Numerical study on bi-material interface crack using symplectic analytical singular element

A novel Symplectic Analytical Singular Element (SASE), defined by the analytical symplectic eigen expanding terms, is used within the framework of the finite element method (FEM), to obtain the dynamic stress intensity factors (DSIFs) of bi-material interface cracks under dynamic loading. In the space domain, the vicinity of the crack tip is represented by using the SASE, while the other area is meshed with conventional elements. In the time domain, the precise time domain expanding algorithm is adopted, in which a self-adaptive technique is carried out to improve computing accuracy. Taking advantage of the SASE, DSIFs can be obtained directly without any post-processing through the relationship between the DSIFs and the eigen expanding coefficients. The numerical accuracy and stability of the proposed method are investigated carefully through the conducted numerical examples. The results show that the present method is effective and efficient.