## JMI2011A-2 Shape derivative of potential energy and energy release rate in fracture mechanics (pp.21-31)

Author(s)： Masato Kimura and Isao Wakano

J. Math-for-Ind. **3A** (2011) 21-31.

- File： JMI2011A-2.pdf (168KB)

Abstract

We study a 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 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.

Keyword(s). shape derivative, variational principle, energy release rate, fracture mechanics