A new DBEM for solving crack problems in arbitrary dissimilar materials

Abstract

Abstract In this paper, a new and efficient Dual Boundary Element Method (DBEM) named Dual Boundary-Interface Integral Equation Method (DBIIEM) is presented to solve crack problems in objects composed of arbitrary number of different materials. The conventional DBEM has been widely used in crack analysis and proved to be one of the most effective BEM for solving crack problems, however it cannot be directly employed to solve more complicated multi-medium crack problems. The presented DBIIEM can remedy this deficiency by dually collocating the displacement boundary-interface integral equation on one of the multi-medium crack surface and traction boundary-interface integral equation on the other. The newly derived displacement and traction boundary-interface integral equations are naturally fit for solving multi-medium elasticity problems, and independent each other, therefore they can be employed together in multi-medium crack analysis. The established DBIIEM inherits the advantage of single -region formulation of DBEM for solving more complicated crack problems. Complex stress intensity factors which characterize the oscillatory singularity of crack tips located at the interface crack are evaluated. Several numerical examples are given to verify correctness of the presented method.