Comptes Rendus
no. 5-6
Asymptotic analysis for the Kelvin–Voigt model for a thin laminate
Grigory Panasenko1, 2  ; Ruxandra Stavre3
1 University of Lyon, Institute Camille Jordan UMR CNRS 5208, 23 rue du Docteur-Paul-Michelon, 42023 Saint-Étienne, France
2 UMI CNRS 2615 Jean-Victor-Poncelet, Moscow, Russia
3 Simion Stoilow Institute of Mathematics of the Romanian Academy, Research unit nr. 6, P.O. Box 1-764, 014700 Bucharest, Romania
Comptes Rendus. Mécanique, Volume 343 (2015) no. 5-6, pp. 365-370.

A two dimensional Kelvin–Voigt model of a visco-elastic thin stratified strip with Neumann condition at the lateral boundary is considered. The dimension reduction combined with the homogenization procedure allows us to construct a complete asymptotic expansion of the solution and to justify the limit one dimensional model containing the long-fading memory term while the initial model corresponds to the short memory.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2015.04.001
Mots clés : Solid mechanics, Linear visco-elasticity, Kelvin–Voigt model, Asymptotic expansion, Dimension reduction, Homogenization
Grigory Panasenko 1, 2 ; Ruxandra Stavre 3

1 University of Lyon, Institute Camille Jordan UMR CNRS 5208, 23 rue du Docteur-Paul-Michelon, 42023 Saint-Étienne, France
2 UMI CNRS 2615 Jean-Victor-Poncelet, Moscow, Russia
3 Simion Stoilow Institute of Mathematics of the Romanian Academy, Research unit nr. 6, P.O. Box 1-764, 014700 Bucharest, Romania 
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Grigory Panasenko; Ruxandra Stavre. Asymptotic analysis for the Kelvin–Voigt model for a thin laminate. Comptes Rendus. Mécanique, Volume 343 (2015) no. 5-6, pp. 365-370. doi : 10.1016/j.crme.2015.04.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.04.001/

[1] D. Caillerie Thin elastic and periodic plates, Math. Methods Appl. Sci., Volume 6 (1984), pp. 159-191

[2] G.P. Panasenko Boundary layer in homogenization problems for non-homogeneous media, BAIL 4 (1986)

[3] G.P. Panasenko; M.V. Reztsov Averaging the 3-D elasticity problem in non homogeneous plates, Dokl. Akad. Nauk SSSR, Volume 294 (1987), pp. 1061-1065 (in Russian). English transl. in Sov. Math. Dokl., 35, 1987, pp. 630-636

[4] G.P. Panasenko Asymptotic analysis of bar systems, I, Russ. J. Math. Phys., Volume 2 (1994), pp. 325-352

[5] G.P. Panasenko Asymptotic analysis of bar systems, II, Russ. J. Math. Phys., Volume 4 (1996), pp. 87-116

[6] G. Panasenko, Springer (2005), p. 398

[7] N.S. Bakhvalov; K.Yu. Bogachev; M.E. Eglit Investigation of effective dispersion equations describing the wave propagation in heterogeneous thin rods, Dokl. Akad. Nauk SSSR, Volume 387 (2002), pp. 749-753 (in Russian)

[8] S.A. Nazarov Asymptotic Analysis of Thin Plates and Bars, vol. 1, Nauchnaya Kniga, Novosibirsk, 2002 (in Russian)

[9] E. Sanchez-Palencia (Lecture Notes in Physics), Volume vol. 127 (1980), p. 398

[10] G.A. Francfort; P.M. Suquet Homogenization and mechanical dissipation in thermoviscoelasticity, Arch. Ration. Mech. Anal., Volume 96 (1986), pp. 265-293

[11] H.I. Ene; M.L. Mascarenhas; J. Saint; Jean Paulin Fading memory effects in elastic-viscoelastic composites, Math. Model. Numer. Anal., Volume 31 (1994), pp. 927-952

[12] Z. Abdessamad; I. Kostin; G. Panasenko; V.P. Smyshlyaev Memory effect in homogenization of a viscoelastic Kelvin–Voigt model with time dependent coefficients, Math. Models Methods Appl. Sci., Volume 19 (2009), pp. 1603-1630

[13] N.S. Bakhvalov Averaging of partial differential equations with rapidly oscillating coefficients, Dokl. Akad. Nauk SSSR, Volume 224 (1975), pp. 351-355 (in Russian)

[14] N.S. Bakhvalov; G. Panasenko (Math. Appl., Sov. Ser.), Volume vol. 36, Nauka, Moscow (1984), p. 352 (in Russian). English translation in, 1989, Kluwer Academic Publishers, Dordrecht–Boston–London, pp. 366

[15] B.E. Pobedrya, Moscow State University Publ., Moscow (1984), p. 336 (in Russian)

[16] A.N. Kolmogorov; S.V. Fomin Elements of the Theory of Functions and Functional Analysis, Nauka, Moscow, 1976 (in Russian). English translation: Graylock Press, Rochester, New York, 1957, vol. 1, p. 129, vol. 2, p. 127

[17] J. Orlik, Shaker Verlag, Aachen, Germany (2000), p. 128 (Ph.D. thesis)

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