Finite-size mechanical metamaterials modelled as a relaxed micromorphic continuum
Résumé
<latex> Nowadays is clearer and clearer that peculiar micromechanical effects can only be described through non local and higher-order models in the framework of elastic wave propagation. In particular, the study of finite-size solids is of great interest since for such cases these effects are magnified. The two peculiar micromechanical effects here studied are the so called \textitsize effects, which shows how, for a given wave load, the scattered filed changes as the ratio between the size of the unit cell and the dimension of the finite domain changes, and the presence of the so called \textitband gaps, which are frequencies ranges for which the propagation of waves in a solid is inhibited. A relaxed micromorphic model is here proposed [1]-[2] in order to mimic both these micromechanical effects with an elastic continuous material. The comparison in the mechanical response for several frequencies between a finite-size domain for a given microstructure ([2]) and both the micromorphic and Cauchy solids equivalent to this microstructured material acts as a reliability test for this model. \em References \beginthebibliography99 \vspace-5pt \bibitemd'Ago Marco Valerio d'Agostino, Gabriele Barbagallo, Ionel-Dumitrel Ghiba, Bernhard Eidel, Patrizio Neff, Angela Madeo. Effective description of anisotropic wave dispersion in mechanical band-gap metamaterials via the relaxed micromorphic model. \textitJournal of Elasticity, pp 1-31, 2019. \vspace-7pt \bibitemalexis Alexios Aivaliotis, Domenico Tallarico, Marco-Valerio d'Agostino, Ali Daouadji, Patrizio Neff and Angela Madeo. Frequency- and angle-dependent scattering of finite-size meta-structures via the relaxed micromorphic model. \textitSubmitted. </latex> Acknowledgements: Angela Madeo acknowledge funding from the French Research Agency ANR, ?METASMART? (ANR-17CE08-0006). Angela Madeo and Gianluca Rizzi acknowledges support from IDEXLYON in the framework of the ?Programme Investissement d?Avenir? ANR-16-IDEX- 0005.