance Figure 15). As expected, due to the extra flexibility of the experimental test setup, the numerical model is less flexible than the experimental one. This is a common problem when comparing numerical vs. experimental structural responses [65]. The magnitude of the stiffness in the numerical model was dependent on the adopted final geometry and support conditions, therefore due to its unknown variability, it is not expected to reach the same value as the one obtained in the experimental campaign. For the 15 mm cover, there is a clear overestimation of the maximum reaction for both reduced and full integration, which is associated with the tensile matrix resistance and longitudinal 1-2 shear resistance being overestimated. Furthermore, the adopted value of the fracture energy was estimated, not measured, in an experimental campaign. However, for the 70 mm cover, the maximum reaction is near the average experimental one, since the bearing is in the collapse mode, and this is associated with the compressive resistance, which was not estimated. It is observed that for the 15 mm cover, there is no clear difference between adopting a residual stress of 15% or 80% since the collapse mode is shear-out. However, for the 70 mm cover, clearly, the 80% residual compressive stress produces better results when compared with the post-peak values of the experimental campaign. The final shear 1-2 damage field for all numerical models with reduced and full integration is portrayed in Figure 18, in which it is possible to perceive that for the 15 mm cover, it is clearly a full shear-out collapse, but for the 70 mm cover, there is a bearing collapse followed by a partial shear-out mode that is not finalized. This is in accordance with the findings from the experimental campaign up to a 5 mm relative displacement. Figure 16: Adopted 3D mesh for 70 mm cover (**a**) and 15 mm cover (**b**) and symmetry conditions for 15 mm cover (**c**) and 70 mm cover (**d**) for the double-lap test. Furthermore, only for the 70 mm cover can it be seen in Figure 18 that some differences exist in the final shear damage field distribution for 15% and 80% residual compressive stress. Similar to the structural response in Figure 19, there are some differences in the final shear damage field distribution for reduced and full integration with 80% residual compressive stresses. In Figure 20a, the shear stress and shear damage evolution are presented in the Gauss point nearest the circular opening perimeter at 30\({}^{\circ}\) of the symmetry axis in the GFR plate. The findings are shown for both 15 mm and 70 mm covers, with residual compressive stress levels of 15% and 80%. These findings are significant because they show that increasing the residual compressive stress has almost no effect on the residual shear stress and that this is more related to the level of cover, which influences the stress field indirectly. This is also the case for the shear damage evolution displayed in Figure 20b. Finally, to better understand that the proposed ITE algorithm does not overestimate the viscous energy and consequently the viscous damage, the elastic damaged energy (ESE) and the viscous dissipation energy (VSE) are exhibited in Figure 21. As expected for the RED_15%_15, there is a big reduction of force after 0.4 s, as shown in Figure 17, and as expected in this case, both the value of ESE and VSE increase, but after a given time step, VSE stabilizes and ESE increases, demonstrating that the VSE does not dominate the structural response. For RED_80%_70, this does not occur due to the small force reduction during the structural response, in which VSE is always very small. Figure 17: Force vs. displacement for (**a**) 15 mm cover and (**b**) 70 mm cover for the double-lap test.