An interaction integral method for 2D elastodynamic crack problems

In this paper, a domain formed interaction integral is derived for the evaluation of dynamic stress intensity factors (DSIFs) for arbitrary 2D cracks in non-homogeneous materials. The interaction integral is formulated by superimposing the actual and auxiliary fields on the path independent J-integral. By selecting the appropriate auxiliary fields, the derived interaction integral does not involve any derivatives of material properties compared to the available expressions in the literature. Moreover, it can be proved that the integrand is valid even when the integral domain contains material interfaces. Therefore, the integrand is simpler in form and it can be applied in more general situations. The numerical implementation of the new expression of interaction integral is then combined with the extended finite element method (XFEM) without tip enriched functions and a benchmark and test problem is presented. Finally, a non-homogeneous cracked body under dynamic loading is employed to investigate dynamic fracture behavior such as the variation of DSIFs for different material properties.