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A panorama of dispersion curves for the weighted isotropic relaxed micromorphic model
Author(s) -
d'Agostino Marco Valerio,
Barbagallo Gabriele,
Ghiba IonelDumitrel,
Madeo Angela,
Neff Patrizio
Publication year - 2017
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600227
Subject(s) - panorama , isotropy , tensor (intrinsic definition) , dispersion (optics) , parametric statistics , metamaterial , inertia , mathematical analysis , mathematics , physics , statistical physics , geometry , classical mechanics , computer science , optics , statistics , artificial intelligence
We consider the weighted isotropic relaxed micromorphic model and provide an in depth investigation of the characteristic dispersion curves when the constitutive parameters of the model are varied. The weighted relaxed micromorphic model generalizes the classical relaxed micromorphic model previously introduced by the authors, since it features the Cartan‐Lie decomposition of the tensors P , tandCurlP in theirdevsym , skew and spherical part. It is shown that the split of the tensor P , tin the micro‐inertia provides an independent control of the cut‐offs of the optic banches. This is crucial for the calibration of the relaxed micromorphic model on real band‐gap metamaterials. Even if the physical interest of the introduction of the split of the tensorCurlP is less evident than in the previous case, we discuss in detail which is its effect on the dispersion curves. Finally, we also provide a complete parametric study involving all the constitutive parameters of the introduced model, so giving rise to an exhaustive panorama of dispersion curves for the relaxed micromorphic model.