Transparent anisotropy for the relaxed micromorphic model: Macroscopic consistency conditions and long wave length asymptotics
Barbagallo, G. and Madeo, A. and d'Agostino, M.V. and Abreu, R. and Ghiba, I.-D. and Neff, P.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
Volume: 120 Pages: 7-30
In this paper, we study the anisotropy classes of the fourth order elastic tensors of the relaxed micromorphic model, also introducing their second order counterpart by using a Voigt-type vector notation. In strong contrast with the usual micromorphic theories, in our relaxed micromorphic model only classical elasticity-tensors with at most 21 independent components are studied together with rotational coupling tensors with at most 6 independent components. We show that in the limit case Lc → 0 (which corresponds to considering very large specimens of a microstructured metamaterial) the meso- and micro-coefficients of the relaxed model can be put in direct relation with the macroscopic stiffness of the medium via a fundamental homogenization formula. We also show that a similar homogenization formula is not possible in the case of the standard Mindlin-Eringen-format of the anisotropic micromorphic model. Our results allow us to forecast the successful short term application of the relaxed micromorphic model to the characterization of anisotropic mechanical metamaterials. © 2017 Elsevier Ltd