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.

Relaxed micromorphic model of transient wave propagation in anisotropic band-gap metastructures

“…For the explicit expression of the matrix D, we refer the interested readers to [6]. The algebraic system (19) admits non-trivial solutions v = (û 1 ,û 2 ,P 11 ,P 12 ,P 21 ,P 22 ) T if and only if…”

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

“…Doing so, the first main advantage of the relaxed micromorphic model is that the number of constitutive coefficients is drastically reduced. A second strong point of the relaxed model is that it is possible to show that in the limit case L c → 0 (which corresponds to considering very large specimens of a microstructured meta-material) the mesoand micro-coefficients C e and C micro of the relaxed model can be put in direct relation with the macroscopic stiffness of the medium via a fundamental homogenization formula, in contrast to the Eringen-Mindlin theory [17,39], where it is impossible to obtain this kind of results, see [4,47].…”

On the dispersion of waves for the linear thermoelastic relaxed micromorphic model

“…This new model is now called the 'relaxed micromorphic continuum model' in the literature. Papers by Neff et al [25,20,6,5,27] and Ghiba et al [12], contain the prominent foundation and explanations of the relaxed micromorphic continuum theory. They pointed out that in the new relaxed micromorphic model, the free energy is not uniformly point-wise positive-definite, but the new energy is positive semi-definite only.…”