# Mesoscale Modelling of the Mechanical Behavior of Metaconcretes
## 6 Conclusions and Future Directions  
A two-dimensional mesoscale model has been developed to reproduce uniaxial-compression tests on metaconcretes, explicitly representing steel cores, rubber coatings, and the interfacial transition zone. Numerical predictions agree well with the experiments, capturing both stiffness and strength reductions. The parametric study quantifies these reductions: inserting a single resonator (\(\rho\approx 1.5\%\)) already lowers the reference compressive strength by 30%, while the highest ratio examined (\(\rho=31.8\%\)) produces an 80% loss, which defines the asymptotic plateau of the strength curve. Keeping the resonator content below \(\rho\approx 5\%\) preserves at least 55% of the baseline strength and more than 85% of the plain-concrete Young's modulus. At an intermediate ratio (\(\rho=10.6\%\)), large-core inclusions (\(D_{\mathrm{a}}\geq 30\) mm) with thin rubber coatings (\(t\leq 1.3\) mm) restrict the stiffness penalty to \(<\)10% and the strength reduction to 15-20%. Overall, an optimal practical window of \(\rho\approx 3\)-5%, combined with large-diameter, thin-coated resonators, achieves the desired locally resonant behavior while limiting the compressive-strength penalty to \(\leq\)45%.  
Based on the findings of this study, future research should focus on the following points regarding such a new engineered material:  
* Extending to 3D simulations through three-dimensional modeling to capture out-of-plane effects, triaxial stress states, and more realistic resonator placements;
* Refining coating material characterization so as to incorporate nonlinear or viscoelastic constitutive models for elastomers that could improve predictive accuracy, particularly under long-term or dynamic loading;
* Examining alternative resonator designs to investigate lattice-like inclusions, composites, or other geometries that may help broaden the feasible design space;
* Integrating dynamic and fatigue analyses of metaconcrete to attenuate vibrations and shocks and evaluate fatigue and impact responses would yield a complete performance assessment;
* Validating at-large scales from testing on metaconcrete would confirm mesoscale findings and guide further design recommendations;
* Extending the mesoscale framework to metaconcrete columns subjected to lateral confinement to quantify its influence on compressive strength and ductility, drawing on experimental insights;
* Investigating the interaction of recycled crumb-rubber particles and chemically treated rubber coatings with OPC and alkali-activated slag binders, assessing their impact on compressive strength, durability, and interfacial chemistry, and developing mitigation strategies for the associated strength loss.  
Addressing the research gaps above will improve confidence in specific metaconcrete technologies and facilitate their transition into broader engineering practice.  
Conceptualization, A.M.R., G.S.-A., M.P.A. and M.B.; methodology, A.M.R., G.S.-A., M.P.A. and M.B.; software, G.S.-A. and M.B.; validation, G.S.-A. and M.B.; formal analysis, G.S.-A. and M.B.; investigation, A.M.R., G.S.-A., M.P.A. and M.B.; resources, M.P.A.; data curation, A.M.R.; writing--original draft preparation, A.M.R., G.S.-A. and M.B.; writing--review and editing, A.M.R., G.S.-A. and M.B.; visualization, A.M.R., G.S.-A. and M.B.; supervision, A.M.R., G.S.-A., M.P.A. and M.B.; project administration, A.M.R.; funding acquisition, A.M.R. All authors have read and agreed to the published version of the manuscript.