Abstract

We extend previous results on the dual formulations for an elastic body without fractures to a model of a homogeneous elastic body with fractures. In particular, in the framework of Legendre-Fenchel duality, we were able to provide three equivalent formulations for the problem where the displacement, the stress, and the strain are the unknowns respectively. We also provide a characterization of the image of the convex cone of admissible displacements under the linearized strain tensor.

Author information

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

Riuji Sato

Dept. of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, U.S.A.

risato@wpi.edu

Bogdan Vernescu

Dept. of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, U.S.A.

vernescu@wpi.edu

Keywords

  • Duality
  • fractures
  • elasticity
  • minimization

Mathematics Subject Classification

74B05, 74G35, 74R99, 35Q74, 47N50

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Suggested citation

R. Sato, B. Vernescu. “Dual Formulations of the Elasticity Problem for a Homogeneous Elastic Body with Fractures.” Journal of Convex Analysis 29 (2022), No. 3, 649–668. https://doi.org/10.68381/jca29037

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press LLC.