Development of classical boundary element analysis of fracture mechanics in gradient materials

Abstract

Over the last decade, the authors have extended the classical boundary element methods (BEM) for analysis of the fracture mechanics in functionally gradient materials. This paper introduces the dual boundary element method associated with the generalized Kelvin fundamental solutions of multilayered elastic solids (or Yue’s solution). This dual BEM uses a pair of the displacement and traction boundary integral equations. The former is collocated exclusively on the uncracked boundary, and the latter is collocated only on one side of the crack surface. All the singular integrals in dual boundary integral equations have been solved by numerical and rigid-body motion methods. This paper then introduces two applications of the dual BEM to fracture mechanics. These research results include the stress intensity factor values of different cracks in the materials, some fracture mechanics properties of layered rocks in rock engineering.