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The effective equilibrium law for a highly heterogeneous elastic periodic medium

Published online by Cambridge University Press:  22 May 2013

Hamid Charef  and
Ali Sili
Hamid Charef
Affiliation:
Departement de Mathématiques, Université du Sud Toulon–Var, BP 20132, 83957 La Garde Cedex, France (sili@univ-tln.fr)
Ali Sili
Affiliation:
Departement de Mathématiques, Université du Sud Toulon–Var, BP 20132, 83957 La Garde Cedex, France (sili@univ-tln.fr)
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Abstract

We study the homogenization of the linearized system of elasticity standing for the equilibrium equation of a highly periodic heterogeneous elastic medium submitted to small deformations and made of two different materials: a very rigid material located in a set Fε (ε being the size of the period of the medium) of vertical fibres surrounded by a soft elastic material localized in the set Mε. The ratio between the coefficients of the elasticity tensor of the two materials is assumed to be 1/ε4. We deal with the general case without any special assumption, such as isotropy, on the material.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 3 , June 2013 , pp. 507 - 561
Copyright
Copyright © Royal Society of Edinburgh 2013 

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