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Archive for Rational Mechanics and Analysis

, Volume 201, Issue 2, pp 575–629 | Cite as

Fracture Surfaces and the Regularity of Inverses for BV Deformations

  • Duvan HenaoEmail author
  • Carlos Mora-Corral
Article

Abstract

Motivated by nonlinear elasticity theory, we study deformations that are approximately differentiable, orientation-preserving and one-to-one almost everywhere, and in addition have finite surface energy. This surface energy \({\mathcal{E}}\) was used by the authors in a previous paper, and has connections with the theory of currents. In the present paper we prove that \({\mathcal{E}}\) measures exactly the area of the surface created by the deformation. This is done through a proper definition of created surface, which is related to the set of discontinuity points of the inverse of the deformation. In doing so, we also obtain an SBV regularity result for the inverse.

Keywords

Fracture Surface Cavitation Nonempty Open Subset Distributional Derivative Positive Radon Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie CurieParis Cedex 05France
  2. 2.Basque Center for Applied Mathematics (BCAM)DerioSpain

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