A panorama of dispersion curves for the weighted isotropic relaxed micromorphic model. Issue 11 (16th May 2017)

• Record Type: Journal Article
• Authors: d'Agostino, Marco Valerio; Barbagallo, Gabriele; Ghiba, Ionel‐Dumitrel; Madeo, Angela; Neff, Patrizio
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 97:Issue 11(2017)
• Page Start: 1436
• Page End: 1481
• Publication Date: 2017-05-16
• Subjects: Planar harmonic waves -- relaxed micromorphic model -- generalized continua -- dynamic problem -- micro‐elasticity -- size effects -- wave propagation -- band gaps -- 74A10 (stress) -- 74A30 (nonsimple materials) -- 74A35 (polar materials) -- 74A60 (micromechanical theories) -- 74B05 (classical linear elasticity) -- 74M25 (micromechanics) -- 74Q15 (effective constitutive equations) -- 74J05 (Linear waves); Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201600227
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: 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, t and Curl P in their dev sym, skew and spherical part. It is shown that the split of the tensor P, t in 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 tensor Curl P 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. Abstract : 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, t and Curl P in their dev sym, skew, and spherical part. It is shown that the split of the tensor P, t in 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 tensor Curl P 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.