A general Boundary Element Analysis of 2-D Linear Elastic Fracture Mechanics

This paper presents a boundary element method (BEM) analysis of linear elastic fracture mechanics in two-dimensional solids. The most outstanding feature of this new analysis is that it is a single-domain method, and yet it is very accurate, efficient and versatile: Material properties in the medium can be anisotropic as well as isotropic. Problem domain can be finite, infinite or semi-infinite. Cracks can be of multiple, branched, internal or edged type with a straight or curved shape. Loading can be of in-plane or anti-plane, and can be applied along the no-crack boundary or crack surface. Furthermore, the body-force case can also be analyzed. The present BEM analysis is an extension of the work by Pan and Amadei (1996a) and is such that the displacement and traction integral equations are collocated, respectively, on the no-crack boundary and on one side of the crack surface. Since in this formulation the displacement and/or traction are used as unknowns on the no-crack boundary and the relative crack displacement (i.e. displacement discontinuity) as unknown on the crack surface, it possesses the advantages of both the traditional displacement BEM and the displacement discontinuity method (DDM) and yet gets rid of the disadvantages associated with these methods when modeling fracture mechanics problems. Numerical examples of calculation of stress intensity factors (SIFs) for various benchmark problems were conducted and excellent agreement with previously published results was obtained.