Sensitivity of cracks in 2D-Lamé problem via material derivatives

Abstract.

The Lamé model of a two-dimensional solid with a crack under the stress-free boundary condition of the Neumann type at the crack faces is considered. We investigate the sensitivity of the problem to the crack perturbation. By constructing the material derivatives of the solution as iterative solutions of the same elasticity problem with specified right-hand sides, derivatives of the energy functional and of the stress intensity factors with respect to the crack length of an arbitrary order are obtained providing the corresponding asymptotic expansions. In particular, this implies the local optimality condition for finding of the crack length and the quasi-static model of the local crack propagation by the Griffith rupture criterion.