A novel variable power singular element in G space with strain smoothing for bi-material fracture analyses

This paper aims to formulate a triangular five-node (T5) singular crack-tip element in G space with strain smoothing to simulate an rλ−1 (0<λ<1) stress singularity for bi-material fracture analyses. In the present formulation, a direct point interpolation with a proper fractional order of extra basis functions is specially employed to construct variable power type singular shape functions that are in a G1 space. Within strain smoothing, the singular terms of functions as well as mapping procedures are no longer necessary to compute the stiffness matrix. Furthermore, thanks to the point interpolation, the proposed singular element eliminates the need to shift the position of the side nodes adjacent to the crack-tip, and is thus quite straightforward and easily implemented in existing codes. The effectiveness of the present singular element is demonstrated via numerical examples of a wide range of material combinations and boundary conditions.