Abstract

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 L2L^2 topology.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Homogenization
  • Mosco convergence
  • Gamma convergence
  • elasticity

Mathematics Subject Classification

35B07, 35J86, 74Q05

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Suggested citation

R. Sato, B. Vernescu. “Homogenization of the Elasticity Problem for a Material with Fractures.” Journal of Convex Analysis 28 (2021), No. 2, 711–724. https://doi.org/10.68381/jca28039

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press LLC.