Masato Kimura, Isao Wakano
Published 2008-06-20Version 1
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.
Solutions of Neumann problems in domains with cracks and applications to fracture mechanics
Volume constrained minimizers of the fractional perimeter with a potential energy
The gradient flow of the potential energy on the space of arcs
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