Real wave propagation in the isotropic relaxed micromorphic model

TL;DR

This paper demonstrates that in the isotropic relaxed micromorphic model, planar harmonic waves have real velocities under positive energy conditions and establishes weaker criteria for real wave propagation, connecting to classical elasticity theories.

Contribution

It provides a new necessary and sufficient condition for real wave velocities in the relaxed micromorphic model, extending understanding beyond positive definiteness of energy.

Findings

Real wave velocities occur under positive energy assumptions.

Weaker conditions than positive definiteness ensure real wave propagation.

Strong ellipticity does not guarantee real wave velocity in micropolar elasticity.

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 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.