A numerical Green's function BEM formulation for crack growth simulation

This paper presents a crack growth prediction analysis based on the numerical Green's function (NGF) procedure and on the minimum strain energy density criterion for crack extension, also known as S-criterion. In the NGF procedure, the hypersingular boundary integral equation is used to numerically obtain the Green's function which automatically includes the crack into the fundamental infinite medium. When solving a linear elastic fracture mechanisms (LEFM) problem, once the NGF is obtained, the classical boundary element method can be used to determine the external boundary unknowns and, consequently, the stress intensity factors needed to predict the direction and increment of crack growth. With the change in crack geometry, another numerical analysis is carried out without need to rebuilding the entire element discretization, since only the crack built in the NGF needs update. Numerical examples, contemplating crack extensions for two-dimensional LEFM problems, are presented to illustrate the procedure.