# Experimental and Numerical Investigation of the Mesoscale Size Effect in Notched Woven Composites
## 3 Results
### Elastic Properties  
Table 3 shows the elastic properties of the tow identified through the data-driven optimization scheme, running the optimization algorithm for the unnotched specimen.  
As the surrogate optimization algorithm makes use of random sampling, its results were not deterministic. It was observed that the optimization converged after 100-150 iterations.  
While the transverse elastic modulus is comparable to those typically obtained for unidirectional composite, the longitudinal modulus is slightly lower than typical values. This difference can be ascribed to the finite element model. Bundles sway from the in-plane direction and bend in the through-thickness direction, which results in a local change in the elastic property along the bundle itself, according to the curvature of the bundle. In particular, the elastic properties decrease with the bundle curvature according to the classical laminate theory. This geometrically induced elastic variation is not retained in the finite element model as it is assumed that all the elements of longitudinal rows present the same elastic properties. As such, the elastic properties of longitudinal bundles are lower  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Property** & **E\({}_{1}\) [GPa]** & **E\({}_{2}\) [GPa]** & **G\({}_{12}\) [GPa]** & \(\upsilon_{12}\) \\ \hline Mean & 102.388 & 15.519 & 1.891 & 0.050 \\ St. dev. & 2.504 & 0.905 & 0.093 & 0.001 \\ CoV\% & 2.45 & 5.83 & 4.93 & 1.15 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Average material properties from three successive optimization runs. These values were used in the remainder of the study.  
Figure 6: DIC-determined strain fields: (**a**) longitudinal strain; (**b**) transverse strain; (**c**) shear strain.  
than those typical of unidirectional carbon fiber composite. On the contrary, the effect of tow curvature does not affect the elastic properties of the transverse bundles and the obtained transverse modulus is in accordance with that typical of unidirectional composite.  
To validate the mesoscale model calibrated with the data-driven procedure, the identified properties were used to model a notched specimen in a mesoscale fashion. A constant displacement rate was applied to the specimen and the global stress and strain curves from the tensile tests, and the strain maps were compared with the experimental results. As shown in Figure 7, the FE model well captures the elastic behavior of the tested specimens, thus validating the obtained material properties. This can also be appreciated through the comparison of the strain map in the longitudinal direction reported in Figure 7b. The model is able to capture the strain variation to a good degree due to the material heterogeneity which combines with the strain intensification in the proximity of the circular notch. The diagonal banding effect in the strain field is also well represented, including the opposite direction diagonal banding due to the 90\({}^{\circ}\) layer.  
Regarding the stress-strain curves, it is also worth observing the slightly nonlinear behavior of the experimental curves in the proximity of the final failure, which results in a slight discrepancy to the finite element model. The FE model indeed did not retain a damage law and assumed for simplicity an elastic behavior until the final failure.