Transparent anisotropy for the relaxed micromorphic model: Macroscopic consistency conditions and long wave length asymptotics. (1st August 2017)

• Record Type: Journal Article
• Authors: Barbagallo, Gabriele; Madeo, Angela; d'Agostino, Marco Valerio; Abreu, Rafael; Ghiba, Ionel-Dumitrel; Neff, Patrizio
• Is Part Of: International journal of solids and structures. Volume 120(2017)
• Page Start: 7
• Page End: 30
• Publication Date: 2017-08-01
• Subjects: Relaxed micromorphic model -- Anisotropy -- Arithmetic mean -- Geometric mean -- Harmonic mean -- Reuss-bound -- Voigt-bound -- Generalized continuum models -- Homogenization -- Multi-scale modeling; 74A10 (stress) -- 74A30 (nonsimple materials) -- 74A35 (polar materials) -- 74A60 (micromechanical theories) -- 74B05 (classical linear elasticity) -- 74E10 (anisotropy) -- 74E15 (crystalline structure) -- 74M25 (micromechanics) -- 74Q15 (effective constitutive equations); Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2017.01.030
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: 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.