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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2015.04.001
Keywords: 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

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