Shape derivative of potential energy and energy release rate in fracture mechanics

Details Shape derivative of potential energy and energy release rate in fracture mechanics Shape derivative of potential energy and energy release rate in fracture mechanics

2008-06-20

arxiv.org/abs/0806.3449v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

We study general mathematical framework for variation of potential energy with respect to domain deformation. It enables rigorous derivation of the integral formulas for the energy release rate in crack problems. Applying a technique of the shape sensitivity analysis, we formulate the shape derivative of potential energy as a variational problem with a parameter. Key tools of our abstract theory are a new parameter variational principle and the classical implicit function theorem in Banach spaces.

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