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 L2 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

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.

Copyright Heldermann Verlag 2021