Bloch wave homogenization of linear elasticity system

Ganesh, Sista Sivaji ; Vanninathan, Muthusamya (2005) Bloch wave homogenization of linear elasticity system ESAIM: Control, Optimisation and Calculus of Variations, 11 (4). pp. 542-573. ISSN 1292-8119

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In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three dimensions. The Bloch wave method for homogenization relies on the regularity of the lower Bloch spectrum. For the three dimensional linear elasticity system, the first eigenvalue is degenerate of multiplicity three and hence existence of such a regular Bloch spectrum is not guaranteed. The aim here is to develop all necessary spectral tools to overcome these difficulties. The existence of a directionally regular Bloch spectrum is proved and is used in the homogenization. As a consequence an interesting relation between homogenization process and wave propagation in the homogenized medium is obtained. Existence of a spectral gap for the directionally regular Bloch spectrum is established and as a consequence it is proved that higher modes apart from the first three do not contribute to the homogenization process.

Item Type:Article
Source:Copyright of this article belongs to EDP Sciences.
Keywords:Bloch Waves; Homogenization; Linear Elasticity
ID Code:55403
Deposited On:18 Aug 2011 07:08
Last Modified:18 May 2016 07:41

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