# Mesoscale Modelling of the Mechanical Behavior of Metaconcretes
## 3 Validation of the Proposed Model
To perform a mesh size sensitivity analysis, element sizes of 0.5, 1.0, 2.0, 3.0, 4.0, and 5.0 mm were considered. As shown in Figure 3, the mesh-size sensitivity analysis was based on [PERSON]'s modulus, compressive strength, and the cracking pattern (inferred from the tensile damage variable). In the CDP model, the degradation of tensile strength is tracked through a scalar variable representing tensile damage. The value of the scalar tensile-damage variable is equal to 0 when the material is undamaged (see blue elements in the figure). Conversely, a value close to 1 indicates complete tensile failure (see red elements in the figure). Consequently, mapping the spatial distribution of the scalar tensile-damage variable offers an indirect representation of cracks. Refinement of the mesh reveals that the predominant crack trajectories align vertically, in agreement with the experimental results cited above ([PERSON] et al., 2018). All three parameters converge reasonably well from a mesh size of 1.0 mm onward. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Experimental Data 2** & **Numerical Results** \\ \hline \(E_{0}\) [GPa] & 25.42 \(\pm\) 1.01 & 24.42 \\ \(f_{0}\) [MPa] & 67.49 \(\pm\) 0.99 & 67.17 \\ \hline \hline \end{tabular} \({}^{1}\) It assumes a concrete specimen, contrasting the data obtained from the proposed FEM numerical model. \({}^{2}\) According to the data from ([PERSON] et al., 2018). Source: own calculation.  
\end{table} 
Table 2: Chart comparing [PERSON]’s modulus (\(E_{0}\)), and the compressive strength (\(f_{c0}\)) \({}^{1}\). Figure 2: Comparison of stress–strain curves for concrete specimens, including experimental data ([PERSON] et al., 2018) and the proposed FEM. Source: own elaboration. As shown in Figure 4, stress-strain curves have been obtained from these three configurations using the proposed model and compared to the three experimental curves reported in [36]. In addition, the figure presents the cracking patterns obtained for each analyzed case. The numerical results show good agreement with the experimental data. Table 3 shows the mean values and standard deviations (SD) of [PERSON]'s modulus and compressive strength for concrete specimens containing 10.6% resonators. Based on a comparison between experimental data obtained from the study and those collected from FEM results, the investigation showed that the predicted [PERSON]'s modulus exhibits an error of about 20%. In contrast, the compressive strength error remains below 1%. Acknowledging the substantial discrepancy observed in the prediction of [PERSON]'s modulus  
Figure 4: Comparison of stress–strain curves for concrete specimens with a 10.6% resonator ratio, including experimental data [36] and the proposed FEM. Source: own elaboration. Figure 3: Mesh size sensitivity analysis of [PERSON]’s modulus (\(E\)), compressive strength (\(f_{c}\)), and corresponding cracking patterns derived from the tensile damage variable. Source: own elaboration from numerical calculations. is imperative. However, the lack of information on rubber characteristics in [PERSON] et al. 's experiments explains this difference [36]. Consequently, generic values for the rubber's Young's modulus were used to estimate the material properties. These findings suggest that the proposed model accurately captures the mechanical behavior of metaconcretes, particularly in predicting [PERSON]'s modulus and key strength parameters, including compressive strength and failure strain.