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.

本文提出了一种新的高效的双边界元方法（DBEM），称为双边界界面积分方程法（DBIIEM），用于解决由任意数量的不同材料组成的物体中的裂纹问题。传统的DBEM已被广泛用于裂纹分析，并被证明是解决裂纹问题最有效的BEM之一，但是它不能直接用于解决更复杂的多介质裂纹问题。提出的DBIIEM可以通过将位移边界界面积分方程对置在一个介质裂纹表面上，将牵引边界界面积分方程对置在另一个位置上，来弥补这一缺陷。新推导的位移和牵引力边界界面积分方程很自然地适合解决中等弹性问题，并且彼此独立，因此可以将它们一起用于中等裂纹分析。建立的DBIIEM继承了DBEM的单区域公式化的优点，可以解决更复杂的裂纹问题。对表征位于界面裂纹处的裂纹尖端的振荡奇异性的复杂应力强度因子进行了评估。给出了几个数值例子，以验证所提出方法的正确性。