A new path-independent interaction integral for the SIFs of interfacial crack

A new path-independent interaction integral, which is derived from the dynamic Ĵ integral, is developed to compute the stress intensity factors (SIFs) of interfacial crack and the path-independence of the new interaction integral is theoretically proven. In the calculation, the second derivative of the displacement is avoided since the explicit analytical expressions of the auxiliary stress fields near an interfacial crack tip are utilized. In addition, for non-homogenous materials the computation of the derivatives of material properties is not required by introducing the appropriate incompatibility auxiliary fields. This study significantly enhances the application of the interaction integration technique since the determination of SIFs of interfacial crack between two homogeneous or non-homogeneous materials under static or dynamic loadings can be conducted efficiently by the new interaction integral. For more efficient crack modeling, a local refinement technique using the variable-node element (VNE) is implemented into the framework of the extended finite element method (XFEM). The efficiency and accuracy of the proposed new interaction integral are demonstrated by numerical examples.