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

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We consider configurational variations of a homogeneous (anisotropic) linear elastic material $$\Omega \subset \mathbb {R}^n$$ΩźRn 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.