Introduction to mechanical metamaterials and their effective properties

Xueyan Chen; Nicolas Laforge; Qingxiang Ji; Huifeng Tan; Jun Liang; Gwenn Ulliac; Johnny Moughames; Samia Adrar; Vincent Laude; Muamer Kadic

doi:10.5802/crphys.30

Introduction to mechanical metamaterials and their effective properties
[Introduction aux métamatériaux mécaniques et à leurs propriétés effectives]

Xueyan Chen ^1,² ; Nicolas Laforge ¹ ; Qingxiang Ji ^1,² ; Huifeng Tan ² ; Jun Liang ^3,² ; Gwenn Ulliac ¹ ; Johnny Moughames ¹ ; Samia Adrar ¹ ; Vincent Laude ¹ ; Muamer Kadic ¹

¹ Institut FEMTO-ST, UMR 6174, CNRS, Université de Bourgogne Franche-Comté, 25000 Besançon, France
² National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology; 92 Xidazhi Street, Harbin, 150001, PR China
³ Institute of Advanced Structure Technology, Beijing Institute of Technology, No. 5 South Zhongguancun Street, Haidian District, Beijing, 100081, PR China

Comptes Rendus. Physique, Volume 21 (2020) no. 7-8, pp. 751-765.

Résumé
Abstract

Les métamatériaux sont des composites de conception rationnelle constitués de briques élémentaires qui sont composées d’un ou plusieurs matériaux constitutifs. Les propriétés des métamatériaux peuvent aller au-delà de celles des matériaux constitutifs, à la fois qualitativement et quantitativement. En outre, leurs propriétés peuvent être mises en correspondance avec certains modèles de milieux continus généralisés. Nous présentons une procédure générale de conception de métamatériaux élastiques à base de systèmes de type masses et de ressorts. Nous montrons quavec cette approche simple, nous pouvons concevoir tout un ensemble de propriétés effectives, y compris celles de métamatériaux élastiques non linéaires avec instabilités ou parties programmables — définis par un module de masse, de cisaillement et une masse volumique. Nous présentons des designs et calculs numériques afin dillustrer les lois de comportement. Enfin, nous discutons de l’apport d’un stimulus thermique aux métamatériaux mécaniques.

Metamaterials are rationally designed composites made of building blocks which are composed of one or more constituent materials. Metamaterial properties can go beyond those of the ingredient materials, both qualitatively and quantitatively. In addition, their properties can be mapped on some generalized continuum model. We present the general procedure of designing elastic metamaterials based on masses and springs. We show that using this simple approach we can design any set of effective properties including linear elastic metamaterials,—defined by bulk modulus, shear modulus, mass density—and nonlinear metamaterials,—with instabilities or programmable parts. We present designs and corresponding numerical calculations to illustrate their constitutive behavior. Finally, we discuss the addition of a thermal stimulus to mechanical metamaterials.

Première publication : 2020-11-19
Publié le : 2021-01-19

DOI : 10.5802/crphys.30

Keywords: Metamaterials, Effective parameters, Elasticity, Anisotropy, Waves, Cauchy elasticity, Navier equation
Mot clés : Métamatériaux, Paramètres effectifs, Élasticité, Anisotropie, Ondes, Élasticité de Cauchy, Équation de Navier

Affiliations des auteurs :

Xueyan Chen ^{1, 2} ; Nicolas Laforge ¹ ; Qingxiang Ji ^{1, 2} ; Huifeng Tan ² ; Jun Liang ^{3, 2} ; Gwenn Ulliac ¹ ; Johnny Moughames ¹ ; Samia Adrar ¹ ; Vincent Laude ¹ ; Muamer Kadic ¹

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Xueyan Chen and Nicolas Laforge and Qingxiang Ji and Huifeng Tan and Jun Liang and Gwenn Ulliac and Johnny Moughames and Samia Adrar and Vincent Laude and Muamer Kadic},
     title = {Introduction to mechanical metamaterials and their effective properties},
     journal = {Comptes Rendus. Physique},
     pages = {751--765},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {21},
     number = {7-8},
     year = {2020},
     doi = {10.5802/crphys.30},
     language = {en},
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%A Johnny Moughames
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Xueyan Chen; Nicolas Laforge; Qingxiang Ji; Huifeng Tan; Jun Liang; Gwenn Ulliac; Johnny Moughames; Samia Adrar; Vincent Laude; Muamer Kadic. Introduction to mechanical metamaterials and their effective properties. Comptes Rendus. Physique, Volume 21 (2020) no. 7-8, pp. 751-765. doi : 10.5802/crphys.30. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.30/

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