## 4 Results and Discussion
### Final Solid Model  
This Final Solid model was created by introducing two different meshed areas connect by a global-local conditions. Indeed, in the specimen impacted area, where most of the damage is supposed to develop (Figure 16) a ply-by-ply refined discretization was considered with each ply represented by a single layer of 3D solid elements C3D8R with a reduced integration scheme. On the contrary, the external global domain has been modeled with a coarser continuum shell mesh. With this discretization scheme, an accurate study can be performed by reducing, at the same time, the computational effort [40].  
Figure 15: Contact force comparison between analytical and numerical boundary conditions.  
For 3D solid elements, the intra-laminar damage model introduced in Section 2.2 was applied by means of a VUMAT. Moreover, since the inter-laminar damages are likely to occur only between plies with different fiber orientation, zero-thickness cohesive layers were placed only in these locations. As highlighted in Figure 17, cohesive layers were connected to the adjacent layer by means of tie-constraint. Table 2 reports the mechanical properties of the cohesive material system, which were experimentally evaluated by means of three-point bending (E\({}_{n}\), E\({}_{t}\), E\({}_{s}\)), double cantilever beam (N\({}_{\text{max}}\), G\({}_{\text{IC}}\)), and end notched flexure tests (T\({}_{\text{max}}\) and S\({}_{\text{max}}\), G\({}_{\text{IIc}}\) and G\({}_{\text{IIIc}}\)).  
Both solid and cohesive elements have been discretized by 1 \(\times\) 1 mm\({}^{2}\) elements. The external global domain, which has been modeled by one layer of Continuum shell \(SC8R\) elements along thickness direction, has been discretized with an element in-plane size of 4 mm. The specimen is constrained by a fixture and four clamps, modeled with R3D4 rigid elements. The impactor was modeled as a sphere of 16 mm diameter modeled with 3D Solid C3D8R elements. A surface-to-surface contact was used between the impactor and the specimen. During the analysis, the completely damaged elements were removed from the model to increase the computational efficiency. In particular, when cohesive  
Figure 16: Domain and boundary conditions.  
Figure 17: Exploded model (detail).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Property [unit]** & **Value** \\ \hline E\({}_{n}\) [_MPa/mm_] & 1.155 \(\times\) 10\({}^{6}\) \\ E\({}_{t}\) [_MPa/mm_] & 6 \(\times\) 10\({}^{5}\) \\ E\({}_{s}\) [_MPa/mm_] & 6 \(\times\) 10\({}^{5}\) \\ N\({}_{\text{max}}\) [_MPa_] & 62.3 \\ T\({}_{\text{max}}\) [_MPa_] & 92.3 \\ S\({}_{\text{max}}\) [_MPa_] & 92.3 \\ G\({}_{\text{IC}}\) [_k/m\({}^{2}\)_] & 0.18 \\ G\({}_{\text{IIc}}\) [_k/m\({}^{2}\)_] & 0.5 \\ G\({}_{\text{IIIc}}\) [_k/m\({}^{2}\)_] & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Cohesive mechanical properties.  
elements were removed, plies can touch each other at the interfaces. Hence, a general contact on the whole model was defined (except for the already defined impact surfaces) to take into account this behavior. A friction coefficient with a value of 0.5 was introduced for both impactor-to-ply contact andply-to-ply contact. Enhanced hourglass control was set to decrease hourglass problems related to the reduced integrated elements.