Applied Mathematics & Optimization

, Volume 75, Issue 1, pp 99–116 | Cite as

A Simple Derivation and Classical Representations of Energy Variations for Curved Cracks

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Abstract

We consider configurational variations of a homogeneous (anisotropic) linear elastic material \(\Omega \subset \mathbb {R}^n\) with a crack K. First, we provide a simple way to compute configurational variations of energy by means of a volume integral. Then, under increasing information on the regularity of the displacement field we show how to obtain classical representations of the energy release due to Eshelby, Rice and Irwin. A rigorous functional setting for these representations to hold is provided.

Keywords

Energy release Eshelby tensor J-integral Stress intensity factors 

Mathematics Subject Classification

74A45 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PaviaPaviaItaly

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