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Journal of Convex Analysis 28 (2021), No. 2, [final page numbers not yet available]
Copyright Heldermann Verlag 2021



Homogenization of the Elasticity Problem for a Material with Fractures

Riuji Sato
Dept. of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, U.S.A.
risato@wpi.edu

Bogdan Vernescu
Dept. of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, U.S.A.
vernescu@wpi.edu



We consider the stationary linear elasticity problem for a solid with fractures, and review, in the framework of Legendre-Fenchel duality, three equivalent formulations for the problem in terms of displacement, stress, and strain. For periodically distributed fractures, we prove a homogenization result using Mosco convergence in the L2 topology.

Keywords: Homogenization, Mosco convergence, Gamma convergence, elasticity.

MSC: 35B07, 35J86, 74Q05.

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