## 6 Numerical Investigation and Validation
### Compact Tension Test  
The compact tension test is a traditional test to assess fracture energy, usually in isotropic materials [62], and was recently extended to also estimate the fracture energy in orthotropic GFRP specimens [58]. The full details of the experimental campaign for the tensile compact test can be found in [58], including the test setup and description of the imposed displacement. The specimen geometry, test setup, and supporting conditions are all depicted in Figure 4. For the adopted mesh, to reduce the computational cost, the zone outside the notch was simulated with linear orthotropic GFRP behavior that already existed in the ABAQUS material library. The extra part of the notch was simulated with the proposed UMAT, in which the fracture will take place. These two used different meshes, since the zone in the notch needs an extra refinement, and later were connected using tie constraints. The circular supports were modelled with linear isotropic steel also presented in the ABAQUS material library (\(E_{S}=195~{}GPa,~{}v=0.3\)). The interaction between the supports and the GFRP specimen was simulated with hard contact formulation, and with a friction coefficient of 0.2. To even further reduce the computational cost, only half of the thickness was simulated, therefore transversal symmetry conditions were implemented in Figure 5. When the mesh was generated, it imposed near-cubic shapes for all solid finite elements, and several meshes were tested to prevent any mesh dependency. A full 3D non-linear analysis was performed using the ABAQUS standard with C3D8 solid finite elements using full integration. As a result of the structural response presenting softening during the last experimental campaign, displacement control was used when applying a vertical load. All the material properties in plane 1-2 of the GFRP are in Tables 1 and 2, and these were obtained in the experimental campaign of [58]. For the interlaminar material properties, it was admitted these were the same as the matrix properties, due to some isotropic behavior in the transverse direction. Three different tests were performed to evaluate the numerical accuracy of the new proposed algorithm: The first test consists of a full implicit material integration with correction parameter \(\varpi=1.0\); the second test consists of a full explicit material integration considering \(\varpi=0.0\); the third test uses ITE with the correction parameter of expression (47). It is important to point out that the UMAT was used for the GFRP using the ABAQUS  
Figure 4: Geometry and test setup for the classical compact tension test (CT) [58]. (**a**) Geometry [mm]; (**b**) experimental layout; (**c**) laboratory conditions. standard, so the governing system was solved using the implicit predictor-correct algorithm for the three tests. By observing Figure 6, it is important to realize that all three tests provided the same structural response, even during the softening branch. The stiffness is the same in all three tests, but the maximum force is slightly higher in the second test (explicit) as expected. All numerical models present a higher maximum force than the experimental campaign, but this was also observed by other authors [63]. Interlamin properties are supposed to be the same as the matrix properties, and this assumption can create slight gaps between numerical and experimental results. Moreover, boundary conditions of simulations may contain minor discrepancies compared to the experimental test, generating small differences in the structural response. The final matrix damage field distribution for all three numerical tests is also presented in Figure 7a, in which it is not possible to determine the differences between each of the material time integration methods. Figure 7b also shows the vertical stress distribution and matrix damage for a specific vertical strain. Finally, Figure 8 compares the final matrix damage field distribution using full implicit material integration, explicit and the ITE algorithm.