Comptes Rendus
no. 4
Thin linearly piezoelectric junctions
[Jonctions minces linéairement piézoélectriques]
Christian Licht1, 2  ; Somsak Orankitjaroen2  ; Patcharakorn Viriyasrisuwattana2, 3  ; Thibaut Weller1
1 LMGC, UMR-CNRS 5508, Université Montpellier-2, case courier 048, place Eugène-Bataillon, 34095 Montpellier cedex 5, France
2 Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
3 Department of Mathematics, Faculty of Science and Technology, Suan Sunandha Rajabhat University, Bangkok 10300, Thailand
Comptes Rendus. Mécanique, Volume 343 (2015) no. 4, pp. 282-288.

Par une analyse mathématique rigoureuse, nous présentons divers modèles asymptotiques pour une jonction mince piézoélectrique entre deux corps linéairement élastiques ou piézoélectriques. Selon l'ordre de grandeur relatif entre un paramètre de rigidité et l'épaisseur, le joint est remplacé par une liaison (électro)mécanique ou par une surface matérielle piézoélectrique.

Through a rigorous mathematical analysis, we present various asymptotic models for a thin piezoelectric junction between two linearly piezoelectric or elastic bodies. Depending on the relative behavior of a stiffness parameter with respect to its thickness, the joint is replaced by either a(n) (electro)mechanical constraint or a piezoelectric material surface.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2015.01.001
Keywords: Piezoelectricity, Thin junctions, Asymptotic modeling
Mot clés : Piézoélectricité, Jonctions minces, Modélisation asymptotique
Christian Licht 1, 2 ; Somsak Orankitjaroen 2 ; Patcharakorn Viriyasrisuwattana 2, 3 ; Thibaut Weller 1

1 LMGC, UMR-CNRS 5508, Université Montpellier-2, case courier 048, place Eugène-Bataillon, 34095 Montpellier cedex 5, France
2 Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
3 Department of Mathematics, Faculty of Science and Technology, Suan Sunandha Rajabhat University, Bangkok 10300, Thailand 
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Christian Licht; Somsak Orankitjaroen; Patcharakorn Viriyasrisuwattana; Thibaut Weller. Thin linearly piezoelectric junctions. Comptes Rendus. Mécanique, Volume 343 (2015) no. 4, pp. 282-288. doi : 10.1016/j.crme.2015.01.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.01.001/

[1] C. Licht; S. Orankitjaroen; P. Viriyasrisuwattana; T. Weller Bonding a linearly piezoelectric patch on a linearly elastic body, C. R. Mecanique, Volume 342 (2014) no. 4, pp. 234-239

[2] C. Licht; S. Orankitjaroen Dynamics of elastic bodies connected by a thin soft inelastic layer, C. R. Mecanique, Volume 341 (2013) no. 3, pp. 323-332

[3] C. Licht; A. Léger; S. Orankitjaroen; A. Ould Khaoua Dynamics of elastic bodies connected by a thin soft viscoelastic layer, J. Math. Pures Appl. (2013), pp. 685-703

[4] A. Aitmoussa Modélisation et études des singularités de contraintes d'un joint collé très mince, Université Montpellier-2, France, 1989 (Ph.D. thesis)

[5] E. Acerbi; G. Buttazzo; D. Percivale Thin inclusions in linear elasticity: a variational approach, J. Reine Angew. Math., Volume 386 (1988), pp. 99-115

[6] C. Licht; G. Michaille A modelling of elastic adhesive bonded joints, Adv. Math. Sci. Appl., Volume 7 (1997) no. 2, pp. 711-740

[7] C. Licht Some new mathematical modelings of junctions, East-West J. Math., Volume 13 (2011) no. 1, pp. 23-33

[8] M. Serpilli An asymptotic model of a multimaterial with a thin piezoeletric interphase, C. R. Mecanique, Volume 342 (2014) no. 4, pp. 258-262

[9] M. Serpilli Asymptotic analysis of a multimaterial with a thin piezoelectric interphase, Meccanica, Volume 49 (2014) no. 7, pp. 1641-1652

[10] T. Weller; C. Licht Asymptotic modeling of thin piezoelectric plates, Ann. Solid Struct. Mech., Volume 1 (2010), pp. 173-188

[11] W. Geis, G. Mishuris, A.-M. Sändig, Asymptotic models for piezoelectric stack actuators with thin metal inclusions, preprint 2004/001, Universität Stuttgart, Germany.

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