Abstract: Owing to the mesh-independent crack modeling, the extended finite element method (XFEM) is up to now most effective approach for modeling crack problem. In order to consider small cracks in the analysis of large structure or improve the accuracy around the cracks at a low cost, the fine-scale mesh is generally required around the cracks, whereas the coarse-scale mesh is used outside the cracks. A multiscale XFEM for three-dimensional crack modeling is proposed, which enables one to use a refined mesh only where it is required. The arbitrary-node hexahedron element is developed based on the point interpolation method. The eight-node hexahedron element is used for any scale element; thus the arbitrary-node hexahedron element can conveniently and effectively connect elements with different scales. The three-dimensional stress intensity factors are evaluated with the interaction integral method. Examples including an edge-crack problem and a central circle crack problem are given to illustrate the correctness and efficiency of the proposed method.

Key words: extended finite element method(XFEM), three-dimensional cracks, arbitrary-node hexahedron element, multiscale, interaction integral method, stress intensity factors