The Hybrid Boundary Element Method Applied to Linear Fracture Mechanics

The hybrid boundary element method, a variational formulation introduced in 1987 by the first author, has proven to be a powerful tool for dealing with a great variety of problems of potential, elastostatics and elastodynamics. One of the most recent endeavors of the research team at PUC-Rio is the application of the method to problems of the linear elastic fracture mechanics. In the M.Sc. dissertation of the second author, several possible formulations were introduced and discussed. Aim of the present paper is the outline of the main conceptual results of this dissertation, which are to be further elaborated in the frame of a Ph.D. work. The mechanical consistency of the hybrid boundary element method enables the adequate mathematical description of the stress field related to a cracked continuum. The effects of opening and sliding of the crack surfaces are considered by means of a hypersingular stress function, which is dealt with adequately in the frame of the variational formulation. Moreover, it is shown that the stress series proposed by Williams for the local field around a crack tip may be considered as a Green’s function. As a consequence, the stress intensity factors corresponding to both modes I and II are directly obtained as primary unknowns of the problem. Some numerical examples are presented in order to validate the formulations proposed.