This work emphasizes that the main objective is not only the fitting of three different approaches, but the development of a semi-analytical fitting algorithm and the underlying consistency of the relaxed micromorphic model with respect to the material properties and some geometric characteristics of the represented metamaterial. Through complex analytical expressions of the asymptotes, it is possible to obtain a numerical fit of all material parameters using only the numerical values calculated with Comsol Multiphysics® and the apparent mass density ? of the unit cell. It is highlighted that only the k = 0 cuts and the k ? 8 asymptotes are used to calculate the material parameters, while the shape of the curves for intermediate values of k arises automatically.
The procedure has been fully implemented in Mathematica, allowing the use of symbolic calculations. The essential part of this fitting employs the NMinimize algorithm with the RandomSearch method to minimize the mean square error between the asymptotes of the relaxed micromorphic model and the numerical values obtained through the finite element approach in Comsol Multiphysics®. However, it is noted that if a local minimum is found, it cannot always be guaranteed to correspond to a global optimum.
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This study reinforces the importance of accurate numerical models and their applicability in different fields, aligning with our mission to offer efficient technological solutions based on the most advanced knowledge in the sector.
