Complete band gaps including non-local effects occur only in the relaxed micromorphic model

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• 作者：Angela Madeo^a ; ^b ; ^{angela.madeo@insa-lyon.fr" class="auth_mail" title="E-mail the corresponding author} ; Patrizio Neff^c ; ^{patrizio.neff@uni-due.de" class="auth_mail" title="E-mail the corresponding author} ; Marco Valerio d'Agostino^a ; ^{marco-valerio.dagostino@insa-lyon.fr" class="auth_mail" title="E-mail the corresponding author} ; Gabriele Barbagallo^d ; ^{gabriele.barbagallo@insa-lyon.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Relaxed micromorphic model ; Band gaps ; Generalized continuum models ; Long wavelength limit ; Macroscopic consistency ; Cauchy continuum ; Homogenization ; Multi-scale modeling ; Parameter identification ; Non-redundant model
• 刊名：Comptes Rendus Mécanique
• 出版年：2016
• 出版时间：November-December 2016
• 年：2016
• 卷：344
• 期：11-12
• 页码：784-796
• 全文大小：1553 K

文摘

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 Curl P of the micro-distortion P, and a variant of the standard micromorphic model, in which the curvature depends only on the divergence Div P 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 Div P and Curl P shows that such a model is similar to the standard Mindlin–Eringen model, which can eventually show only a partial band gap.