# Multiscale Modeling and Optimization of Aluminum Foam Material Properties Under Dynamic Load
## 5 Conclusions  
In this study, a comprehensive approach was developed and validated for evaluating the dynamic behavior of metallic foams, using a combination of experimental, numerical, and data-driven techniques. The integration of computed tomography (CT) scans with modal vibration testing allowed for an in-depth understanding of both the internal microstructure and the global dynamic response of foam specimens. By subjecting the samples to sine load excitation, key modal parameters such as the resonance frequency were extracted with high accuracy. These values were then used to back-calculate the effective elastic modulus through a parameter-based inverse optimization method, correlating density and resonance frequency. Based on the analysis, the following conclusions provide a comprehensive overview of the methodology's strengths, limitations, and practical implications:  
* **Efficient characterization strategy** The methodology successfully reduces experimental effort by requiring only a single CT scan and one dynamic test to estimate material behavior across different foam densities--a clear practical advantage for early-stage assessments or industrial constraints. * **Mixed performance of modeling approaches** The TPMS and stochastic RVE models provided useful comparative insights but showed notable limitations in frequency prediction accuracy. TPMS had ~25% errors, and the RVE model ~37%, indicating these models may be more suitable for qualitative trend analysis than precise prediction. * **Limited added value from stochastic RVE modeling:** While intended to reflect more realistic microstructures, the stochastic RVE approach did not significantly improve dynamic response accuracy and added computational complexity, raising questions about its practical benefit in this context. * **Amplitude predictions were consistent:** Despite discrepancies in frequency, both modeling approaches captured amplitude responses well, suggesting their potential for predicting certain dynamic characteristics even if frequency tuning remains imprecise. * **Optimization workflow demonstrated strong potential:** The inverse identification process, particularly using OptiSLang, yielded resonance frequency and amplitude predictions within 5% of experimental values, confirming its robustness and potential as a reliable calibration tool. * **Useful damping estimation technique:** The ability to indirectly estimate damping coefficients from available resonance data adds practical value, especially in cases where direct measurements are not feasible. * **Applicable for trend-level industrial use:** While not suitable for high-precision modeling of dynamic behavior, the proposed framework captures overall trends effectively, making it a valuable tool for applications where broad dynamic behavior is more critical than exact local accuracy--such as in preliminary design for automotive or aerospace components. Conceptualization, L.M. and J.K.; methodology, A.-N.B. and S.-V.G. ; validation, L.M. ; formal analysis, A.-N.B. and S.-V.G. ; investigation, A.-N.B. and S.-V.G. ; resources, L.M. and J.K.; data curation, A.-N.B. ; writing--original draft preparation, A.-N.B. ; writing--review and editing, S.-V.G. and L.M. ; supervision, L.M. and J.K.; funding acquisition, L.M. and J.K. All authors have read and agreed to the published version of the manuscript. This research was funded by the Slovak Academy of Sciences and the Romanian Academy under the Mobility project contract RA-SAS-22-01, Project: Applications of metallic foams in intelligent panels and seismic absorbers. Not applicable. Data Availability Statement: The data in this study are available on request from the authors. The data are not publicly available because they are part of ongoing studies. The authors declare no conflicts of interest. The following abbreviations are used in this manuscript: