Complete band gaps including non-local effects occur only in the relaxed micromorphic model - 10/11/16
Abstract |
In this paper, we substantiate the claim implicitly made in previous works that the relaxed micromorphic model is the only linear, isotropic, reversibly elastic, nonlocal generalized continuum model able to describe complete band-gaps on a phenomenological level. To this end, we recapitulate the response of the standard Mindlin–Eringen micromorphic model with the full micro-distortion gradient ∇P, the relaxed micromorphic model depending only on the CurlP of the micro-distortion P, and a variant of the standard micromorphic model, in which the curvature depends only on the divergence DivP of the micro distortion. The Div-model has size-effects, but the dispersion analysis for plane waves shows the incapability of that model to even produce a partial band gap. Combining the curvature to depend quadratically on DivP and CurlP shows that such a model is similar to the standard Mindlin–Eringen model, which can eventually show only a partial band gap.
Le texte complet de cet article est disponible en PDF.Keywords : Relaxed micromorphic model, Band gaps, Generalized continuum models, Long wavelength limit, Macroscopic consistency, Cauchy continuum, Homogenization, Multi-scale modeling, Parameter identification, Non-redundant model
Plan
Vol 344 - N° 11-12
P. 784-796 - novembre 2016 Retour au numéroBienvenue sur EM-consulte, la référence des professionnels de santé.