# Multiscale Modeling and Optimization of Aluminum Foam Material Properties Under Dynamic Load
## 3 Results
### FEA Results  
The material properties obtained through material modeling techniques were considered in the finite element analysis and then compared with the experimental data.  
In Figure 19, the comparison between the experimental data on Specim B2 and the numerical simulations made using the material properties generated through RVE and TPMS techniques can be observed. The results showed a good correlation for the acceleration response, as both methods had less than 1% error. On the other hand, we observe a 24.77% error in the frequency for the TPMS method and a 37.09% error for the Random Particle Method. These could be caused by the geometrical accuracy of the material models. The TPMS method typically has a better approximation of the regularity and connectivity of cellular material, leading to more realistic stiffness and mass distribution; on the other hand, the random particle model often introduces irregularities, disconnected pores, or non-uniform stress distribution, which can lead to an overestimation of stiffness and higher resonance frequencies, hence the 37% error.  
Following the analysis of the data presented in the previous subsection, the density values were determined analytically by measuring and weighing each specimen. It was concluded that the key parameter requiring optimization was the elastic modulus, since density was already aligned with the experimental values.  
To achieve this, the experimental simulation setup was preserved unchanged, except for updating the density input to match the real measured value of the specimen. A parameter optimization study was conducted using OptiSLang by ANSYS (2025 R1), a robust tool for automated design exploration and optimization. The objective of the optimization process was to minimize the error between the simulated and experimental resonance frequency, specifically targeting a deviation of less than 1% from the experimental value.  
In the optimization workflow, the elastic modulus of the material was treated as the design variable, while the density was held constant. The target response was the first resonance frequency, with the optimization goal set to match the experimentally measured value of 275 Hz, within a 1% tolerance.  
As shown in Figure 20, Design 11 emerged as the optimal configuration. In this scenario, the elastic modulus was iteratively adjusted until the simulation reached a resonance frequency sufficiently close to the experimental reference. The best match was a simulated frequency of 272 Hz, which resulted in a relative error of around 0.83%.  
Following the same methodology used for Specimen B2, the full process was repeated from the beginning for Specimen A1. The only modification consisted in replacing the geometry based on the CT scan of Specim A1. All other steps, material modeling, simulation setup, and frequency extraction, remained identical. At the final stage, elastic modulus was identified by correlating the resonance frequency from the numerical simulation with the experimental result, as shown in Figure 21, ensuring consistency in methodology and validation.  
Figure 19: Acceleration response: FEA vs. test comparison for Specimen B2.  
Figure 20: Optimized E (**right**, 10.4 GPa) for the experimental resonance frequency (**left**, 272.7 Hz).