Real wave propagation in the isotropic relaxed micromorphic model
  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. 
Patrizio Neff, Angela Madeo, Gabriele Barbagallo, Marco Valerio   d'Agostino, Rafael Abreu, Ionel-Dumitrel Ghiba
math-ph math.MP