13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Development of classical boundary element analysis of fracture mechanics in gradient materials Zhong-qi QuentinYue1,*, Hongtian Xiao2 1 Department of Civil Engineering, The University of Hong Kong, Hong Kong, China 2 College of Civil Engineering and Architecture, Shandong University of Science and Technology, Qingdao, 266590, China * Corresponding author: yueqzq@hku.hk 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. Keywords boundary element method, generalized Kelvin solution, FGMs, fracture mechanics, singular integrals 1. Introduction The functionally gradient materials (FGMs) are applicable to many engineering fields. In FGMs, the composite medium is processed in such a way that the material properties are continuous functions of the depth or thickness coordinate. The knowledge of fracture mechanics in FGMs is important in order to evaluate their integrity. Crack problems in FGMs have become one of the hottest topics of active investigation in fracture mechanics [1]. The boundary element method (BEM), also known as the boundary integral equation method, has firmly established in many engineering disciplines and is increasingly manifested to be an effective numerical approach. The attraction of BEM can be largely attributed to the reduction in the dimensionality of the problem and to the efficient modeling of the stress concentration. Thus, BEM can overcome the limitations associated with FEM or other numerical methods in accurately and efficiently analyzing the crack problems. Aliabadi [2] pointed out that fracture mechanics has been the most active specialized area of using BEM and probably the one mostly exploited by industry. If the material properties of FGMs vary in a complicated form along a given direction, it would be difficult to obtain their fundamental solutions. This limits the application of the BEM to analyze fracture mechanics of FGMs. Yue [3] obtained the fundamental solutions for the generalized Kelvin problems of a multilayered elastic medium of infinite extent subjected to concentrated body force vectors, which is referred to as Yue’s solution. The potential application of the solutions is to formulate the BEM suitable for the multilayered media and graded materials encountered in science and engineering.
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