Nonstandard micro-inertia terms in the relaxed micromorphic model: well-posedness for dynamics

Sebastian Owczarek (1) , Ionel-Dumitrel Ghiba (2, 3) , Marco Valerio D’agostino (4) , Patrizio Neff (5)

1 Faculty of Mathematics and Information Science [Warszawa]
2 UAIC - Alexandru Ioan Cuza University of Iași = Universitatea Alexandru Ioan Cuza din Iași
3 Institute of Mathematics "Octav Mayer"
4 M2S - Mécanique des Matériaux et des Structures
5 Fakultät für Mathematik der Universität Duisburg-Essen

We study the existence of solutions arising from the modelling of elastic materials using generalized theories of continua. In view of some evidence from physics of metamaterials, we focus our effort on two recent nonstandard relaxed micromorphic models including novel micro-inertia terms. These novel micro-inertia terms are needed to better capture the band-gap response. The existence proof is based on the Banach fixed-point theorem.

Mots clés: Wave propagation; generalized continua; micro-inertia

Domaines: Equations aux dérivées partielles [math.AP]

Sebastian Owczarek, Ionel-Dumitrel Ghiba, Marco Valerio D’agostino, Patrizio Neff. Nonstandard micro-inertia terms in the relaxed micromorphic model: well-posedness for dynamics. Mathematics and Mechanics of Solids, 2019, ⟨10.1177/1081286519838311⟩. ⟨hal-02076964⟩