Journal of Convex Analysis 28 (2021), No. 2, 711--724
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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