title: Real wave propagation in the isotropic-relaxed micromorphic model.
abstract: 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 the 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, whereas it does in isotropic linear elasticity.
authors.affiliation: Nonlinear Analysis and Modelling , Fakultät für Mathematik , Universität Duisburg-Essen , Mathematik-Carrée , Thea-Leymann-Straße 9 , 45127 Essen , Germany.
authors.forename: Patrizio
authors.initials: P
authors.lastname: Neff
authors.affiliation: LGCIE SMS-ID, INSA-Lyon, Université de Lyon, 20 avenue Albert Einstein, 69621 Villeurbanne Cedex, France; IUF, Institut Universitaire de France, 1 rue Descartes, 75231 Paris Cedex 05, France.
authors.forename: Angela
authors.identifier: 0000-0003-1940-9853
authors.initials: A
authors.lastname: Madeo
authors.affiliation: LGCIE SMS-ID, INSA-Lyon, Université de Lyon, 20 avenue Albert Einstein, 69621 Villeurbanne Cedex, France; LaMCoS-CNRS, INSA-Lyon, Université de Lyon, 20 avenue Albert Einstein, 69621 Villeurbanne Cedex, France.
authors.forename: Gabriele
authors.initials: G
authors.lastname: Barbagallo
authors.affiliation: LGCIE SMS-ID , INSA-Lyon , Université de Lyon , 20 avenue Albert Einstein , 69621 Villeurbanne Cedex , France.
authors.forename: Marco Valerio
authors.initials: MV
authors.lastname: d'Agostino
authors.affiliation: Institut für Geophysik , Westfälische Wilhelms-Universität Münster , Corrensstraße 24 , 48149 Münster , Germany.
authors.forename: Rafael
authors.initials: R
authors.lastname: Abreu
authors.affiliation: Lehrstuhl für Nichtlineare Analysis und Modellierung, Fakultät für Mathematik, Universität Duisburg-Essen, Thea-Leymann Straße 9, 45127 Essen, Germany; Department of Mathematics, Alexandru Ioan Cuza University of Iaşi, Boulevard, Carol I, No. 11, 700506 Iaşi, Romania; Octav Mayer Institute of Mathematics of the Romanian Academy, Iaşi Branch, 700505 Iaşi, Romania.
authors.forename: Ionel-Dumitrel
authors.initials: ID
authors.lastname: Ghiba
keywords: acoustic tensor; ellipticity; positive definiteness; rank-one convexity; real wave velocity; relaxed micromorphic model