A new path-independent interaction integral for dynamic stress intensity factors of cracked structures

A new interaction integral derived from the path-independent (J) over cap integral is proposed for the computation of stress intensity factors (SIFs) in both cracked homogeneous and non-homogeneous materials under the dynamic loading. The new interaction integral is theoretically proven to be path-independent and does not contain any derivatives of material properties by introducing the incompatibility auxiliary fields. In addition, the local refinement technique is introduced to the SIFs analysis in the framework of the extended finite element method (XFEM), where the initially generated mesh around the crack tip is refined and the variable-node element (VNE) is used to connect the refined elements and the adjacent elements. Several numerical examples determining the SIFs of cracked structures of homogeneous and non-homogeneous materials in static, dynamic and crack propagation are analyzed to test the accuracy of the proposed new interaction integral and more accurate SIFs can be obtained than those by the traditional ones.