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

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• 作者：M. Negri
• 关键词：Energy release ; Eshelby tensor ; J ; integral ; Stress intensity factors
• 刊名：Applied Mathematics & Optimization
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：75
• 期：1
• 页码：99-116
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Phy
• 出版者：Springer US
• ISSN：1432-0606
• 卷排序：75

文摘

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.