# Mesoscale Modelling of the Mechanical Behavior of Metaconcretes
## 5 Discussion  
The results presented in the previous section reveal several vital insights regarding the influence of resonator characteristics on the mechanical properties of MCs. First, the analysis of the resonator ratio shows a clear trend: both Young's modulus and compressive strength decrease with increasing resonator ratio. Notably, the compressive strength experiences a pronounced reduction, exceeding 25% with the inclusion of just one resonator, before approaching an asymptotic value that is approximately 20% lower than that of the plain concrete. The observed asymptotic behavior can be attributed to localized weakening around the inclusion. Once enough resonators are included, further increments in damage and crack initiation produce limited additional global weakening, as these phenomena dominate the overall response. This behavior is consistent with a mixing law [54; 55], where the addition of a secondary phase (in this case, resonators) progressively diminishes the effective load-bearing area. The low dispersion in the measured values (SDs  
Figure 8: Normalized compressive strength \(f_{c}/f_{\partial 0}\) and normalized Young’s modulus \(E/E_{0}\) as a function of coating stiffness \(E_{r}\), for metaconcretes with either steel or lead cores. Solid lines represent compressive strength (right axis), and dashed lines represent Young’s modulus (left axis). The results indicate that both \(E\) and \(f_{c}\), when normalized for plain mortar values, remain largely unaffected by the core material or coating stiffness. Source: own elaboration. below 3%) confirms that the spatial distribution of resonators has a relatively minor effect on these macroscopic properties. Second, it has investigated the effect of resonator dimensions, specifically the resonator diameter, as well as the relation between the core size and the coating thickness on the mechanical response of the MC. The data indicate that variations in [PERSON]'s modulus remain within 10%, while compressive strength varies by approximately 15-20% as the resonator size decreases. The corresponding cracking patterns corroborate these findings, showing that cracks initiate at the resonators and follow predominantly vertical paths. As the number of resonators increases, the connectivity of cracks increases, thereby reducing the overall compressive strength. Finally, the study of material properties--examining both the elastomer coating and the core material--demonstrates that modifications in the coating's [PERSON]'s modulus produce modest changes in the overall mechanical response. Although the compressive strength varies by about 6% across the range of elastomer moduli tested, [PERSON]'s modulus primarily remains insensitive to these changes. Furthermore, substituting the steel core with a lead core has a minimal impact on the mechanical properties of the resonator dimensions considered, suggesting that the macroscopic behavior of the composite is governed more by the resonator geometry and distribution than by the specific material properties of the core. Additionally, the low dispersion in almost all the results is noteworthy, indicating that the spatial distribution of the resonators has a relatively minor, yet slightly more pronounced, influence on the compressive strength compared to [PERSON]'s modulus. This is relevant, as it suggests that slight variations in spatial distribution during fabrication are unlikely to result in substantial changes to mechanical properties. Overall, these findings suggest that the optimal design of MCs involves using larger resonators with thinner rubber coatings and a lower resonator ratio, thereby ensuring a balance between enhanced dynamic behavior and acceptable mechanical strength. The consistency of these trends with experimental observations reported in the literature [36] further validates the proposed numerical model.