Real wave propagation in the isotropic-relaxed micromorphic model

Patrizio Neff (1) , Angela Madeo (2) , Gabriele Barbagallo (3, 2) , Marco Valerio d'Agostino (2) , Rafael Abreu (4) , Ionel-Dumitrel Ghiba (5, 6, 1)

1 Universität Duisburg-Essen = University of Duisburg-Essen [Essen]
2 LGCIE - Laboratoire de Génie Civil et d'Ingénierie Environnementale
3 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
4 Institut für Geophysik [Münster]
5 UAIC - Alexandru Ioan Cuza University of Iași = Universitatea Alexandru Ioan Cuza din Iași
6 Institute of Mathematics "Octav Mayer"

For the recently introduced isotropic relaxed micromorphic generalized continuum model, we show that under the assumption of positive definite energy, planar harmonic waves have real velocity. We also obtain a necessary and sufficient condition for real wave velocity which is weaker than positive-definiteness of the energy. Connections to isotropic linear elasticity and micropolar elasticity are established. Notably, we show that strong ellipticity does not imply real wave velocity in micropolar elasticity, while it does in isotropic linear elasticity.

Mots clés: rank-one convexity; real wave velocity; micropolar; Cosserat; acoustic tensor; generalized continuum; ellipticity; micromorphic; positive-definiteness; planar harmonic waves

Domaines: Physique mathématique [math-ph]; Mécanique des solides [physics.class-ph]

Patrizio Neff, Angela Madeo, Gabriele Barbagallo, Marco Valerio d'Agostino, Rafael Abreu, et al.. Real wave propagation in the isotropic-relaxed micromorphic model. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017, 473 (2197), ⟨10.1098/rspa.2016.0790⟩. ⟨hal-01720523⟩